Economics as Classical Mechanics

Prediction of the Kamchatka July 29, 2025, earthquake by the evolution of low-magnitude seismicity recovered using waveform cross-correlation at IMS seismic arrays (Part 2)

2026-06-06T07:41:54.603+02:00

There are dozens of REB events in Figure 21 that are not matched in the XSEL. The reason behind this underperformance could be related to the WCC processing and the quality of the REB events obtained during the interactive review. Figure 22 displays the frequency distribution of SNR values for the first P-phases associated with all REB events on July 30, 2025. All SNR estimates are sourced from the IDC database. The pattern is controversial. There are 5241 arrivals with SNR>10, which are high-quality signals not shown in Figure 22 because they are well matched by the XSEL. The curve between 0 and 10 includes 15802 values in 0.2-wide bins. There are 4872 detections with SNR<3.4, with 244 of them having a default value of -1.0 and fixed at the SNR=0 point. They fall below the automatic detection thresholds at the IMS stations and were added by IDC analysts. The peak of the distribution below 3.4 is around 2.0, with 2049 arrivals having SNR <2.0, and 321 with SNR <1.0.

Figure 22. Frequency distribution of SNR values reported by the IDC for all P-phases associated with the REB events on July 30, 2025.

The quality of REB detections added by analysts is formally defined only by their experience and the task not to miss events of concern. The SNR estimates for the added signals, assuming they are correct, pose a challenge for any detector, including those based on the WCC. These detections were missed by the IDC automatic detector primarily due to their low quality. Furthermore, detections lacking SNR estimates should not be included in the database, as their quality is crucial for GA processing. The XSEL, when based on routine WCC processing, may encounter internal limitations in recovering events during periods of extremely high activity, which consequently affects the quality of the REB events.

Statistical power

The XSELs include numerous events with statistical significance controlled by the LA parameters for a given detection list. The question of their statistical power is related to the match of REB events in the XSELs with various LA versions and origin-time tolerance. The strict LA version with low tolerance has to be adjusted to create event hypotheses matching the REB and a small number of new XSEL events which could match the REB-potentially missed in the IDC processing and recovered by the WCC. Table 4 lists the match statistics for two LA versions and the origin-time tolerance of 2.0 s, as adopted by the REB. The first number in the “XSEL matched” column is for the weak version and the second for the strict version. The “REB only” and “SEL3” columns split the “REB total” into automatic and interactive production stages. “XSEL LA matched” refers to the match by XSELs for individual MEs before the CR is applied.

Table 4. Statistics of REB and SEL3 match in the XSEL for the period 2025201-2025210.

Day of 2025	Q	REB total	XSEL matched	REB only	XSEL matched	SEL3	XSEL matched	XSEL LA matched	New XSEL
201	Q2	109	104 / 81	27	22 / 8	82	82 /73	108/96	113 / 15
	Q3	75	70 /63	14	12 / 8	61	59 / 55	74 / 69	120 / 17
	Q4	51	50 / 44	8	8 / 3	43	42 /41	51 / 48	113 /27
202	Q1	31	30 / 29	4	3 / 2	27	27 / 27	30 /30	120 / 24
	Q2	45	38 / 37	10	6 / 5	35	32 / 32	41 / 41	129 / 24
	Q3	44	42 / 41	10	9 / 5	34	33 / 33	44 /42	141 / 25
	Q4	23	22 / 18	5	4 / 1	18	18 / 17	22 / 18	121 / 23
203	Q1	55	52 / 46	20	17 / 13	35	35 / 33	55 / 50	102 / 16
	Q2	31	30 / 30	4	3 / 4	27	27 / 26	30 / 30	116 / 23
	Q3	20	20 / 18	8	8 / 6	12	12 / 12	20 / 18	118 / 24
	Q4	11	10 / 10	2	1/ 1	9	9 / 9	11 / 11	112 /18
204	Q1	4	4 / 4	0	0	4	4 / 4	4 / 4	101 / 24
	Q2	5	5 / 5	1	1 / 1	4	4 / 4	5 / 5	123 / 33
	Q3	11	11 / 11	0	0	11	11 / 11	11 /11	134 / 47
	Q4	9	9 / 9	2	2 / 2	7	7 / 7	9 / 9	91 / 19
205	Q1	7	7 / 7	1	1 / 1	6	6 / 6	7 / 7	99 / 24
	Q2	10	10 / 10	3	3 / 3	7	7 / 7	10 / 10	105 / 17
	Q3	6	6 / 5	3	3 /2	3	3 / 3	6 /6	133 / 37
	Q4	22	22 / 22	5	5 / 5	17	17 / 17	22 /22	131 / 28
206	Q1	16	16 / 16	4	4 / 4	12	12 / 12	16 / 16	164 / 45
	Q2	4	4 / 4	1	1 / 1	3	3 / 3	4 / 4	137 / 36
	Q3	2	2 / 2	0	0	2	2 / 2	2 / 2	129 / 33
	Q4	6	6 / 6	0	0	6	6 / 6	6 / 6	122 / 23
207	Q1	3	3 / 3	0	0	3	3 / 3	3 / 3	87 / 15
	Q2	4	4 / 4	1	1 / 1	3	3 / 3	4 / 4	107 / 28
	Q3	9	9 / 9	1	1 / 1	8	8 / 8	9 / 9	90 / 19
	Q4	4	4 / 4	0	0	4	4 / 4	4 / 4	107 / 37
208	Q1	0	0	0	0	0	0	0	110 / 24
	Q2	4	4 / 4	1	1 / 1	3	3 / 3	4 /4	89 / 16
	Q3	0	0	0	0	0	0	0	93 / 27
	Q4	5	5 / 4	2	2 / 1	3	3 / 3	5 / 5	89 / 24
209	Q1	3	2 / 3	2	1 / 2	1	1 /1	3 / 3	131 / 29
	Q2	2	2 / 2	0	0	2	2 / 2	2 /2	84 / 16
	Q3	1	1 / 1	0	0	1	1 / 1	1 /1	80 / 13
	Q4	1	1 / 1	0	0	1	1 / 1	1 / 1	135 / 38
210	Q1	2	2 /2	0	0	2	2 / 2	2 / 2	127 / 33

Total		635	604 / 555	139	119 / 81	496	472 / 454	626 /593	4103 / 921

The period between the J20 and J29 earthquakes is likely the best time to assess the statistical power of the XSEL events. Two days following the J20 are characterized by rates ranging from 100 to 30 REB events per 6 hours. The second quarter-day (Q2) of 2025201 includes 109 REB events. The XSEL for the weak LA version matched 104 out of 109, and the strict version matched 81. This difference between the weak and strict versions is relatively large, but it is decreasing with time from the J20. Since the second half of 2023203, there is no difference in the matches between the weak and strict versions for SEL3 events or for the pure REB. The watershed is likely 30 events per quarter-day. The larger the number of REB events the lower the match rate, and the reason for this deviation is discussed in the previous section.

The final column in Table 4 lists the number of new XSEL events. The weak LA version produces 114±19 events per 6 hours, whereas the strict version produces 26±9 events per 6 hours for the studied period. This difference is expected, given to the design of the detection threshold, which results in a decreasing number of XSEL events as the pair order number or the corresponding magnitude threshold increases. The number of new events in the strict LA version is slightly larger than 50% to 100% of the number of REB events with the expectation of approximate equality, as related to the exercises with interactive review of XSEL bulletins. For the 0.25-second tolerance case, the number of XSEL events after the 2025203 ranges between 2 and 11. This pair of the LA version and tolerance case is designated as the transition to the REB. The statistical power of the XSELs used in this study is demonstrated by a perfect alignment with the REB, encompassing both actual and potential REB-ready events.

The importance of the results in Table 4 lies in the equal statistical significance of XSEL events that match the REB and those that do not. This implies that a complete match of the REB events during the period of relatively high activity between July 22 and July 29, 2025, can be extended to other XSEL events, thereby assigning them the same quality as the REB. In turn, the XSELs for the period between 201 and 210 of 2025 were obtained using the same procedure as before the J20 earthquake. The WCC processing introduced in [Kitov, 2026] and further developed in this study can be applied to IMS data for earthquakes across various regions. This approach guarantees both statistical significance and statistical power for the XSEL event hypotheses.

Results

General aspects of WCC processing and its specific characteristics across different levels of seismic activity have been discussed. The seismicity within the studied region before and after the J20 and J29 earthquakes was also examined. The selection procedure and structure of the ME set were customized to fulfill the processing objectives. All calculations in this study were performed using identical WCC settings, ensuring direct compatibility throughout the entire processing period and across specific areas. The results include XSELs for individual MEs as well as the final XSELs obtained via the CR process. The full processing period spans from July 12 to July 31. Additionally, the best 100 MEs were subjected to an extended processing period from July 6 to August 3. Finally, two 3-day periods without REB events were processed using this 100 best ME set, providing a baseline reference for XSEL interpretation.

XSEL seismicity during low seismicity and periods without REB events

The two 3-day periods without REB events allow for the estimation of recurrence curves exclusively for XSEL events. The first period, spanning November 29 to December 1, 2023 (jdate = 2023333-2023335), can be extended into the second quarter (Q2) of day 2023332. Additional calculations were performed for December 2 (5 REB events) and December 3 (1 event) to analyze the transition from a quiet period to the activity captured in the REB events. Similarly, the quiet period from February 24 (2024055) to February 26 (2024057), 2024, was also extended by two days exhibiting REB activity. Because this study focuses on rapid fluctuations in seismic activity below the IDC detection level, the data are processed in quarter-days intervals (Q1-Q4). Given that the activity levels can be exceptionally low, with zero XSEL events across several consecutive quarters, a four-quarter moving sum, denoted as MS(4), is calculated with a one-quarter step to ensure robust event statistics.

The results of the WCC processing using the best 100 MEs are displayed in Figure 23. The upper panel shows the recurrence curves, where the x-axis represents the order numbers. These XSEL recurrence curves demonstrate the feasibility of converting these order numbers into magnitudes; furthermore, deviations from the regression lines are potentially related to fluctuations in seismic activity near a specific magnitude level. The curves between 333.125 (Q1/333) and 335.875 (Q4/335) follow exponential trends, exhibiting deviations from these trends that increase in amplitude as the order number increases. The summary curve for the entire 15-quarter quiet period yields an R²=0.98. On day 2023336, 5 REB events occurred, and two curves 336.875 and 337.125 - show a dramatic 3- to 4-fold increase in seismic activity throughout all the curves. This predominant growth is concentrated within the mid-range tolerance values of the strict LA version, peaking between 1.0 s and 2.0 s. A similar behavior is observed in the curves for some, but not all, quiet days. The most prominent deviations occur toward the end of the quiet period, while the summary curve shows a low-amplitude deviation for a 1-second tolerance.

Figure 23. The recurrence curves of the moving sum of four consecutive 6-hours intervals for 12 XSELs from v₁c₁ to v₂c₆with order number from 1 to 12. Upper panel: days between Q2/2023332 to Q4/2023337. Each curve is marked by its end quarter: curve 333.175 is the sum of 4 quarter-days between Q2/2023332 and Q1/2023333. Lower panel: the days between 2024055 and 2024059.

The recurrence curves illustrate the integral characteristics of the XSEL event distribution over a linear scale, such as a magnitude-like one. This representation is important as it proves the quality of the observational tool and the unambiguous conversion of the order number of the version/case into a magnitude scale. The scale is not standard in terms of the measurement procedure underlying the values. There are many magnitude scales, each with slightly different characteristics, taken from different parts of the signal wavetrain from the first P-wave to Love waves. An inverse representation of these scales is also possible similar to that described for Figure 18.

The time evolution of the seismic process for a set of magnitude thresholds is crucial for understanding the earthquake preparation process. The numbers of XSEL events for 12 thresholds are shown in Figure 24 for the quiet period 2023332-2023335 with an extension into the days 2023336 and 2023337 with REB events. The XSEL curves, which represent the MS(4) of the previous four quarter-days, look smooth and synchronized for each LA version over the entire period including the quiet and active seismicity periods.

Figure 24. The evolution of the number of XSEL events in 6 weak cases (upper panel) and 6 strict cases (lower panel). Vertical dashed line – the origin time of the m_b=3.95 event occurred at 17:22:35 on December 2, 2023. Hypocenter is ~100 km due south of the J29 earthquake: 51.60ºN, 159.86ºE, d=0 km.

The origin time of the largest event on 2023336 with m_b=3.95 is indicated by a vertical red line. There is a noticeable increase in the XSEL numbers starting two quarter-days before this event. The only deviation is the drop in the 0.25 s curve for the strict LA version, which began approximately 20 hours before the earthquake. The ratios of the weak and strict LA versions for all six cases are displayed in Figure 25. These curves highlight the variances in seismic activity above the respective thresholds. The 0.25 s ratio curve begins to rise three quarter-days before the earthquake, peaks roughly 8 hours prior to the earthquake, and then declines as it approaches the red line. A similar pattern was observed in the 0.25 s curve for the May 24, 2013, Sea of Okhotsk earthquake, while the other five curves exhibit different behaviors. The resemblance in the peaks in the 0.25 s curve is likely coincidental, but similar patterns before other major earthquakes are the objects of this study. For the 2023336 earthquake, the increase in the 0.25 s curve may be observable due to the absence of larger-magnitude seismic activity during the previous 96 hours.

Figure 25. The ratios of the XSEL for the weak and strict LA versions and the same origin time tolerance case. The curve for the 0.25 s tolerance has a peak approximately 10 hours before and then falls just before the earthquake at 17:22:25. This peak corresponds to the fall in the XSEL for strict LA version in Figure 23.

The 3-day quiet period in 2024 is shown in Figure 26. It displays a pattern similar to that observed in 2023, with a peak in the 0.25 s ratio curve. Figure 27 depicts this curve starting to rise 5 quarter-days before peaking a day before the event on February 28 at 11:11:31. The epicenter coordinates are 53.93°N, 160.34°E, with a depth of 75.4 km, and m_b=3.85. This peak is observed long before the event origin time, and the event itself is not large. Therefore, there may be no causal link between the peak and the earthquake. Nevertheless, the peak and the events are measured independently and are where they are.

There were no significant changes observed in the XSEL numbers throughout the entire period between February 24 and February 29. However, the strict LA version demonstrated larger variations. The day of February 29 was added to the initial interval due to a sudden rise in the 0.25 s curve right up to the end of February 28, as observed in Figure 27. This rise is related to the decreasing 0.25 s curve for the strict LA version in the lower panel. The only REB event on February 29 occurred at 19:37:35 at a depth of 499 km, far to the west of the J29 epicenter (51.45°N, 151.28°E). The magnitude was 3.47, large enough for the event to be detected by almost all IMS stations worldwide.

igure 26. Same as in Figure 24 for the quiet period between 2024055 and 2024057 extended into 2024058-061.

Figure 27. Same as in Figure 25 for the quiet period between 2024055 and 2024057 extended into 2024058-059.

Seismic activity prior to the J20 earthquake

During the quiet periods, the seismic activity detected by the WCC is nearly identical to that observed during the periods of low activity periods preceding the J20 earthquake. Figure 28 displays the trajectories of the running four-quarter moving sum, MS(4), of the quarter-day-long XSELs between July 6 and July 20, 2025. This period was fully processed using the best 100 MEs and presents a baseline reference for relatively low seismicity prior to the J20 M7.4 earthquake (see Figure 19), which featured only one large REB event on July 14 (origin time: 21:38:01, epicenter: 46.66°N, 151.30°E, depth: 87 km, Mw~5.7-5.8). Results for both the weak (upper panel) and strict (lower panel) LA versions, each including six origin-time tolerance cases from 5.0 s to 0.25 s, are shown.

Several intervals with significant variations in the MS(4) are marked by ovals. Between July 10 and 12, there was deep through, with all curves for both the weak and strict version changing almost synchronously. The strict/0.25 s curve dropped down to 1 XSEL per day during three consecutive quarter-days. There were four quarter-days without XSEL events in a row and only one XSEL event during a day and a half. There were also no REB events on 2025189. Given that the final REB event on 2025188 occurred at approximately 16:00 and the first event on 2025191 appeared at 06:00, the total event-free period lasted roughly 38 hours. The strict LA version with a 0.25 s origin time tolerance exhibits approximately the same sensitivity as the REB.

This serves as an interesting example of a rapid 2- to 3-fold decline in low-magnitude seismicity within a very large geographical region, especially when compared to the subsequent 38-hour REB-event-free period between the morning of 2025197 and the late evening of 2025198. During this latter period, all curves for the weak LA version rise and then fall back to their initial levels. In this case, the strict/0.25 s curve also demonstrates growth, albeit emerging from a trough at the end of 2025196.

Figure 28. The evolution of the running MS(4) of the quarter-day number of XSEL events between 2025187 and 2025201. The weak (upper panel) and strict (lower panel) with six origin time tolerance cases (from 5.0 s to 0.25 s) each are shown. Several intervals of with significant variations are marked by ovals.

Figure 29 compares two LA versions and two cases, highlighting the periods of synchronous and asynchronous behaviors across various version/case permutations. When seismicity fluctuates simultaneously at all magnitude levels, the corresponding ratios evolve in sync. Conversely, the asynchronous onset of growth and decline may be attributed to waves of low-magnitude seismicity passing through the magnitude thresholds that correspond to the respective version/case order numbers. The weak LA curves are nearly synchronous, with the exception of the final quarter-day (201.125, representing the first six hours of July 20). Specifically, the weak/0.25 s curve, which remains systematically below the weak/0.5 s curve, exhibited a sharp increase to align with the 0.5 s curve level. The strict curves did not mimic this behavior; consequently, the weak-to-strict ratio for the 0.25 s tolerance increased, as illustrated in Figure 30. This is an example of low-seismicity progress through the magnitude range confined between the weak and strict versions.

Figure 29. Comparison of the 0.25 s and 0.5 s cases illustrating the synchronous in asynchronous behavior of the two LA versions and two cases.

Figure 30. The ratio of weak-to-strict LA versions for six origin tolerance cases between 2025187 and 2025203. The event at 21:38:01 on July 14 is marked by a black vertical dashed line.

Periods of significant decline in the strict/0.25 s curve compared to the weak curve were observed several times during the period between 2025187 and 2025201. The weak-to-strict ratio rose to high values, albeit against the background of decaying seismic activity. A prominent spike reaching a value of 38 occurred in the 0.25 s ratio curve in the second quarter-day of 2025189, when the XSEL count for the strict version fell to 1. A broader peak was observed on 2025195, when the strict curve dropped to a level of 3. Similarly, a sharp peak in the fourth quarter-day of 2025196 was induced by an abrupt decline in the strict LA version. This specific point marked the onset of growth in the strict version at a faster rate than in the weak version. This corresponding peak likely indicated the transition to the event on July 20.

The two weeks preceding the J20 earthquake demonstrate a variety of peaks and troughs in the MS(4) of quarter-day XSELs and in the ratio of the weak and strict MS(4) XSELs. These peaks are most prominent in the curves for the 0.25 s origin-time tolerance, which defines the magnitude range closest to the corner magnitude of the REB recurrence curve and generates the most statistically significant XSEL event hypotheses. The XSEL ratio for this specific case may reveal the preparation for an impending earthquake, provided it is induced by an increasing number of events in the weak LA version, as was previously observed for the Sea of Okhotsk earthquake.

An ex post analysis allows for the differentiation of two distinct classes of peaks in the ratio curves. The first class is associated with a rapid drop in the number of events in the strict XSELs, accompanied by a much slower decline or no decrease at all in the weak XSEL version. The resulting peaks are sharp and exhibit large amplitudes, which are likely associated with periods of extremely low seismic activity. Statistically, recording only one to three events per day within a highly seismic region of a size of approximately 2000 km × ~1400 km is inherently characterized by statistical uncertainty. In contrast, the peaks in the weak-to-strict ratio curves observed prior to the J20 earthquake are supported by more robust statistics within the strict LA version.

The 0.5 s ratio curve also demonstrates peaks in nearly the same time intervals; however, these peaks are systematically lower, whereas the underlying MS(4) XSEL curves remain higher than the 0.25 s curves. The 0.5 s ratio curve exhibits a peak along the growth trend two quarter-days prior to the J20 earthquake and then decreases slightly. This behavior differs from that observed before the Sea of Okhotsk earthquake, where the 0.5 s curve began to rise a few quarter-days before the 0.25 s curve, after which both curves peaked synchronously right before the mainshock. This sequence was interpreted as a wave of events with an increasing magnitude progressing through a set of magnitude thresholds defined by the increasing order number of the LA version/origin-time tolerance case.

The four other curves also exhibit minor shifts toward the peaks of the 0.25 s curve. There is an episode of countermotion near 2025189, where the other five curves form a trough while the 0.25 s curve approaches its peak value. The significance of XSEL bulletins with the largest origin time tolerances depends on the sensitivity of the observational networks and the magnitude of the earthquake under study. For the Sea of Okhotsk earthquake, all six XSEL ratio curves contributed specifically to estimating the level and tracking the progression of the seismic activity wave from the lowest magnitudes to the mainshock. In contrast, for the study of the Kamchatka earthquakes, they likely serve only as a baseline reference, assisting in the reconstruction of the recurrence curve, such as those presented in Figure 18.

Seismic activity between the J20 and J29 earthquakes

The period between the J20 and J29 earthquakes is of special interest because it involves seismic activity that is significantly higher than that observed prior to the July 20 earthquake. Although the J20 aftershock sequence decays rapidly toward the J29, as illustrated in Figure 19, it could pose a potential challenge for the WCC processing to distinguish between the REB matching and new XSEL events before the J29 mainshock. While the REB matching statistics in Table 4 illustrate the efficacy of the WCC in detecting REB events, it remains a question whether the WCC can differentiate between the mixture of low-magnitude J20 aftershocks and J29 foreshocks, or if this mixture represents a single, continuous process of earthquake preparation. Up to this point, the XSELs included all events, encompassing both the REB-matching and newly detected ones. The latter subset of XSEL events does not differ significantly from the total version for quiet days, and could therefore be utilized instead of the total number for earthquake prediction purposes.

The period between the J20 and J29 events, however, is not characterized by seismic quietness. Figure 31 compares the total number of events with the number of new XSEL events for both the weak and strict LA versions under the 0.25 s and 5.0 s origin-time tolerance cases. The difference between these curves represents the number of REB-matching XSEL events. It rises across both versions and for both cases. Within the strict version, the gap between the 0.25 s and 5.0 s cases is small on the first day after the J20 event and practically disappears after the J29 mainshock. For the weak version, the 5.0 s total and new curves virtually coincide after 2025207, whereas the 0.25 s curves converge only two days prior to J29. In contrast, the 0.25 s strict total and new curves retain the gap until the final minute prior to the J29. Overall, because the total XSEL counts inherently include J20 aftershocks up to the onset of the J29, these aftershocks and the J29 foreshocks cannot be distinguished. Nevertheless, the J20 earthquake failed to follow the J29 evolution steps, suggesting that the overall preparation for the mega-earthquake may not be disrupted by a relatively small loss of the total elastic energy accumulated in the entire region in J20 mainshock and its aftershocks.

Figure 31. Evolution of weak (upper panel) and strict (lower panel) MS(4) numbers in the total XSEL vs. only the new events XSEL. Two origin time tolerances are used: 0.25 s and 5.0 s.

The evolution of the MS(4) for the total XSEL curves between 2025200 and 2025211 is presented in Figure 32. Six curves representing all cases within the same versions move nearly synchronously, displaying only a few minor deviations. Furthermore, curve pairs sharing the same origin-time tolerance case appear highly similar across both LA versions. The principal divergence among the curves in Figure 32 is observed during the day preceding the J29 mainshock. The 0.25 s curve for the weak version demonstrates a clear upward trend, whereas the strict version exhibits a downward trend common to all six cases, punctuated by a minor peak two quarter-days prior to the J29 rupture.

The weak-to-strict ratios for the six origin time tolerance cases in Figure 33 illustrate a synchronous evolution of the MS(4) metric, characterized by an overall positive trend from 2025200 to 2025211. The most pronounced variations in these ratios are confined to the 0.25 s and 0.5 s cases. This pattern is common to all events analyzed thus far: the Sea of Okhotsk, the J20, and the J29 events, as well as the two quiet periods. Following the J29 earthquake, all six ratio curves drop sharply to a baseline level of 2, a feature that is directly linked to the abrupt drop in the MS(4) levels illustrated in Figure 20. Because of the smoothing effect inherent to the running sum window, the first three quarter-days following the mainshock still incorporate MS(4) values from the pre-seismic interval, thereby smoothing the transition to the lower post-seismic baseline. A ratio value of 2 corresponds to a regime where the number of newly detected XSEL events is negligibly small compared to those matching the REB bulletin. In other words, the magnitude threshold for the WCC processing is shifted very close to the corner magnitude of the total recurrence curves in Figure 15 or 17, depending on the respective depth estimates in the REB and XSEL.

Figure 32. The MS(4) curves between 2025200 and 2025211.

The weak-to-strict ratios for the 0.25 s and 0.5 s tolerance cases in Figure 33 rise from a level of 4.0-4.5 up to 7.0 during the last two to three quarter-days prior to the J29. This peak is observed within the last 5 hours preceding the mainshock, which occurred at 23:24:48 (IDC origin time). The last hour of 2025210 was excluded from the pre-event WCC processing. This last hour was also omitted from the post-seismic processing because both the REB and XSEL are severely biased by extraordinary noise levels. There is a study devoted to the recovery of aftershocks in the initial minutes following the J29 [Kitov et al., 2026]. The exclusion of this hour should not introduce any measurable bias into the weak-to-strict version ratio, as it affects both versions proportionally and exhibits no discernible influence on the three cases ranging from 2.0 s to 5.0 s. The 1.0 s case demonstrates an increase, peaking near 5.5.

Figure 33. The ratios of the number of XSEL events in the weak and strict LA versions for the period of time between 2025200 and 2025215.

The peaks in the 0.25 s and 0.5 s curves immediately preceding the J29 mainshock, with the depth fixed at the free surface, represent a potential short-term earthquake prediction trigger. A similar precursor was previously observed prior to the Sea of Okhotsk M8.3 earthquake. The consistent behavior of low-magnitude seismicity in both cases provides compelling evidence in favor of such a hypothesis.

Recurrence curves for the ME sets

The best 100 MEs constituted the initial configuration covering the entire studied region. Thus far, this specific set has been utilized in the calculation of the XSEL bulletins, as well as the corresponding time series of the MS(4) metrics and the weak-to-strict ratios. There is another ME set consisting of 195 REB events, each featuring a mandatory associated P-wave arrival at station PDYAR. This latter set also covers the same geographical area and depth range but was selected from the REB after 2023, following the upgrade of this station to an operational array at the end of 2022. A cumulative total of 295 MEs were utilized to create the XSEL events; both constituent sets are illustrated in the left panel of Figure 13.

The expanded set allows for the investigation of several critical problems related to the precursory peaks observed in the 0.25 s and 0.5 s weak-to-strict ratio curves in Figures 30 and 33. First, it is necessary to determine which of the two configurations exhibits greater efficiency in generating XSEL events, given their subtle variations in spatial distribution and sample size. The top 100 MEs are likely characterized by superior sensitivity and resolution, a feature supported by their selection procedure, which relies on a comprehensive pairwise WCC analysis with neighboring REB events. The ME set anchored by station PDYAR is larger and directly benefits from the high sensitivity of this array to seismic events within Flinn–Engdahl region 19 (Kuril–Kamchatka).

The subsequent question involves resolving the geographical provenance of the XSEL events that drive the precursory trigger shown in Figure 33. The earthquake preparation processes may structurally encompasse the entire regional volume bounded by coordinates 45°N - 65°N, 145°N - 165°N and a depth range from 0 km to 700 km. Alternatively, the preparation zone can be restricted to a small spot, such as the J20 aftershock sequence in Figure 12, concentrated in the lithosphere, or a broader spatial envelope corresponding to the J29 aftershock distribution. To test these hypotheses, the total 295 ME set is partitioned into four distinct geographic domains in the right panel of Figure 13:

· The entire region including the subducting Pacific plate.

· The localized zone surrounding the potential asperity that arrested the slip propagation of the J20 event along the eventual J29 rupture line (hereafter referred to as the "Asperity" zone, which excludes a single deep-focus event within its boundary and incorporates 49 MEs).

· The remaining spatial domain outside this core zone, designated as "Out of Asperity".

· The southwestern periphery situated beyond the immediate J29 aftershock zone, designated as the "Rim" region, which utilizes 79 MEs from the “PDYAR” configuration.

This spatial subdivision is baseline-exploratory, aimed at identifying potential regional accents in the precursory signal. If necessary, this tentative division can be optimized during a subsequent technical calibration procedure. One such optimization parameter involves the recurrence curve, which characterizes the performance of the WCC pipeline in terms of how accurately the order numbers of specific version-case pairs correspond to a uniform sequence of magnitude thresholds. The upper panel of Figure 34 illustrates this parameter computed for the period between 2025193 and 2025201. The curve for the best 100 MEs is identical to that presented in Figure 16, whereas the «JOINT» curve represents the complete set of 295 MEs. The «JOINT» bulletin is not a simple cumulative sum of the best 100 and 195 “PDYAR” XSELs; rather, it is the direct product of joint processing incorporating a Conflict Resolution (CR) algorithm those cross-rejects redundant XSEL events between the two constituent bulletins. For instance, the «JOINT» XSEL yields 3752 events in the v₁c₁ pair (weak version, 5.0 s tolerance), whereas the standalone best 100 MEs generate 2625 events and the “PDYAR” configuration produces 2642 events. For the v₂c₆ pair (strict, 0.25 s), the event counts are 140, 74, and 92 events, respectively. Thus, the value added to the «JOINT» XSEL bulletin scales from 50% for the v₁c₁ pair to nearly 100% for the v₂c₆pair.

The respective curves in the upper panel of Figure 34 evolve synchronously, displaying similar low-amplitude deviations within the weak LA version. However, the strict LA version for the “PDYAR” subset generates larger numbers of XSEL events across all six tolerance cases. This behavior is likely attributed to the larger number of MEs physically encompassing a broader spatial domain during the high-resolution grid search, which operates with a maximum radius of 43.2 km in the strict LA version. For the weak version, the grid radius is 81 km, and the neighboring MEs have overlapping search areas leading to the CR process. This phenomenon is important for the future ME setting – the number of MEs should be sufficient to cover the whole region without detection-creation blind zones. The “PDYAR” master subset was partially introduced to address this issue, and the «JOINT» set is likely an important step on the way to an optimal ME number and distribution. The increasing number of MEs can yield additional XSEL events, but it would require higher computing power or longer processing time.

There are minor deviations from the «JOINT» XSEL exponential regression line within the strict version XSELs. The lower panel of Figure 34 presents the recurrence curves from the upper panel, normalized to their respective maximum values for the v₁c₁ pairs. These relative variations effectively highlight the outliers across the configurations. The highest coefficient of determination, R²=0.9805, is yielded by the top 100 MEs set. This value is statistically significant enough to validate the correlation between the order numbers and the uniform sequence of magnitude thresholds. This robust correspondence represents a key feature underlying the reliability of the weak-to-strict version ratio as a predictive parameter. The largest fluctuations are demonstrated by the “Rim” curve with R²=0.94. This specific curve exhibits a progressive deficit in XSEL events when approaching the highest order numbers. Both regression lines have the same slope of -0.31.

Figure 34. Recurrence curve characteristics evaluated across distinct Master Event (ME) sets. Upper panel: The recurrence curves for the 12 LA version/tolerance case pairs computed for different ME configurations. Lower panel: The corresponding recurrence curves from the upper panel, normalized to their respective absolute levels in the v1c1 configuration to highlight relative morphological variations and outliers.

Evolution of the number of XSEL events

Because the weak-to-strict version ratio represents a measurable parameter designed to serve as an operational trigger for a major earthquake alert, the fundamental properties of the underlying calculations become crucial. For each monitoring interval, six distinct ratio curves are evaluated, corresponding to the six origin-time tolerance figures ranging from 0.25 s to 5.0 s. These metrics are derived from the respective XSEL bulletins generated by the WCC detection and LA procedures for individual MEs. The aggregation of these individual XSELs into a consolidated final XSEL is governed by a CR procedure, which is finely calibrated against the baseline daily event rates observed during the periods between major earthquakes. The backbone of this entire WCC processing pipeline comprises a spatial network of MEs combined with waveform templates of the first P-wave recorded across all stations associated with each respective ME.

A standalone ME creates event hypotheses strictly within the spatial grid search radius relative to its own hypocentral position reported in the REB. While the probability of detecting an event situated outside this grid boundary is non-zero, its reconstructed location will be artificially shifted inside the grid. This artifact can introduce significant errors in the absolute location, a limitation that is highly common in automatic bulletins. The REB events are also inherently mislocated relative to their true positions; however, the confidence ellipses derived from travel time residuals provide an estimate of the 95% probability contour containing the actual source. In general, a larger number of associated stations reduce the dimensions of this confidence ellipse. These structural parameters, alongside potential phase misassociation, render the choice of MEs highly vulnerable to location errors and template quality.

The set of 295 MEs includes REB events of varying quality regarding absolute location accuracy, the number of associated stations, and the availability of valid templates of the first P-phase. The operational efficacy of individual MEs can vary significantly across the studied region. This variability can introduce measurable fluctuations in both the resolution and sensitivity of the WCC processing, directly affecting the final XSEL bulletins. Smaller ME subsets assigned to specific geographical areas may exhibit localized underperformance due to poor ME quality, which could be misinterpreted as low seismic activity. Genuine spatial fluctuations in seismic activity across the selected could be erroneously interpreted as instrumental or algorithmic underperformance.

The partitioning into these geographical subsets is accomplished using simple straight lines that delineate quasi-rectangular areas. The probability space within which an individual ME can generate a valid event hypothesis can readily extend into adjacent zones. A discrete XSEL bulletin can incorporate events that geographically belong to a different ME subset. Within the complete ME network, however, these overlapping MEs would generate competing hypotheses that are ultimately resolved by the CR procedure. For example, the "Out of Asperity" domain contains numerous MEs situated immediately along the boundary of the "Asperity" core zone. This spatial overlapping introduces a non-zero bias in the independent XSEL estimates computed for each discrete subset. Within the integrated «JOINT» master set, this specific spatial bias is successfully suppressed by the presence of the MEs that explicitly belong to the "Asperity" set.

The operational performance of all individual ME subsets can be systematically compared to the «JOINT» set as an aggregated output of all MEs in all subsets. Panel a) in Figure 35 depicts the six weak-to-strict ratios between 2025193 and 2025201 for the «JOINT» set. There are notable differences observed in the behavior of the 0.25 s and 0.5 s curves when compared to the best 100 MEs subset in Figure 30. The precursory peak amplitude in the «JOINT» 0.25 s curve decreases to 13.1, compared to 15.4. The double-peak structure preceding the J20 event in Figure 30 is smoothed, and the highest peak moved to the first place in their sequence. The peak at 2015199 lost its relative amplitude to 8.8 from 14.7 for the best MEs 100 set. The third peak near 2025197 is the highest for the presented interval. The period before 2025194 is not shown as the calculations for the «JOINT» set were conducted from 2025193 to 20252012. The 0.5 s curves are nearly the same for both sets with slightly lower amplitude relative to the highest peak. The remaining four tolerance curves are almost identical across both sets.

Overall, the 0.25 s curve has not lost its predictive capability, despite the fact that the weak MS(4) curve in Figure 36a exhibits only a single upward shift prior to the J20 event, while the strict MS(4) curve declines at a faster rate than the weak curve, followed by a sharp increase along the final leg preceding the J20 rupture, which is marked by the vertical red line. For the «JOINT» curve, the broader morphology of the precursory peak is driven primarily by an accelerated decline in the strict curve, mimicking the behavior observed during previous peak intervals. This underlying mechanism differs significantly from the forcing factors that govern the standalone best 100 MEs set.

The “PDYAR” subset in Figure 35b is characterized by a broader precursory peak that begins to grow three days before the J20 mainshock. The prominent trough near 2025200, which is clearly observed in the best 100 and «JOINT» ME sets, loses its depth in the “PDYAR” subset, appearing instead as a smooth transition between two individual maxima. Both of these peaks are driven by a faster decline in the strict curve relative to the weak LA version. The final quarter-day preceding the J20 event is characterized by a rapid amplitude rise in the strict curve – signaling an increasing activity of the XSEL events closer to the corner magnitude of the REB recurrence curve – which occurs alongside a more gradual increase in the weak curve. The peak level of the 0.25 s curve is 16.8, strongly supporting its precursory character. The 0.5 s curve begins to decline three quarter-days prior to the J20 earthquake, consistent with the behaviors documented in the other two ME sets. This synchronous signature further reinforces the hypothesis of an impending major earthquake.

The 0.25 s ratio curve for the “Asperity” ME subset in Figure 35c exhibits features similar to those of the “PDYAR” subset, albeit with a few distinct deviations. The “Asperity” curve also starts to rise on 2025198, but reaches its peak value of 14.5 five quarter-days prior to the J20. Unlike in the «JOINT» and “PDYAR” subsets, there is a peak near 2025195 induced by a deep trough in the strict curve. There is a similar peak in the best 100 MEs curve. This empirical observation suggests that the sharp declines in the strict curves are driven by local conditions and depend on individual ME quality and spatial distribution, rather than encompassing the entire region. Such local peaks are effectively smoothed by the cumulative activity in the «JOINT» set. Only the largest anomalies remain visible in the curves that cover the entire region. For instance, the prominent peak near 2025197 is clear for the best 100, “PDYAR”, and «JOINT» sets, yet it remains statistically significant within the “Asperity” curve. Furthermore, the final precursory peak preceding the J20 event is significantly smoothed and displays a lower amplitude relative to the other maxima analyzed above.

The “Out of Asperity” 0.25 s ratio curve in Figure 35d demonstrates two distinct high-amplitude peaks: one near 2025197 and another three quarter-days prior to the J20. The latter maximum reaches an absolute value of 21.4. It could serve as an optimal short-term precursor to the J20 earthquake, especially given that its culmination is immediately followed by a systematic two-quarter-day decline leading directly to the J20 origin time. This peak is driven by a fast decline in the strict curve in Figure 36d, followed by an equally accelerated recovery that initiates three quarter-days before the J20. The growing number of events in the strict version XSEL is a feature potentially related to earthquake preparation. The geographical distribution of MEs within the “Out of Asperity” set suggests that the seismic activity prior to the coseismic phase was concentrated outside the zone of the “Asperity” subset.

The “Rim” subset is presented in Figure 35e. It was designed to cover the area beyond the aftershock sequence of the J29 mega-earthquake. It should inherently remain insensitive to any seismic activity related to the preparation of the J20 and J29 earthquakes. It has an extremely high peak near 2025199. While similar peaks are observed across the sets covering the entire region, they are much lower in relative amplitude, thereby confirming the strictly localized character of this anomaly. The “Rim” set in the southwestern periphery of the region undergoes its own independent seismic activity on 2025197, which should not be factored into the core J20/J29 nucleation process. There is another sharp peak with an amplitude of 42.0 four quarter-days before the J20. Its amplitude is directly related to the drop in the strict curve to the level of 1 to 2 per day, as illustrated by the corresponding MS(4) curves in Figure 36e. Despite its high amplitude, this peak is statistically insignificant due to the extremely small sample size. Mechanically, this anomalous spike can be attributed to the over-the-border spatial sensitivity of MEs positioned near the primary preparation zone of the J29 earthquake.

Figure 35. Evolution of the weak-to-strict LA version ratios calculated across six origin time tolerance levels preceding the J20 earthquake. Five distinct master event (ME) configurations are presented to resolve the spatial and geographical dependence of the precursory ratios: a) «JOINT» configuration comprising the complete macro-set of 295 MEs; b) Standalone “PDYAR” master subset incorporating 195 MEs with a mandatory associated arrival at station PDYAR; c) "Asperity" subset consisting of 49 MEs (excluding one deep-focus event located within the horizontal boundaries of the asperity area) clustered within the immediate epicentral zone of the J20 and J29 events, capturing the stable tectonic asperity that arrested the J20 rupture propagation; d) "Out of Asperity" subset comprising 245 MEs situated outside the core zone; e) "Rim" subset incorporating 79 MEs from the “PDYAR” configuration located along the southwestern periphery of the analyzed domain.

Figure 36. Comparison of the curves for the weak and strict LA versions and the origin-time tolerances of 0.25 s and 0.5 s for the same five ME configurations as in Figure 35.

Initially, the J20 earthquake was not the primary target of this study, with the original objective to analyze the J29 mega-earthquake. However, the fundamental physical mechanisms underlying major earthquake preparation remain consistent within a given seismogenic zone; consequently, the nucleation phase of a catastrophic rupture can overlap with and mask the preparation process of an intermediate event. As a result, the parameters used in the analysis of the J29 earthquake preparation may introduce a systematic bias when applied to the J20 process. Nevertheless, the observations presented in Figures 35 and 36 suggest that the weak-to-strict ratio curve for the 0.25 s origin time tolerance preserves its validity as an operational trigger for short-term earthquake early warning systems. The density and geographical distribution of MEs required to ensure the optimal resolution of this precursor can be systematically calibrated using the REB as a robust source. Furthermore, the core parameters of the WCC pipeline – ranging from individual station detection thresholds to the conflict resolution algorithm – remain fully adjustable. Such a comprehensive network optimization is highly feasible given sufficient computational resources, and thus lies beyond the scope of the current study.

For the J29 mega-earthquake, the weak-to-strict versions ratio for the 0.25 s origin time tolerance exhibits a sharp peak preceding the rupture onset time. The 0.5 s curve in Figure 33 is nearly synchronous with this 0.25 s curve, forming a more robust potential trigger for an earthquake early warning alert. Taken together, these two individual peaks would be sufficient to achieve the objective of the J29 earthquake forecasting. The Sea of Okhotsk earthquake also exhibits two similar peaks right before the mainshock. Their statistical significance is validated by a progressive increase in the number of XSEL events detected within the strict LA version for both the 0.25 s and 0.5 s cases during three consecutive quarter-days preceding the mainshock. The stochastic creation of these strict hypotheses is practically excluded, as the LA defining parameters are calibrated to suppress not only random phase alignments but also extraneous detections related to the side-sensitivity of the highest-weight IMS array stations.

The «JOINT» set of MEs generated XSELs for all 12 LA version-case pairs computed for the period between 2025193 and 2025212. The corresponding weak-to-strict ratios of the MS(4) curves for the six distinct tolerance cases are presented in Figure 37a. The 0.25 s ratio curve exhibits a sharp peak in the fourth quarter of July 29, immediately preceding the mainshock, which is marked by the vertical black line. The curve undergoes a rapid acceleration over two consecutive quarter-days, reaching a maximum amplitude of 7.0. This value is marginally higher than the respective peak in the best 100 MEs subset illustrated in Figure 33. This peak is driven by the rise in the weak curve, as observed in Figure 36a. The strict curve retains a practically constant level during the two days prior to the J29 earthquake. This behavior is nearly identical to that demonstrated by the respective curves of the 100 best MEs subset, despite the difference in the XSELs total numbers of events, as shown in Figure 34.

The 0.5 s curve peaks at a level of ~5 in the «JOINT» configuration, likely smoothed out by the competing MEs from the “PDYAR” subset. The geographical position of MEs generating extra XSEL events for the 0.5 s weak-to-strict ratio is not clear yet. Otherwise, the «JOINT» and the best 100 MEs curves are characterized by highly synchronous evolution between 2025202 and 2025212, punctuated by two distinct low-amplitude peaks on 2025204 and 2025207. These peaks are likely driven by the increased seismic activity after two earthquakes on 2025203 and 2025206, both featuring a body-wave magnitude (m_b) of approximately 5.5, as illustrated in Figure 19.

The «JOINT» set and the best 100 MEs subset can both serve as effective predictive tools, displaying only minor differences. In contrast, the “PDYAR” subset in Figure 37b demonstrates a markedly different behavior. The 0.25 s ratio curve is characterized by a broader peak, with a maximum amplitude of 7.3 that is shifted chronologically to Q3/2025209. This peak is driven by a steady decline in the strict curve, which reaches its lowest point in Q3/2025209, as illustrated in Figure 36b. The strict curve then rises faster than the weak curve, causing the weak-to-strict ratio to decline continuously up to Q3/2025210. In Q4/2025210, the strict curve drops by 2 events relative to the preceding quarter-day, while the weak version retains its level. The Q4 lasts only 5 hours, as the J29 origin time is approximately at 23:25. A secondary, lower peak with an amplitude of 5.5 is observed immediately preceding the J29 mainshock, likely corresponding to the primary precursory maxima identified in the «JOINT» set and the best 100 subset. The 0.5 s ratio curve exhibits an isolated peak reaching an amplitude of 6.2 in Q4/2025209, followed by a gradual decline to the level of the remaining four tolerance curves right before the mainshock. As for the 0.25 s curve, this 0.5 s peak can be explained by the decrease in the strict curve between Q1 and Q4 of 2025209.

The predictive capability of both the 0.25-s and 0.5-s curves appears partially suppressed by the high ambient seismicity within the boundaries of the "Asperity" zone. This core domain represents a relatively compact area characterized by the highest level of historical seismicity and the nucleation of several extremely large historical earthquakes (Figures 12 and 13). While the primary mechanical source of the precursory indicator marking an impending rupture is clearly situated within this focal zone, the low-magnitude seismic activity recovered by the WCC pipeline likely incorporates events generated by alternative, long-term tectonic processes that operate concurrently with the immediate mainshock preparation cycle.

The "Out of Asperity" ME subset yields results that are highly similar to those of the «JOINT» master set. Specifically, the 0.25-s version ratio curve exhibits a sharp peak immediately preceding the J29 mainshock, reaching maximum amplitude of approximately 7.0. Prior to the J29 event, the "Out of Asperity" 0.5-s curve reaches a level marginally higher than that recorded by the integrated «JOINT» configuration. This close similarity is primarily attributed to the absolute sample size of this subset; the "Out of Asperity" network incorporates 245 out of the total 295 MEs deployed in the «JOINT» configuration. Crucially, the operational performance and predictive capability of this subset do not suffer any significant degradation when the "Asperity" core events are entirely omitted from the processing stream. This empirical outcome demonstrates that the critical short-term earthquake preparation processes operate effectively across the broader spatial domain encompassed by these 245 master events, rather than being strictly restricted to the focal asperity itself.

Figure 37. Same as in Figure 35 for the earthquake on July 29, 2025

The "Rim" subset serves as a critical counterpoint to establish the statistical significance of precursory anomalies. The 0.25-s version ratio curve presented in Figure 37e demonstrates high-frequency fluctuations in amplitude, with its maximum peak emerging during Q4 of day 2025209. During the entire day preceding the J29 mainshock, this 0.25 s curve drops to a flat baseline level between 5.0 and 6.0, displaying no anomalous peak that could be interpreted as a precursor. This behavior demonstrates that the crustal volume encompassed by the "Rim" configuration remains structurally independent of the seismogenic and mechanical processes operating across the core preparation zone of the studied region. Figure 36e illustrates this conclusion by the effect of the weak (and strict) LA version curves for all origin-time tolerance cases fail to reach the post-seismic level observed after the J29 mega-earthquake in Figure 20. The other four configurations in Figure 36 demonstrate this essential feature of the XSEL recurrence curves.

The 79 MEs defining this southwestern “PDYAR” subset can be safely excluded from the direct investigation of the seismic process leading to the J29 rupture. This spatial selectivity is robustly supported by the corresponding findings related to the preceding J20 earthquake. Mechanically, the largest peak observed in the MS(4) ratio curve during the fourth quarter of 2025209 is artificially induced by a sharp drop in the strict curve down to a baseline of only 4 events per day, as illustrated by the running sum trajectory in Figure 36e.

Discussion

The ultimate objective of this study is the recovery of low-magnitude seismicity prior to a major earthquake. The IMS array stations represent the best global seismic network, providing lower detection thresholds for remote regions. In the standard beamforming detection technique, this is achieved by the destructive interference of ambient noise accompanied by constructive interference of the sought signals. The WCC-based processing creates a pipeline that provides additionally reduced detection thresholds, effective suppression of detections not relevant to the studied localized areas, and accurate local association of the preselected detections with the event hypotheses created by high-quality master events. The conflicts for the same physical signals associated with independent hypotheses created by two or more neighboring master events are resolved in a Conflict Resolution procedure, which optimizes the resulting bulletin to the actual event rate – from very low to that observed during the first hours after the mega-earthquakes such as Sumatra in 2004, Tohoku 2011, and Kamchatka 2025.

The WCC-based approach was advocated by Schaff and co-authors [2025] as a technique to obtain information on the seismic processes not detectable by the standard methods. The WCC processing has been widely used to detect low-magnitude events at regional and teleseismic distances. One of the problems associated with low-magnitude events is that one cannot accurately estimate their standard magnitudes from amplitude and period measurements, as the detected signals are hidden in the ambient noise. In this study, we further developed the technique based on a set of threshold defined by the statistical significance of valid events introduced by Kitov [2026ab]. For the Kamchatka 2025 major earthquakes and their aftershocks, these thresholds were directly linked to standard magnitude estimates. This finding allowed us to follow the evolution of low-magnitude seismicity across a set of increasing magnitude thresholds toward the onset times of the J20 and J29 earthquakes. The measurable parameter potentially useful as a mega-earthquake precursor is based on the ratio of the numbers of XSEL events above two thresholds. This parameter signals that the rate of such events increases in the corridor between the thresholds. Alternatively, a decreasing rate above the upper threshold also leads to a rise in the ratio, but does not indicate an approaching large event.

The absolute duration of the investigated interval was limited to approximately two weeks, primarily due to available computing power. However, this period was sufficient to resolve highly specific precursory features preceding the J29 mainshock and its potential foreshock, the J20 mainshock. A few days prior to the J29 megathrust failure, the acceleration in seismic activity progressed into the most statistically significant v₁c₁-v₂c₁bin configuration – the parameter space situated closest to the historical corner magnitude of the Kamchatka recurrence curve. An identical manifestation was previously documented before the Sea of Okhotsk earthquake.

There are several important findings in this study made possible by the IMS array stations and the sensitivity and flexibility of the WCC processing. Firstly, the 12 independent version-case configurations, based on different Local Association criteria and varying origin time tolerances, can be mathematically converted into a standard body-wave magnitude scale. This transformation yields robust recurrence curves that successfully resolve actual seismicity down to a baseline of approximately magnitude 2.0, extending the catalog completeness into the sub-noise register where no official REB event hypotheses are available. Secondly, synchronous, high-amplitude peaks in the 0.25 s and 0.5 s weak-to-strict version ratio curves are consistently observed immediately preceding major seismic ruptures. The stability and predictive power of this dual-window operational trigger have been robustly verified across distinct geodynamic settings, encompassing the 2013 deep-focus Sea of Okhotsk earthquake as well as the 2025 Kamchatka major earthquakes. Thirdly, the partitioning of the comprehensive «JOINT» master event catalogue into discrete geographic subareas exposes the underlying spatial sensitivity of the WCC pipeline. The interaction between overlapping grid search radii and the automated Conflict Resolution cross-rejection process successfully suppresses spatial cross-talk and boundaries blurring between adjacent zones. Fourthly, the multi-parametric spatial test effectively divides the investigated subduction region into zones that are highly significant and zones that are insignificant for precursory signal localization. The analysis demonstrates that while the core tectonic asperity acts as the primary mechanical driver of the impending rupture, the accelerated micro-seismic preparation process is heavily concentrated outside this immediate core, mapping out a wide precursory activation envelope on the periphery of the fault plane. Conversely, remote reference configurations, such as the "Rim" subset, display a flat background variance, confirming the absolute spatial selectivity and statistical significance of the developed method.

There were several precursor-like peaks found in the data before the J20 and J29 earthquakes. They were all statistically insignificant and caused by a severe drop in the XSEL number of the strict LA version. However, it is not excluded that some statistically significant precursory signals might not end in a catastrophic earthquake. Further studies are needed to understand the abundance and properties of false positive related to the precursor-like signals. This methodological projection involves several critical aspects. First, a high rate of false alarms does not constitute a viable alternative to the unmitigated impact of a catastrophic event. Comprehensive false-alarm statistics must be systematically gathered over a multi-year baseline, encompassing both high-activity clusters and prolonged seismically quiet intervals. While this verification requires significant computational resources and time, isolating signatures similar to those reported before the 2013 Sea of Okhotsk and 2025 Kamchatka events would not only precisely constrain the empirical false-alarm probability but also unlock invaluable insights into the aggregate mechanical behavior of the subducting Pacific plate.

Tectonic preparation processes that fail to reach the final co-seismic rupture stage, alongside their precise spatial positions and hypocentral depths, are directly governed by the internal architecture of the slab and the space-time evolution of stresses under regional driving forces. On a macro-scale horizon, these observations may hold greater significance for structural geophysics than the isolated estimation of false-alarm rates. For instance, the J29 mega-earthquake was preceded by an almost collocated J20 event that failed to overcome the stable local asperity, terminating as a localized m_b=5.39 (IDC) event instead of immediately triggering the final M8.8 rupture that materialized ten days later. A highly analogous precursory sequence was documented two days prior to the 2011 Tohoku earthquake, whereas no such distinct foreshock activation was resolved before the catastrophic December 26, 2004, Sumatra-Andaman megathrust failure.

For future investigations of the Kuril–Kamchatka subduction zone, it will be highly informative to systematically assess the large aftershock that occurred on September 18, 2025. Furthermore, as a historic alternative to the modern, well-instrumented J29 case, the major earthquake of November 15, 2006, will be analyzed. That historical event nucleated within the southwestern boundary of the active domain, explicitly belonging to the "Rim" master event configuration. To achieve maximum operational efficiency, this localized "Rim" template database will be strategically extended using core anchors selected from the top 100 MEs configuration. In 2006, a significantly reduced IMS network topology was operational, completely lacking the critical near-regional array PETK (Petropavlovsk-Kamchatskiy, Russia; 53.108°N, 157.699°E) and the highly sensitive regional array PDYAR (Peleduy, Russia; 59.655°N, 112.441°E). Additionally, the regional events of May 19, 2013, and December 20, 2018, will be investigated to complete a comprehensive re-evaluation of all major earthquakes within this domain since 2001.

The Kamchatka Peninsula represents one of the most seismically active and well-instrumented subduction zones globally; however, some other regions capable of generating catastrophic earthquakes suffer from deficient instrumentation. For instance, the IMS network across South America comprises exclusively three-component (3-C) stations, a network that catches significantly fewer phases, elevates the baseline WCC detection threshold, and prevents the high-resolution recovery of low-magnitude sub-noise seismicity. Because Chilean megathrust earthquakes exhibit structural mechanisms highly analogous to those of the Kamchatka Peninsula, they warrant thorough investigation once the regional observational assets are upgraded to match the strict array configuration requirements of the WCC pipeline.

The March 11, 2011, Tohoku earthquake commands both a catastrophic magnitude and an exceptional instrumentation baseline, captured by multiple IMS arrays operating at regional distances. Conversely, the December 26, 2004, Sumatra earthquake exhibited a catastrophic rupture volume but was recorded by relatively poor network instrumentation during the early operational years of the IMS network. Both of these historical mega-earthquakes are currently under active investigation using the optimized WCC pipeline. The compelling structural divergence between them resides in the drastically different levels of ambient micro-seismic activity operating immediately prior to their respective mainshocks.

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Prediction of the Kamchatka July 29, 2025, earthquake by the evolution of low-magnitude seismicity recovered using waveform cross-correlation at IMS seismic arrays (Part 1)

2026-06-06T06:52:24.954+02:00

Abstract Waveform cross-correlation (WCC), when used for detection at seismic arrays, allows for a reduction in threshold by an order of magnitude compared to beamforming. An additional benefit of WCC detection is the significant suppression of signals unrelated to the studied area. This effect simplifies and improves the accuracy of local phase association with event hypotheses located near corresponding master events. All the advantages of WCC-based processing are best utilized in the detailed study of low-magnitude seismicity prior to mega-earthquakes. For the Sea of Okhotsk Mw8.3 earthquake that occurred on May 24, 2013, WCC processing detected the onset and subsequent evolution of intensive, low-magnitude seismicity during the five days leading up to the mainshock. The Kamchatka earthquake on July 29, 2025, is analyzed using a similar WCC-based processing extended by a detailed study of the recurrence curves of the cross-correlation bulletin (XSEL). The transition to the coseismic phase was marked by a progressive increase in the intensity of seismic activity with growing magnitude. These XSEL events fell below the detection level of the International Data Centre, which utilizes the same data stream from the International Monitoring System.

Key words: waveform cross-correlation, Kamchatka July 29, 2025 earthquake, preparation process, mid-term prediction, International Data Centre, International Monitoring System

Introduction Earthquake prediction is a major task in geophysics. Seismicity is generated by the Earth's internal dynamics and its interaction with extraterrestrial objects. Seismology provides information on the elastic and inelastic properties of the Earth's interior, allowing for the estimation of the distribution of principal geophysical parameters and their evolution over various time scales. Larger earthquakes are one of many mechanisms for the Earth's internal energy release. Magnitude 8.0+ earthquakes directly illustrate plate tectonics and demonstrate the relative motion of plates. The tremendous elastic energy generated by such earthquakes is a threat to human beings. Long-term forecasting of the largest earthquakes is based on the assumption of their repeatability with periods observed in the past. At this point, threats to the population and infrastructure can be mitigated through building codes and general awareness. Immediate, partly post-factum prediction is based on the possibility of transferring information faster than seismic waves propagate. Having a few seconds’ warning before the destructive wave arrives can be very helpful in avoiding life-threatening risks. Short-term prediction is crucial for reducing all types of risks and threats. It should involve continuous monitoring based on a set of reliable, measurable parameters indicating the current state of potential catastrophic earthquake zones. An alert should be issued when one or more parameters reach their corresponding threshold values, which are well-estimated based on previous experience and historical data. In [Kitov, 2026b], it was shown that the waveform cross-correlation (WCC) method applied to seismic arrays of the International Monitoring System (IMS) of the Provisional Technical Secretariat (PTS) of the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) in Vienna, Austria, allowed for finding a large number of low-magnitude events before the May 24, 2013, Sea of Okhotsk earthquake (M24). It had coordinates 54.89°N, 153.31°E, Mw(USGS)=8.3, mb(IDC)=6.27, and a hypocenter depth of 604 km. The depth of this event and its position within the subducting Pacific plate effectively separate it from any other seismic activity. The International Data Centre (IDC) of the PTS CTBTO has reported ~100 seismic events in this zone since 2001. This makes the Sea of Okhotsk earthquake a laboratory case for WCC testing. It was found that the flux of low-magnitude events jumped by a factor of ~5 approximately three days before the M24 mainshock, and the evolution of the event sizes indicates the possibility of being related to the earthquake preparation process. Shallow seismicity near the Kamchatka Peninsula is very active, and the earthquake preparation process has to be recovered and separated from the background process. This is the next challenge for the study of earthquake preparation processes with potential prediction capabilities, all based on the synergy of the WCC and seismic arrays of the IMS as the most sensitive tools in global and regional seismic observations. Seismic arrays were proposed as a measure to reduce the detection threshold for underground nuclear test monitoring [e.g., Sultanov, 1996]. The concept of a phased antenna for seismic waves was tested in the early 1960s in many countries and demonstrated excellent results. The IMS includes more than 30 array stations distributed across continents. Station aperture varies from a few hundred meters to over 40 kilometers. Theoretically, for the case of stochastic and non-additive noise, the gain of an array station is proportional to the square root of the number of individual sensors. The array aperture and the number of individual sensors depend on the target seismic phase and are tuned to the number of wavelengths, i.e., the wave apparent velocity and frequency band [Schweitzer et al., 2012]. For low-velocity and high-frequency local phases, the aperture can be less than 1 kilometer. For regional P-wave phases with velocities of 6.0 to 8.5 km/s and frequencies up to 10 Hz, the optimal array aperture is between 1 and 5 km. For teleseismic phases, an aperture of 15 or more kilometers can be the best choice. The relative array station sensitivity to various phases is important for assessing network performance relative to a given source location. For the Kamchatka region, IMS arrays for regional observations (PETK, PDYAR, MJAR, and USRK) dominate in events at distances below 40° including the subduction zones near Kamchatka and Japan. Figure 1 shows the IMS stations with available data for this study. IMS arrays between 30° and 60° (ZALV, KURK, MKAR, BVAR, ARCES, FINES, SPITS, LZDM, HILR, NVAR, and PDAR) contribute to a larger portion of events in the IDC bulletin for Kamchatka and its surroundings. There are also several large-aperture arrays beyond 60°: AKASG, NOA, EKA, and WRA, which are sensitive to events worldwide. The distance and azimuth distribution of the IMS arrays is favorable for the task of the weak signals detection. This is not a common case for seismic regions with potentially catastrophic earthquakes. For example, South America lacks regional IMS arrays, making a study similar to that of the Sea of Okhotsk unfeasible there.

Figure 1. IMS seismic stations with data available for the current analysis. Red – primary stations. Black – auxiliary stations. Circles – array stations. Triangles – 3-C stations.

Waveform cross-correlation is a relatively new method of seismic data processing that uses high-quality digital records and historical templates. Digital seismology has been developing since the early 1960s. The WCC-based detection method was well-known long before the era of digital seismology as a core technique of the matched filter [Turin, 1960]. The first attempts to apply WCC to data from 3-C stations were reported in the early 1990s [Israelsson, 1990; Joswig, 1990; Joswig and Schulte-Theis, 1993]. Broader attention to WCC was sparked by the possibility of improving event location accuracy by one to two orders of magnitude [Schaff and Richards, 2003; Gibbons et al., 2007; Waldhauser and Schaff, 2008; Selby, 2010]. The accuracy of seismic magnitude estimates was also improved [Schaff and Richards, 2014; Bobrov et al., 2014]. A major benefit of WCC is its capability to reduce the detection threshold by an order of magnitude, leading to significant improvements in the completeness, consistency, and quality of seismic catalogs and bulletins [Schaff, Richards, 2004]. Array stations have been growing in number and data quality since the first experiments in the 1960s, but the joint use of arrays and WCC started only in the 2000s after the IMS was installed and made available to the broader seismological community [Gibbons, Ringdal, 2004, 2006]. Following the approach developed by Kitov [2026ab], here we apply the same WCC-based methods to the IMS arrays and several near-regional 3-C stations to study the preparation process of the M8.8 Kamchatka July 29, 2025, earthquake (J29). There is also an M7.4 event that occurred on July 20, 2025 (J20) with its hypocenter close to that of the J29 mainshock. The task to detect signals and events below the threshold established by the IDC for the purpose of global monitoring of underground nuclear tests is challenging. Regional seismic networks, on the other hand, have much lower thresholds despite the fact that they are using only 3-C stations. In remote regions without regional networks, the arrays of the IMS provide a much lower detection threshold, and the IDC dominates in global bulletins. In regions like the subduction zone of the Kamchatka Peninsula [Kitov, 2026a] and the Sea of Okhotsk [Kitov, 2026b], where regional networks are onshore and the distance to the closest stations is several hundred kilometers, the IMS arrays and the IDC successfully compete with regional bulletins during times of low seismicity. For the highest seismicity episodes, the arrays demonstrate better results as ambient noise literally blinds regional 3-C stations, while remote 3-C stations are inferior to remote arrays by a factor of 4 or more. The WCC approach allows for detecting much smaller events and can play a crucial role during quiet periods. It is better at locating these small events using regional and teleseismic networks with an azimuth gap lower than that of a one-sided regional network. This new task involves creating event hypotheses that were not detected by any other methods, and identifying signals that are not visible below the noise level. In physics, there is no requirement for the matched filter [Turin, 1960] to only detect signals that are visible to analysts or operators. In seismology, legacy observations were traditionally made by analysts, and this tradition has been maintained throughout the digital era. The new approach is currently under development and requires a detailed description and discussion. Data and WCC methods IDC processing: an example of automatic processing and the source of data The IMS transmits continuous data to the IDC. An extended quality check of the raw data starts the automatic processing. It consists of three stages needed to include late seismic data from primary stations, data segments requested from auxiliary stations, and infrasound data for joint seismic-acoustic analysis. The final outcome of automatic processing, Standard Event List 3 (SEL3), provides initial event hypotheses for the interactive review conducted by IDC analysts. At the interactive stage, a Reviewed Event Bulletin (REB) is produced for further operations related to the CTBT mandate, but these operations do not change the seismological content of the REB. All automatic and interactive stages of the IDC seismic data processing are described in [Coyne et al., 2012]. For the WCC-based methods of detection and phase association, automatic IDC processing serves as the basic scheme for mandatory stages. The official IDC bulletin provides a quality reference for the cross-correlation automatic bulletin (XSEL), since they are both based on the very same IMS data set. The differences in processing are not only in algorithms and parameters, but also in objectives. The IDC has to follow the CTBT mandate and separates seismic stations into two groups: primary and auxiliary. The former define the statistical significance of the event hypotheses, and the latter are only used to improve the estimates of the principal event parameters such as hypocenter, origin time, and magnitudes. For the purpose of the Kamchatka earthquake study and other civil applications of the WCC-based methods, there is no difference between primary and auxiliary IMS stations. Their input to statistics is defined by their historical participation rates in the events listed in the IDC bulletin within the region under investigation. The IDC has to consider each event hypothesis as it is. The objective is to find all the events of concern to the CTBT, and not to miss any. IDC detections with calculated principal characteristics - arrival time, azimuth, slowness, amplitude, period, inter alia - are promoted to the detection list (IDCX). At the station processing stage (StaPro), the initial phase names are assigned to the IDCX detections using their apparent velocities and after their grouping for a single-station location. There are many rejected detections in the IDCX according to their parameters. They are converted into noise phases (N-phases), which can participate but are intentionally excluded from the following phase association process. The detections corresponding to regular seismic phases with the full set of estimated parameters are used in the Global Association (GA) process to create a set of event hypotheses. These hypotheses are then passed on to the SEL3. The core of the GA is a location algorithm searching for potential sources to associate the available phases in the statistically optimal way. At the final GA stage, the "event definition criteria" (EDC) are evaluated. They are based on the event defining parameters of the associated phases: arrival time, station-event azimuth, and scalar slowness. This procedure evaluates the statistical significance (“minimum standards for the amount and type of information required for events included in the bulletins”) of the event hypotheses using fixed weights of the measured defining parameters. For example, the weight of the defining arrival time of the first P-wave at an array station and at a 3-C station is 1.0. The weights of azimuth and slowness are 0.4 at arrays and 0.2 at 3-C stations. The secondary (not the first P) phases have lower weights and are counted in only when the first P is defining. For automatic processing, the EDC control the total number of created event hypotheses. For the interactive review, the EDC require much higher statistical significance for event hypotheses in the final IDC bulletins. These EDC have to balance the rate of valid and false (e.g., not matching the EDC, but potentially physically reliable) events. For the REB, the minimum requirement is at least 3 associated primary stations, two of them arrays with the defining arrival time, azimuth, and slowness. The third station can be a 3-C one, and the arrival time can be the only defining parameter to add weight to the event statistics. The REB is just one of many possible versions that can be created using the same data from the IMS. One of the constraints of the REB is the human resources available for the interactive analysis. The number of event hypotheses in the SEL3 should not exceed the IDC human capacity to process all of them in accordance with the standard procedure. After the Sumatra M9.1 earthquake occurred on December 26, 2004, interactive analysis was impossible due to an unprecedented number of SEL3 seeds and an indigestible number of phases that needed to be considered by IDC analysts. The statistical approach to the creation of event hypotheses is common among seismological agencies and varies depending on their objectives. WCC processing also follows the same design of automatic processing, with natural differences in the defining parameters and station/phase weight definitions related to the results of cross-correlation with high-quality signals generated by historical events characterized by accurate locations and magnitude estimates. The requirement of at least 3 associated stations is adopted in the WCC phase association to make it possible to directly compare the XSEL to the REB and achieve high statistical significance for the WCC-created event hypotheses. The generic approach to the event definition criteria of the IDC, as based on adjustable station/phase weights, allows for flexibility in responding to any potential change in the seismic monitoring network. The EDC can also be tuned to the requirements of bulletin reliability and/or sensitivity. Such changes, if implemented, may result in significant shifts in the reliability, completeness, consistency, and accuracy of the final bulletin, not to mention the demand for human resources. The EDC re-optimization in response to possible changes in the requirements of the CTBT, in a world of quick progress in science, technology and international relations, has to be tested accordingly. The WCC processing with multiple sets of EDC proposed in [Kitov, 2026b] and further developed and tested in this paper could be used for EDC testing at the IDC. WCC-based detection By construction, any recurrence curve demonstrates that seismic events in a given region are repeatable in locations and magnitudes, and thus have to generate similar signals observed at the same stations. A WCC detector searches for signals similar to a given waveform template selected from the historical records on the same station. The level of similarity is usually defined by the cross-correlation coefficient (CC). This measure is not appropriate for detection purposes, however, since CC strongly depends on the spectral content and length of the template and the sought signals. In the low-frequency band, the CC value is usually higher than for a high-frequency representation of the same actual signal. But the CC amplitudes for ambient noise are also increasing respectively. Longer templates generate lower CC values as seismic signals are prone to various kinds of dispersion, and the similarity declines quickly with the distance between the sources of templates and sought signals. Detection by the maximum |CC| value from a set of time series obtained for various filters and template lengths would be highly biased. In addition, ambient seismic noise can contain signals similar to the sought one. The signals from the immediate aftershocks of the Kamchatka 2025 earthquake are a good example, as the signals associated with the events created by the IDC are very similar in shape and amplitude to a multitude of unassociated signals. These coherent signals create the ambient noise where WCC has to find valid signals fully coherent to the “noise signals”. Both the beamforming and WCC techniques usually fail to distinguish between identical signals separated by a few seconds, and this decision has to be made by IDC analysts. The Sumatra 2004 case showed that the human resources available at the IDC are not adequate for such a task. The matched filter uses WCC as a quantitative similarity estimator. It requires the noise to be stochastic in order to maximize the signal-to-noise ratio, SNRcc, for the CC-trace. Stochastic noise conditions are necessary for the matched filter to operate as an optimal detector. For a sought signal, the actual properties of the ambient noise can vary from realizations very close to the stochastic case to situations where the signals creating the noise are almost fully coherent with the sought signal. Therefore, the effectiveness of WCC detection depends on three signals: the template, the sought signal, and the noise. The latter signal is subject to significant changes in amplitude of the components coherent with the template and sought signals. In a model case, the fully stochastic noise generated by a computer can be approximately 10 times larger in amplitude than the sought signals, and still the SNRcc would be above the detection threshold of 3.5 [Adushkin et al., 2025a, Kitov, 2026c]. The signal-to-noise ratio technique in the matched filter applied to the CC time series is more efficient than a generic CC-value detector. It becomes even more efficient when extended by the addition of stochastic noise to the filtered waveforms before the CC calculation. For example, it allows for finding aftershocks occurring within minutes from the J29 mainshock and hidden in the extremely high noise coherent to the sought signals at seismic stations [Kitov et al., 2026]. It also helps to find low-magnitude events in the quiet seismic zone before the J29 mainshock [Kitov, 2026a], which can be related to the asperity that had stopped the J20 fault propagation. The SNRcc values are calculated on a CC time series according to the same algorithm as the standard SNR of the IDC [Coyne et al., 2012]. Short-term (STA) and long-term (LTA) average (RMS or absolute) amplitudes represent signal and noise, respectively. The length of the STA running window is usually adjusted to the expected signal rise-time and ranges from 0.5 s to 1.5 s (0.6 s is used in this study). The LTA window can be adjusted to the specific noise properties at a given station, but values between 40 s and 90 s (60 s is used) produce very similar results in most cases. The STA/LTA ratio is defined as the SNRcc value. It is used for signal detection, meaning finding a time count when the average signal amplitude is larger than the noise amplitude by a certain factor, also known as the detection threshold. The STA running window is positioned half its length ahead of the LTA window. When the SNRcc threshold is reached, the LTA is frozen and does not change for a period approximately equal to the template length or the cross-correlation window width (CCWW). This condition prevents signal energy from affecting the LTA estimates. The standard SNR detector is triggered when a signal arrives at a sensor and the energy flux or power (STA) exceeds the average noise level plus a few (detection threshold) standard deviations. As the signal amplitude and power increase over time after the arrival, the SNR also grows with the signal amplitude. The peak amplitude used for magnitude estimation and the maximum SNR are typically reached from a fraction of a second (e.g., for underground explosions) to tens of seconds (e.g., for shallow earthquakes) after the arrival. The IDC uses a 5.5 s segment after the arrival to measure the peak amplitude and SNR because its sources of concern are explosions. The WCC detection procedure aims to cover a variety of potential signal properties such as rise-time, amplitude, length, sequence of regular phases, spectral content, among others. This ensures that all ranges of these parameters are considered to avoid missing low-amplitude signals that are crucial for various scientific studies and technical applications. For a CC time series, the detection threshold does not define the time of signal (energy) arrival. It indicates the start of correlation growth between the running template and the data segment of the same length. The start of CC growth can be related to the sought signal or induced by a random realization of a noise segment coherent with the template. The actual arrival of a sought signal corresponds to a time point when it synchronizes the most with the template. At this moment, SNRcc has to reach its maximum value. Therefore, the time count with the maximum SNRcc is the arrival time. The difference between the trigger time related to the SNRcc threshold and the arrival time can reach tens of seconds. Special measures for the SNRcc trace quality check are implemented to protect the WCC detection procedure from the false alarms related to the noise realizations. Such false detections can mask valid signals between the trigger and arrival times. In standard IDC processing, various regular phases have to be detected and identified by their properties. This is important for creation of an event hypothesis for a unique source not related to any other sources worldwide. A sequence of regional phases Pg, Pn, Sn, Lg, Rg allows for a single station event location and characterization. It is used in automatic processing to create a seed event for the subsequent processing stages, both automatic and interactive. The depth sensitive secondary phases, such as pP and sP, allow for accurate hypocenter location with low depth uncertainty estimates. The WCC-based processing uses the full waveform containing all phases of interest [Bobrov et al., 2014]. There is no need for separation of regular phases as they can be a significant source of information on the similarity between a high-quality template signal and the below-the-noise-level sought signal. The first P-phase is a mandatory part of any template. This rule is based on the observational fact that only P-phases are usually detectable from low-magnitude sources at teleseismic distances. It is used in the EDC adopted by the IDC – no secondary phase is counted in without the first P-wave associated with the same source. The secondary phases can be included in the waveform templates depending on their potential input to the CC obtained from the long-term practice and extended testing. The CCWW can cover a range from 4 seconds for impulse P-phases produced by underground explosions and deep earthquakes, up to 200 or more seconds for near-regional wavetrains of regular phases ranging from Pg/Pn to Rg. For the widest templates, only the longest CC time series has to be calculated with the shorter CCWWs retrieved from it. The CC time series is calculated using the standard definition of the cross-correlation coefficient as a dot product of two (demeaned) vectors: CC(t) = d(t)•m / ǁdǁ•ǁmǁ, where d(t) is the running data vector at time t, and m is the template vector. For an array station, individual CC-traces are calculated, CCi(t), where i is the channel index from 1 to N. Then, the CCi(t) values are averaged for a given t over all channels to obtain the average CC(t) value. There are no beamforming time shifts applied, as the template and sought signals are synchronized in time over all individual sensors. The same procedure is applicable to 3-C stations. For a one-channel case, no averaging is applied. Our objective is to study the evolution of seismic process before, during, and after two major earthquakes that occurred at 06:28:14 on July 20 and at 23:24:48 on July 29, 2025. There were just a few earthquakes detected by the IDC during the two weeks before the J20, and approximately 600 aftershocks between July 20 and July 29. During July 30, there more than 700 aftershocks of the J29 M8.8 mega-earthquake were detected. As of May 2026, there have been several thousand aftershocks of the J29. The post-seismic activity will continue. In Figure 2a, signals from the J20 mainshock and its immediate aftershocks over a 90-minute period are shown at IMS stations PETK (epicentral distance ~5°; station-event azimuth ~70°-120°), PDYAR (R~30°; seaz~90°), MKAR (R~48°; seaz~50°), and WRA (R~75°; seaz~10°). There was an earthquake at 06:02:49 (mb=4.95), which is also seen at all the stations. This could be a foreshock related to the earthquake preparation process. There were three major aftershocks during the first hour. The aftershock at 6:49:00 had a larger magnitude, mb=5.69 (IDC) than the J20 mainshock (mb=5.39) and higher amplitudes at all stations. The second (07:07:41; mb=5.96) and third (07:22:57; mb=5.86) major aftershocks were compatible by amplitude with that of the J20 mainshock. There were many smaller aftershocks as well as those not seen in Figure 2 within the coda-waves of the major aftershocks during the first hour. At PETK (upper trace), the J20 creates a long wavetrain with the peak observed tens of seconds after the arrival in the signal filtered (3rd order, BP) between 0.6 Hz and 4.5 Hz. The coda-wave is a mixture of primary P-phases from different parts of the earthquake fault and secondary phases from the mainshock, including surface waves likely responsible for the peak amplitude. All these phases are coherent with the corresponding phases in a potential sought signal if the J20 or any other events close to it were taken as a master event (ME). At teleseismic stations, the peak amplitudes are observed in the first P-wave, but the length of the coda-wave is even large than that at PETK. This is a result of various velocities of the secondary phases, and their mixture expands in time. The secondary phases attenuate much faster in amplitude and, in relative terms, the coda-wave is not as prominent at WRA as at PDYAR. To detect small aftershocks in such prominent coda-waves is a problem not only for 3-C stations but also for the beamforming and WCC at arrays. At the same time, to validate the advantages of the WCC approach, detection of the smallest REB events together with additional XSEL events with the same statistical properties (as per EDC) is needed.

Figure 2. Waveforms for a) 2025201 (90 min) and b) 2025211 (full day) at stations PETK, PDYAR, MKAR, and WRA. All original records are filtered between 0.6 Hz and 4.5 Hz.

In Figure 2b, data from the same stations are shown for July 30. The number of visible aftershocks is very large, and the others listed in the REB have amplitudes too low to be seen among the mainshock and the largest aftershocks. The noise level is very high during the first hour of July 30. There are also ~30 minutes of high noise on July 29 after the mainshock and no aftershocks reported within the next 10 minutes before 23:34:49 (mb=5.28). Some of the aftershocks within this 10-minute interval were recovered using the WCC with the addition of stochastic noise [Kitov et al., 2026]. Detection of relatively large aftershocks (mb from 3.5 to 5.0) was suppressed during the first hour after the J29 mainshock as Figure 3 shows.

Figure 3. The period from the end of 29 July to noon on 30 July, 2025. The deficit of dozens of events with mb between 4.0 and 4.5 is clear during the first hour after the mainshock.

The templates to find smaller seismic events before the J20 and the J29, as well as after them can be taken from the historical IDC records, including the earthquakes available on the day of processing. Three earthquakes with close epicenters but different depths are listed in Table 1 as examples of MEs for the WCC processing, with the waveforms shown in Figure 4. The focal depth is responsible for the differences between the unfiltered waveforms observed at PETK (Figure 4a). The deep earthquake generates a more impulsive signal and the templates for the two near-surface ones would have a low-amplitude segment before the peak, as better seen in the filtered (3rd order, BP, 2.0-5.0 Hz) version of the waveforms in Figure 4b. These specific features are decisive for the difference in WCC detection of the near-surface and deeper sources as these three MEs demonstrate. A reasonable spacing between the MEs for signals at teleseismic distances ranges from 70 km to 120 km. The spatial resolution is defined by the slowness of the phases, which is low at distances above 30°–60° (0.07–0.08 s/km). Shallow earthquakes are very similar for a given geological structure. The cross-correlation exercise with earthquakes from the southern to the northern part of the Mid-Atlantic Ridge showed high similarity of the waveforms throughout the entire length [Bobrov et al., 2017]. The depth sensitivity requires a smaller spacing due to its effect on the waveform shape. For routine WCC processing at the global level, a set of MEs was prepared within 40-km-thick layers from 0 km to 700 km. The depth of a sought event is fixed to the depth of the corresponding ME, since the depth sensitivity of the first P-wave is very low. When focused on the event depth, WCC can be extended by templates of the depth-sensitive phases together with the first P in order to improve the depth estimates. In any case, the change in signal shape with depth provides a good initial selection of the most relevant ME.

Table 1. Three high quality MEs for further comparison of detection performance

REB ORID	jdate	Origin time	Lat, deg	Lon, deg	Nass	mb	depth, km
23694976	2023068	02:06:51	51.66	159.63	46	5.0	0.0
23689063	2023067	16:10:51	51.62	159.58	54	4.9	12.0
23637715	2023056	06:25:22	51.69	158.43	73	4.5	66.8

Figure 4. a) Unfiltered signals from three MEs in Table 1 at station PETK. b) Same signals. 3-rd order, 2-5 Hz BP filter is applied.

In Figure 5, the evolution of the signal with distance is shown for the deep ME in Table 1. The signals are filtered and demonstrate their high-frequency nature in the first P-wave. The pre-signal noise is not seen at PETK relative to the signal (SNRIDC~10000), with the peak amplitude reached in ~1-2 s after the arrival. At PDYAR, the peak amplitude is observed in ~4 seconds after the arrival; the signal is also long and specific. The coda-wave is much higher than the noise at PDYAR (SNRIDC~33) and at MKAR (SNRIDC~115), where the signal peaks at the same time as at PETK. At WRA, the first arrival is impulsive and the coda-wave is well above the pre-signal noise (SNRIDC~65). All four signals are specific and have high signal-to-noise ratios. Both features are crucial for effective WCC performance.

Figure 5. Templates of the ME on February 25, 2023 (jdate: 2023056) at four IMS array stations: PETK, PDYAR, MKAR, and WRA.

The WCC detection process not only finds signals similar to the templates and reduces the detection thresholds at the IMS array stations, as a realization of the matched filter detector, but also suppresses signals arriving from different azimuths and distances. The latter property refers to the change in relative arrival times of secondary phases with different apparent velocities. The WCC changes the meaning of valid/false detection for the following phase association. For beamforming, the average daily rate of detections varies around some tuned level [Saragiotis, Kitov, 2020], with the deviations depending on the global seismicity. For example, the Sumatra 2004 and the Kamchatka 2025 earthquakes generated an extremely large number of detections at almost all IMS stations, except those in the core shadow zone where only secondary phases were observed. The presence of numerous detections near the detection threshold, with inaccurate estimates of the principal parameters and their tolerances in automatic processing leads to multiple phase misinterpretations (e.g., PP used as P) and misassociations (P wave from a different source). Numerous weaker events in the SEL3, with some of them promoted to the REB, often lose many, or sometimes all, associated phases in the interactive analysis. Analysts have to find or generate new ones in order to create the REB event hypotheses. Mega-earthquakes do not occur often, and the daily seismicity at a representative IMS station is defined by events at teleseismic distances with magnitudes between 3.5 and 5.5 as well as events at regional distances with lower magnitudes. Signals from these events are effectively suppressed by the WCC detector except for those which are close to MEs from a given set, if any. As a result, there are no detections to be misinterpreted or disassociated as such. There are days with just a few signals detected by the WCC for a given ME. This number depends on the seismic activity around the ME. The detection threshold can be adjusted to the current level of activity, however. This operation would increase the number of valid detections and likely increase the probability of false detections related to noise components slightly coherent with the template. There is a task of tuning a WCC detector to an optimal balance between valid detections and false alarms, where the valid detections are those associated with the final set of event hypotheses generated by one ME. All detections made by the WCC are assumed to be associated with (found and not found) events close in space to the corresponding ME. Therefore, the station-event angles and apparent velocities of the regular phases related to the detections are practically the same as for the parent event, with minor adjustments for location discrepancies. For the EDC adopted by the IDC, this is an important source of information for the statistical significance of the REB events with 3 to 6 associated P-phases. For a larger number of associated first P-phases, only arrival times are used. For a WCC detection, in some cases it is impossible to visually confirm a signal below the noise level, even if its signal-to-noise ratio at the CC-trace, SNRcc, is high and it could potentially contribute to creating a hypothesis for the event. Analysts' work with such detections is challenging, and hypotheses generated by the WCC often get dismissed due to a lack of visual verification. Therefore, the WCC detector tuning has to rely on associating phases with reliable event hypotheses. One can formally use statistical significance for an event hypothesis created by the association of the WCC-generated phases. The EDC use the same approach and tested the SEL3 and REB statistical significance in GSETT 3 experiment [Ringdal, 1994]. Statistical significance depends on the probabilities of the detected phase being associated with a source, characterized by its location and origin time, compared to the probabilities of randomly generated detections with SNRcc values distributed by an exponential law being associated with the same source. Thus, the distribution of SNRcc values determines the statistical significance and power of the WCC-based hypotheses. The WCC detection list includes signals with SNRcc above a predetermined threshold, as well as those satisfying several additional criteria, with the primary criterion being the standard SNR threshold. By adjusting this threshold, you can control the detection rate. The standard SNR estimates are taken in a short interval after the CC detection time and in many cases present the peak SNR of the ambient noise not related to the signal below the noise level. An acceptable rate is ~1500 detections per day, with hourly variations of ±30–50% possible for various specific conditions. Most of these detections on quiet days, characterized by the absence of events in the REB in the area of study, are likely to be below the IDC detection threshold. In certain cases, such detections can be due to WCC's side sensitivity to intense sources like the Tohoku earthquake. Spontaneous signals above the threshold are also possible due to data issues such as zeros and spikes. Quality controls can eliminate such cases by imposing strict requirements on the number of consecutive SNRcc estimates above the threshold. One can also use adaptive thresholds to adjust for the actual event flux to the background noise levels. These adaptive thresholds are useful for tuning the WCC during periods of low and high seismicity. During WCC processing at a high threshold value, say 100, a quasi-uniform SNRcc distribution can be generated for a given ME. Under these circumstances, detections do not occur, and all SNRcc estimates represent noise within the LTA time series without interruptions. During quiet times without detected events, we expect that random signal generation will create an SNRcc frequency distribution with a quasi-exponential roll-off. Any departure from this baseline scenario indicates the presence of actual detections, as the template reacts to similar signals within the data set. The point at which this departure occurs can serve as a detection criterion. Over an hour processing interval, the number of SNRcc values should be 3600 times the sampling rate at a given station. IMS stations have sample rates ranging from 20 to 100 per second, with 40 Hz being most common among the IMS arrays and 3-C stations. Figures 6 to 8 show several SNRcc frequency distributions for the same four IMS stations as in Figure 5. The same three MEs from Table 1 are used to evaluate potential variations in individual performance. Two threshold sets are used in the WCC processing: those used in actual processing from 3.1 (PETK, PDYAR, and MKAR) to 3.3 (WRA), and a detection-prohibiting value of 100 for all four stations. In

Figure 6, the results are presented for a quiet day on 2023334, with no REB events between the start of 2023333 and the end of 2023335. A six-hour period is selected between 12:00 and 18:00.

The SNRcc distributions for the threshold of 100 are crucial for understanding the WCC processing. At all the four stations, the corresponding curves for all the three MEs demonstrate a practically exponential roll-off from the peak between ~1.0 (WRA) and ~1.2 (PETK, MKAR) to a maximum SNRcc of 4 to 5 at PDYAR, MKAR, and WRA. At PETK, the maximum SNRcc is ~6, but the exponential roll-off is observed up to ~4. This behavior is expected for a stochastic distribution. At WRA, the exponential decay constant for the third ME in Table 1 is -3.0. This value and the range between the actual threshold (3.3) and the maximum SNRcc of ~4.5 can be used for the modeling of random noise for further use as a benchmark for the evaluation of the statistical significance of the XSEL events. For example, the requirement of SNRcc above 4.5 would reject any random detection. For the actual thresholds, the SNRcc frequency distributions in Figure 6 demonstrate the presence of detections with “frozen” LTA values by a sharp peak near 3.1. When STA/LTA reaches the threshold level, the following SNRcc values should grow with time to the maximum value if they are related to a sought signal. If the STA/LTA ratios immediately after the threshold are not related to the sought signals, sporadically producing a few large values and then dropping back below the threshold, the LTA returns to the “calculated” mode. The maximum SNRcc value is above 10 at PETK and PDYAR, where the longest templates are used. These detections belong to low-magnitude events generating weak signals. The corner magnitude in a recurrence curve does not indicate the absence of events with lower magnitudes but rather the inability of the observational system to detect them following its internal rules. Low-magnitude events always occur in the actual seismic process, and their number grows exponentially with decreasing magnitude. The WCC processing finds some of them, and the SNRcc values of the corresponding signals are above the detection thresholds. The differences in the MEs’ performance for the working detection thresholds are clear in Figure 6. The deep ME is the most sensitive at PDYAR and WRA. The first ME in Table 1 is very effective at PETK, and the second ME is the best at MKAR. These estimates are only for the quiet day when the events are below the IDC detection threshold. For the days of higher activity, the relative performance can change. Figure 7 shows the results for the period between 00:00 and 06:00 on July 20, 2025. This is also a relatively quiet period without REB events, but preceding the J20 earthquake. At first glance, it seems to be even more “quiet”, with lower SNRcc curves at all stations. For example, there is no large SNRcc generated by the third ME at WRA. All the curves are closer to the exponential distribution. This can be an important feature related to the earthquake preparation process. The SNRcc frequency distributions obtained for the period from 00:00 to 06:00 on July 30 are shown in Figure 8. This is the period with the highest seismic activity likely ever detected by the IDC. At PETK and PDYAR, the curves for the working threshold show heavy tails and a significant number of detections above SNRcc ~10. For the small-aperture array MKAR, the highest SNRcc is ~9, while the large-aperture array WRA generates a large number of detections with SNRcc>10. The first ME is the most sensitive at PETK and PDYAR, and almost as sensitive as the third ME at MKAR and WRA. The curves for the threshold of 100 also demonstrate heavy tails. This observation reveals that the detected signals have sharp arrivals with larger amplitudes, as depicted in Figure 2b. The pre-signal LTA includes some elevated CC values, but the peak SNRcc is much higher than the surrounding SNRcc estimates. Figure 6. Frequency distribution (0.1 bin width) of SNRcc at PETK, PDYAR, MKAR, and WRA for a quiet day of 2023334. Three MEs are shown with two detection thresholds: working 3.1 (3.3 for WRA) and a detection-prohibiting of 100. The distributions vary with station and ME.

Figure 7. Same as in Figure 6 for the 6 hours before the J20 earthquake. The rates of detections are lower than for the quiet day 2023334. Almost no detections at remote station WRA.

The number of SNRcc values above the working threshold is very high at all stations but only a few (approximately 60 to 100 per hour) are selected as detections according to the WCC procedure. This detection rate may not be suitable for tasks requiring very high seismicity recovery. Special measures are needed to reduce the distance between subsequent detections in the phase association processing. These tasks are beyond the scope of the current study, which is focused on signals below the noise level that can be detected by WCC before the mainshocks. In this study, aftershocks of major earthquakes serve as a source for the recurrence curves obtained for time intervals of various lengths - from days to the entire observational period since 2001.

Figure 8. Same as in Figure 6 for the most seismically active period between 0:00 and 6:00 a.m., 2025211. The detection rates are high at all stations. Station PETK may suffer significant elevation in the coherent noise amplitude and lower SNRcc.

The earthquake preparation process includes a growth in the size of the sources emitting the sought signals. Simultaneously, the ambient noise at recording stations progressively includes these signals, which rise in amplitude, from all the sources in the area of the mainshock preparation. When using beamforming as a detection method, this noise, coherent with the detected signals, can mask smaller events at the array stations, as suppression is based on destructive interference. The same effect occurs with WCC-based techniques, but it is possible to improve array resolution by adding randomly generated time series to the real data. In a previous study, we used this method and identified several aftershocks that were missed by IDC within the first 10 minutes following the J29 mainshock [Kitov et al., 2026]. Detection thresholds at individual IMS stations were tuned to the total number of detections in numerous tests and studies of different cases. Phase association processing relies on the detection quality and relevance to the corresponding ME, which is selected from the REB. There are some places where only poor REB events are available with a low number of associated stations and low-quality templates. The tuned detection threshold must provide detection rates within a narrow range, but the detections have to be reliable not to bias the final XSEL. Automatic bulletins always face this dilemma between number and quality. The SEL3 of the IDC contains up to 60% of events that are rejected at the interactive stage. A few percentage points of the SEL3 are located at distances within 90°-180° from their final REB solutions. Sometimes, the SEL3 seed events lose all associated phases and are replaced by analysts with different ones. Frequency distributions of SNRcc values for all detections produced by the first (23694976) and second (23689063) ME in Table 1 for the days of the lowest (2023334) and the highest (2025211) activity at stations PETK and WRA are shown in Figure 9. The rates range between 28 (PETK on 2023334) and 44 (WRA on 2023334) detections per hour. These rates are below the target value of 60 per hour for average seismicity with IDC-detected events. On the quiet day, the low rate is likely related to a lack of events, even the smallest ones. On July 29, 2025, the activity was very high as were the ambient noise amplitude and coherence with the sought signals. As a result, the detection rate was also lower than average. For the best 100 MEs used in routine WCC processing, some principal statistical parameters are presented in Table 2. The average detection rate varies from 28±13 (WRA, 2023334) to 42±7 (PETK, 2025211). The maximum rate among all 100 MEs was 59 detections per hour, which is close to the target rate, with a minimum of 7 per hour related to a relatively poor ME in a very quiet part of the studied area. A rate of 30 to 40 per hour results in a time spacing between subsequent detections of about 1.5 to 2 minutes. For a random detection distribution with the same average spacing, it would be difficult for several stations to be associated with a unique source with a fixed location.

Table 2. Statistical information on the performance of the best 100 ME on 2023334 and 2025211.

Station	WRA		PETK
Day	2023334	2025211	2023334	2025211
mean	28	31	33	42
st dev	13	5	6	7
max	56	49	50	59
min	7	16	20	7

Figure 9. Frequency distribution of the SNRcc for all detections made by MEs with orid=23694976 and orid=23689063 at stations PETK and WRA during the whole days of 2023334 (quiet) and 2025211 (most active seismicity).

The quality of an XSEL bulletin should be verified through interactive analysis or by comparing it to a high-quality bulletin from the same area. The REB can serve as a reference for the XSEL in the studied region, allowing a direct arrival-time comparison between associated signals at the same IMS station in two bulletins. According to the procedure adopted by the IDC, it is only necessary to have one common arrival, i.e., two similar signals within the allowed retiming window (±10 seconds), in order to match an XSEL and REB event. This means that these events are related to the same physical source. Local association The WCC arrival list consists of individual lists for each of the used MEs. These individual lists do not intersect but may contain arrivals corresponding to the same physical signals. By design, all templates of a given ME are only able to find signals from other events within a small footprint around its epicenter. For sought events within 1/4 of the signal wavelength, CC can be between 0.95 and 0.99 if the noise is negligible [Arrowsmith et al., 2006; Baisch et al., 2008]. Such a situation was observed for the signals from the DPRK announced underground tests [Selby, 2010; Kitov et al., 2025]. For very high CC and SNRcc values, the accuracy of the arrival time estimate for the sought signal can be as high as 0.001 to 0.005 seconds. As a result, the RMS travel time residuals for a sought event located using the WCC arrivals can be of the same magnitude of 0.005 to 0.01 seconds. In terms of the spatial location accuracy, it corresponds to 40-80 meters for an apparent wave velocity of 8 km/s, such as the Pn-phase. The accuracy of the relative location can be very high, but the absolute location accuracy of a sought event is practically the same as for the corresponding ME. When an ME is located 100 km from its true position, any sought event will also be located with the same error. This effect has to be taken into account when the set of MEs is selected from the REB or any other bulletin. The ME density has to compensate for their potential location errors. The confidence ellipses provide valuable information, but they also serve as estimates of location precision. The relative location of an event hypothesis using all associated phases (stations) and confined to a small area around an ME is called Local Association (LA). The LA version used in this study was described in [Bobrov et al., 2014; Bobrov et al., 2016ab; Kitov and Sanina, 2025ab]. The CC and SNRcc values rapidly fall with the sought event’s distance from a given ME and with the amplitude of the sought signal relative to the noise level. For an array station, a virtual event location moved across the LA grid shown in Figure 10 can change the scalar slowness and azimuth of the arriving plane wave, potentially enhancing or suppressing the multichannel cross-correlation with the template. Changes in the actual event location can also impact the source function of the sought event, and differences in propagation paths may distort the shape of the sought signal compared to that of the ME. The search area for a given ME is defined by the degradation of correlation with distance and the presence of different MEs. In Figure 10, the search area is defined by the distribution of nodes and the size of the mesh cell. There are 16 nodes in both the horizontal and vertical directions between the center and the circle. With a step of 6 km, R=96 km. The number and length of steps can vary, and rectangular cells can be replaced by any appropriate shape to allow for tight and nearly even coverage. To prevent edge effects, if the best event hypothesis is located beyond 0.9R, it is rejected, and adjacent MEs have to be responsible for it. This means that the search radii of neighboring MEs have to overlap to fully cover the studied area.

Figure 10. Virtual location grid. r - vector from the ME in the center to a grid node. S - slowness vector of the plane wave (dashed line) arriving at the station. The circle with radius R limits the distance to the used nodes. For the closest stations, the node position can change the shape of the generated signal and the vector slowness.

A valid event hypothesis is defined by its location and origin time. The origin time for a specific location is determined by the arrival time of the associated phase and the event-station travel time. Arrival time is always a measured parameter. Travel time can be either theoretical, as in the IDC’s GA processing, or empirical, as in the WCC’s LA processing. The GA method seeks the best absolute locations of sources globally and involves a large number of permutations between virtual sources and their signals. The LA focuses on a smaller sequence of signals most likely generated by sources near the corresponding ME location. To estimate the travel time for a signal, the GA uses source hypotheses in various regions and travel-time tables corresponding to various phases, as the phase name can be altered in the GA. The LA has a small footprint with virtual source locations, extremely (0.001 s) accurate empirical travel times taken from the REB (or any other bulletin for different networks), and fixed phase name. Therefore, a virtual event origin time at the (0,0) node can be calculated as the WCC arrival times less the empirical ME-station travel times independent of the status – associated/not associated. The arrival times obtained by the WCC detector at all stations can be reduced to their corresponding origin times at the ME location once and for all. For the other nodes, the travel times have to be corrected for the vector to the node, r, and the slowness vector of the signal at the related station (Figure 10). This is a very accurate time correction, as the node vector is predefined and the slowness vector for a given station does not change much between the nodes of a small grid search area compared to the ME-station distances. For a valid event hypothesis, the origin times for three or more associated signals (stations) have to be within a predefined tolerance. At the IDC, the allowed travel (origin) time residual relative to the theoretical time is 2 s for the first P-phases, and 2.2 s for the Pg- and Pn-waves. These residuals correspond to the desired statistical significance of the REB events. A minimum of three first P-phases at different stations have to be associated with a valid event. These criteria are utilized in the WCC processing to align with the IDC approach and the REB. Since XSEL arrivals potentially have higher relative arrival-time accuracy, the origin-time tolerance can be lower than for the IDC without sacrificing performance efficiency, as measured by the number of valid (matching REB) events. In contrast, automatic IDC bulletins (e.g., SEL3) allow for a travel-time tolerance much larger than 2 s, reaching up to 5 to 7 seconds. This increases the risk of phase misassociation and misinterpretation, leading to the rejection of over 60% of SEL3 hypotheses. The WCC processing, while automatic, strictly adheres to the full list of REB requirements, with the exception of the distinction between primary and auxiliary stations. It is worth noting that there are many physically viable event hypotheses created below the EDC during the interactive review, but rejected during the automatic EDC compliance stage to meet the CTBT requirements for event quality and monitoring threshold distribution. These rejected events could be helpful to tune the WCC processing parameters, but their creation is sporadic. Three or more arrivals with origin times within a ±2 s interval from their average value are not a guarantee of a reliable event hypothesis. There are many arrivals at various stations, and the event hypotheses have an additional degree of freedom - varying location. The REB provides valuable information on IMS station performance for historical events in any seismic region. Some stations contribute to almost all REB events in specific areas, such as IMS stations WRA and ASAR to events within Australia. Therefore, an REB event hypothesis within Australia without these stations, when they are operational, would be rather false even though other parameters may match the EDC. There are also IMS stations contributing only to the largest events in this region or not contributing at all. The difference between the most sensitive and ineffective stations can be described by their participation rates in the REB events. These rates are calculated for each IMS station in regions with repeating seismic events. For example, the first P-phases detected by PETK have the highest probability of being associated with events in the studied area and can be characterized by a station weight (or probability) of 1.0. Table 3 lists the weights of the top 30 stations. To create a statistically significant event hypothesis with three associated stations, two of which must be from the top four, one can establish a minimum event weight of 2.65. This will result in only a few valid three-station configurations. When more than three stations are associated, their weights are combined, and the 2.65 threshold can be matched for many configurations with two stations from the top four participating. For events with more than five associated stations, having one from the top four is typically sufficient, as the association of a station adds statistical significance due to its probability of being associated compared to random chance. Station PETK is not needed for such cases, as evidenced by the REB listing events without PETK for the aftershocks on July 29. Noise can mask the appropriate signals and teleseismic stations are sometimes more efficient. The threshold value of the STA/LTA ratio on a CC trace is a powerful parameter for the detection rate. It also impacts the maximum SNRcc value, as demonstrated in Figures 6 through 8. Figure 9 shows that on a quiet day like 2023334, when the detection algorithm may generate more noise phases, the maximum SNRcc is constrained to an exponential decay trend with only a few signals with SNRcc greater than 5. Station WRA has several signals with SNRcc above 5 and lower weight. It is beneficial for event hypotheses with 5 or more associated stations. Station PETK has ~30 signals with SNRcc>6 and ~60 with SNRcc>5 for the ME with orid= 23694976 during the day of 2023334. This is less than 2 and 3 signals per hour, respectively. Therefore, the maximum SNRcc is a critical parameter for the statistical significance of a hypothesis, in addition to its weight. On quiet days, the SNRcc values are also higher on average than for many other stations, including WRA. Requiring SNRcc>5 for station association in 3- to 5-station events will enhance the statistical significance of these hypotheses. The probability of random association is exceedingly low when considering the detection rates at the top stations and the overall statistics for the best 100 MEs (Table 2). A similar approach to statistical significance related to the probabilities of detections above predefined SNRcc thresholds is the sum of SNRcc values for all associated stations. For 3- to 7-station event hypotheses, this sum assesses the credibility of association for all signals together, as well as any individual signal before it is associated. The threshold for the SNRcc sum has to rely on the statistics of detections for a given region, considering factors such as the distance-azimuth distribution of IMS stations, the history of seismicity, and the quality of MEs, as these may vary.

Table 3. Stations’ weights for the event hypotheses creation.

Station	weight	Station	weight	Station	weight
PETK	1.00	JKA*	0.70	ARCES	0.60
PDYAR	0.90	MJAR	0.69	USRK	0.56
KURK	0.86	PDAR	0.68	SEY	0.55
MKAR	0.85	WRA	0.67	SHEM	0.55
TXAR	0.83	NOA	0.66	SONM	0.52
FINES	0.80	SPITS	0.65	ZALV	0.52
AKASG	0.74	NVAR	0.63	KLR	0.50
ASAR	0.73	YKA	0.63	MA2	0.50
BVAR	0.72	KSRS	0.62	TLY	0.50
ILAR	0.71	CMAR	0.61	YAK	0.50

*3-C stations are highlighted bold

In summarizing the LA setting for the current study, we can formulate several simple rules to adjust the principal parameters to the desired magnitude range: 1) The number of associated stations is 3 or more. Two-station events are not considered, but a minimum of 4 stations is used in some cases of many stations with the weights near 1.0. 2) The origin-time tolerance can vary from 0.1 s to the tolerance adopted in the SEL3. The WCC detection algorithm allows consecutive arrivals to be very close to each other. Therefore, a detection list at a given station has to be checked for the spacing between consecutive arrival times for the same ME. There should be only one arrival at the same station within an association window of twice the tolerance. When data are read in, the next detection closer than the doubled tolerance plus 1 second is removed. This operation results in a decreasing number of detections available for association with an increasing origin time tolerance. It may have a negative impact on the LA efficiency for periods of very high activity with very close arrivals. 3) The minimum total event weight can vary from 1.5 (3 stations with 0.5 weight) to 2.76 (3 top stations). 4) The weight of one of the best stations to be associated with any 3- to 5-station events is between 0.7 (top 11 stations) and 1.0. A lower weight is not supported by the REB for Kamchatka, but in remote regions such as mid-oceanic ridges and transform faults in the Indian Ocean where stations have low participation rates, a weight of 0.6 may be considered reasonable. 5) The minimum sum of SNRcc values for 3-, 4-, and 5-station events is calculated by adding the 3, 4, and 5 lowest detection thresholds. The sum step for larger events is determined by the minimum detection threshold of the next station to be associated. There is no limit to the maximum level. In practice, a sum of 30 for a 3-station solution makes it almost impossible to create events in routine processing. For the DPRK tests, the SNRcc is above 10 for many stations for any explosion as an ME. 6) The lowest possible value for the minimum SNRcc at one of the top stations from 3) is the detection threshold. This minimum can be set at any level depending on the studied case. 7) The grid radius can be a few hundred meters, such as for the DPRK test site. For an event occurring in remote regions, like the French nuclear test site at Mururoa Atoll in the South Pacific Ocean, a radius of 100 or more kilometers is appropriate for the far teleseismic stations since location algorithm minimizes travel time residuals rather than distances. The number of steps is tuned to the time resolution related to the radius and associated phases from Pg to PKPbc. There are other LA parameters that allow for fine-tuning to specific cases of seismicity, such as the aftershock sequence of the J29. These parameters remain unchanged throughout all calculations after being tuned in the test calculations. Conflict resolution By design, each ME generates a detection list, and then the LA creates a set of event hypotheses with a part of all available detections associated with them. Not all detections can be associated since the sensitivity and resolution of the involved stations are not uniform and the best stations may find signals not visible to other stations. Another issue is the generation of detections and creation of hypotheses by adjacent MEs. For example, signals from the six DPRK underground explosions were detected by many IMS stations. When used as an ME, any of them could find all of the others at the stations where it had waveform templates. In turn, for any DPRK test, all the other five can detect signals at the IMS stations with corresponding templates. It is worth noting that the WCC detector, using templates from the larger DPRK tests, can find signals from the low-yield DPRK-1 test at stations where it has no arrivals in the REB [Kitov et al., 2025a; Adushkin et al., 2025b]. For the XSEL, only one event hypothesis from the five available is allowed. The event weight is the most important characteristic of the statistical significance of the related hypothesis. One can use the station weights for the DPRK test site and estimate the total weights for the five competing hypotheses. Let’s assume for this specific example that the event weights created by the DPRK-4 and DPRK-5 explosions are the same. Then the next deciding parameter is the number of associated stations (Nass). This parameter is useful when Nass is high and the lists of associated stations include those with low weights. When the event weights are equal, Nass can differ by one or two stations and resolve the conflict. There is a possibility that the weights and Nass are equal between competing events. Then the final decision is made by the RMS origin-time residual. These values are always different, and the decision is unambiguous. The conflict is resolved. As a result, the best event hypothesis is promoted to the final XSEL and four excellent event hypotheses have to be rejected with their associated phases moved to the list of unassociated. In practice, the MEs are not equal and some of them may create more XSEL hypotheses than the others despite very close quality of template and the same list of stations. For the DPRK test site, the fifth explosion is likely the best for the place [Kitov et al., 2026]. There are tens of thousands of MEs in the global WCC processing, with an average spacing of approximately 1.3° and some places with higher ME density. The depth bins for the ME distribution are 40 km thick, and two ME can be almost collocated and have a depth difference of a few kilometers if they are in different depth bins. This situation is close to the DPRK setting of MEs. Several neighboring MEs can find the same physical source of seismic emission by their respective templates at the same stations. Competition for the same physical signals creates conflicts at stations. These conflicts are resolved unambiguously between all pairs of MEs at all related stations according to the WCC Conflict Resolution (CR) procedure. The final XSEL includes unique solutions only. The principal difference between the DPRK case and the routine WCC processing with thousands of MEs covering a very large area is in the probability of two competing phase not belonging to the same physical source, making the conflict random. The CR makes its choice since the arrival-time difference between the signals is within its responsibility, but one or two rejected phases should not reject the entire event hypothesis when its other associated phases at different stations are not in any conflict. Therefore, an event hypothesis losing one or more arrivals has to be checked against the EDC related to the WCC processing. If it does not pass the test, it has to be rejected. Otherwise, it can be promoted to the final XSEL when no other conflicts have to be resolved. The number of lost stations and the corresponding lost weight could be used to retain the event quality by introducing corresponding tolerances. These are important parameters for the highest seismic activity periods when competition for detections among MEs is enormous. In this study, these parameters are retained at the level tuned to the highest activity after the major events – an event hypothesis can lose up to 12 associated stations and a total weight of 6.0. It does not harm the WCC processing of average activity between the major events as the number of conflicts falls fast with the decreasing number of event hypotheses. Seismicity of the Kamchatka region as per the IDC The Pacific plate subducting under the Kamchatka Peninsula creates active tectonic forces converted into high seismic activity with extremely large events, like the Kamchatka 1952 (Mw=8.8-9.0) and 2025 (Mw=8.8) earthquakes. As of December 2025, the IDC catalog lists ~27,000 events within the studied area: 45°N - 65°N, 145°E - 165°E.

Figure 11 shows the evolution of seismicity since the start of IDC processing in January 2001.

In addition to the July 20 and 29 earthquakes, there were several high-magnitude events expressed by aftershock density, as shown in Figure 12. The most prominent ones occurred on November 15, 2006, May 19, 2013, and December 20, 2018. There are approximately 7-year long gaps between the major events. The locations of the 2006 and 2018 events are far from the other four events, with the 2013 and 2025 earthquakes being almost collocated. The J20 can be considered as a foreshock of the July 29 earthquake, with the event on September 18, 2025, event being its aftershock. The J20 could also be treated as a failed attempt of the J29 [Kitov et al., 2026]. The study area was selected to include the larger aftershock sequences of the neighboring large-scale events. The preparation of the J29 can depend on the processes in the adjacent, seemingly independent, structures. This possibility should be studied in the overall approach to the earthquake preparation process recovered using waveform cross-correlation. Figure 11. Body wave magnitude mb(IDC) as a function of time since the IDC start in 2001. Minimum event magnitude is 2.0 [Coyne et al., 2012]. Maximum magnitude is of 6.30. The J29 event is the largest observed by the IMS stations and processed by the IDC for the studied area. The events in Figure 11 are represented by their mb values since the IDC calculates only body- and surface-wave (Ms) magnitudes. The latter is not available for the low-magnitude events. The difference between mb and Mw is increasing with Mw for the events above magnitude ~6.0 because the body wave magnitude scale saturats when the corner frequency of the event spectrum falls below the lower frequency of the mb-band 0.8 Hz - 4.5 Hz. This magnitude scale difference is not a problem, since the events of interest have magnitudes below the corner magnitude of the recurrence curve for the Kamchatka region and are mainly not detected by the IMS/IDC standard procedure. The Mw estimates are not available for these events. The seismicity map in Figure 12 shows the abundance of potential sources of high-quality templates for the WCC processing. There are aftershocks of the J29 not included in this map, because these events occurred after December 2025. They may prove to be the most efficient MEs. The WCC has been on a learning curve since the start of IDC processing in 2001. For other regions with seismic networks, observational periods may vary in length, but the availability of MEs has to increase in both number and geographical coverage.

Figure 12. Seismic activity within the studied region as per IDC. Aftershock sequences of the 2006319, 2013139, 2018354, 2025201, 2025210, and 2025261 are highlighted.

Master events In seismic applications, waveform cross-correlation is based on templates corresponding to regular signals detected at the stations associated with seismic events. The IMS seismic network uses arrays and 3-C stations to provide data to the IDC. For a 3-C station, one or all three components can be used as templates. All three components are useful for near-regional signals from low-magnitude sources. At larger distances, the ambient noise on the horizontal components is usually higher than the signals from almost all sources. Since all three components are recorded by the same instrument, they are synchronized in time, and the arrival times at the three components of the sought signals are also simultaneous. The difference between 3-C signals from the sought sources and other, unrelated sources arises from the differences in the apparent velocities of the secondary phases and their azimuth- and distance-dependent attenuation and dispersion. The IMS array stations allow for a significant reduction in the detection threshold compared to collocated 3-C stations, and are much more sensitive to the azimuth and scalar slowness of the primary and secondary phases. This makes them a major contributor to the REB events, also because they provide a higher statistical significance to the associated phases due to lower tolerances related to the estimates of arrival time, azimuth, and slowness conducted by beamforming [Schweitzer et al., 2012]. As a waveform template, a multichannel signal at an array station makes the matched filter detector more powerful due to additional signal specificity. The performance of a WCC-based detector, as an implementation of the matched filter detector, depends on the specificity of the template and sought signals, but also on the properties of the ambient noise. These conditions make the selection of the master events with the associated waveform templates a crucial task for the completeness, consistency, and accuracy of resulting bulletin. The most efficient way to select master events (MEs) is to conduct a preliminary study of the level of cross-correlation between REB events within an area where the MEs may compete for the same signals, as described in the CR procedure. The main task of the selection procedure is to identify those REB events that have matched the largest number of neighbors using standard WCC processing. The REB is the best source of meta-information on the locations and magnitudes of all events and their associated phases. The estimates of the signal-to-noise ratio (SNR) for the associated phases are important for the quality checking of the corresponding signals. The latest update of the ME set was completed in 2023, but the current available computing resources are insufficient to repeat it with the new data. There were approximately 1000 MEs in the region for a prototype routine WCC processing at the IDC, which was halted in 2024. For this study, the best 100 out of the 1000 were selected. This reduction in number was primarily due to computer limitations (one i9 processor with 24 cores). The feasibility study status also allows for a reduction in the number of MEs, as the task is to uncover the earthquake preparation processes for further full-scale investigation, including in different regions. The upper panel in Figure 13 shows the geographical distribution of the best 100 MEs (yellow circles) across the region, covering the entire depth range from 0 km to 700 km. The slightly increased spacing between these MEs compared to the 1000 MEs case is partly compensated by their quality, as demonstrated by four years of test routine WCC processing in a prototype IDC pipeline. This represents a basic set of the WCC processing. There was a significant change in the IMS seismic network related to observations in the Kamchatka region – a new sensitive array station, PDYAR, was installed in 2023 to replace the old IMS 3-C station PDY. Since it did not participate in the WCC selection procedure, it is absent from the 100 best MEs set. To address this deficit, a set of 195 MEs was generated, all containing PDYAR. These PDYAR events are more widespread across the region. They are shown by red circled in Figure 13. In total, there are 295 MEs used in this study. The basic assumption is that the whole region has the potential to impact the J29 preparation process. Seismic activity in both the upper and lower latitudes of the area may reveal specific features of this process. An extension of this assumption is to test each potentially independent part separately using the MEs related to these parts. Therefore, the entire set of 295 MEs was processed by the WCC detector. The LA was applied to various subsets, including the whole set. The differences in the resulting XSELs were revealed and interpreted in terms of the potential influence of various parts on the J29 preparation, as described by the evolution of low-magnitude events. Several key geographical parts of the entire seismic activity within the region can be identified from Figure 12. Aftershocks of the J20 earthquake are distributed across a relatively small spot that includes the J29 hypocenter and many of its aftershocks, including those on September 18, as well as the epicenter of the 2013 earthquake and its aftershocks. The inability of the J20 faulting process to follow the path of the J29 fault is likely related to an asperity in its way. This spot also includes the 2013 earthquake and its aftershocks, making it the most seismically active spot in the region based on event density, deserving special consideration. This spot is referred to as the “Asperity” and includes 49 MEs, as shown in the lower panel of Figure 13. In contrast, the other 245 MEs define the area referred to as “Out of asperity”. One out of 50 events within the “Asperity” area is excluded by its depth and is also not included into any of the subsets except the PDYAR set, to which it belongs. The performance of these MEs is a significant factor in understanding elastic energy accumulation and related seismic processes beyond the most active spot. Another important area is the southern rim of the region. Here, the seismic process is likely decoupled from the influence of the J29 earthquake, as indicated by the spread of its aftershocks. On the other hand, it may act as a solid wall or boundary where elastic energy is not released in the aftershock process. This area is referred to as the “Rim PDYAR”, as only MEs from the PDYAR set are selected.

Figure 13. Two representations of 295 MEs used in the analysis of seismicity between July 6 and August 3, 2025. The upper panel includes the best 100 MEs and 195 PDYAR MEs. The lower panel shows geographical excerpts of MEs from the full set. Asperity related 49 MEs yellow circles). Out of asperity 245 MEs (green circles). 79 MEs with PDYAR located on the rim of the studied area (black circles over green ones). The J20 and J29 epicenters are also shown.

Figure 14. Frequency distributions of mb and focal depth for the 295 MEs.

The frequency distributions of the 295 MEs over mb and depth are shown in Figure 14. The deep MEs have lower magnitudes as they are corrected for the source position, and some deep events also have lower Nass, as the deep seismic activity is weak and the ME choice is scarce. Each and every ME, together with all associated templates, follows the same detection and local association processing stages. There are 295 individual detection lists and corresponding XSELs. Each individual XSEL can be compared to the REB before the CR stage, where some event hypotheses can be suppressed. Therefore, the effectiveness of one ME can be assessed at personal and collective levels. Varying the statistical significance threshold for XSEL events The detection lists obtained for thresholds adjusted to the purposes of finding ultra-weak signals contain signals with very low standard SNR values. Sometimes these signals are below the noise level. The SNR threshold is used to reject some of the detections that have appropriate SNRcc but too low-amplitude actual signals. As it works in the gray zone where valid and false detections are in almost equal proportions, its tuning was a mandatory task in the preparations to routine WCC processing on a prototype pipeline. The tuning results are used in this study. Therefore, the SNR filter is applied because it demonstrated an important positive outcome for the rate of associated detections. Since the WCC-detected signals are mainly in the gray zone, the LA process is able to associate only a part of all detections with event hypotheses. These hypotheses are defined by the level of statistical significance based on two principal parameters: the probabilities of association of the corresponding stations with REB events in the region, and the non-random the SNRcc values of the detections. The lower the allowed statistical significance, the larger the number of created XSEL event hypotheses. To understand the effect of the defining parameters in the LA on the generation of XSEL events and their statistical properties, one can introduce a set of thresholds and calculate the corresponding XSELs. The numbers of XSEL events and their distributions over the event weights are then compared to the known bulletins for confirmation or rejection. The REB is the main source of such information. There are several examples of WCC processing at the IDC with the XSEL passing the interactive review stage, which proved that the REB misses from 50% to 100% of REB-ready events. These events must be included in the REB according to the CTBT requirements. All events that could be found in the IMS data have to be found. The REB-ready events that were not found by the IDC but were detected by the WCC are the smallest and most relevant to the CTBT verification regime. When assessing WCC processing, it is important to consider the REB as a reliable source of information for larger events. However, for smaller events it has to be corrected by a factor of 2 to 3. A tentative set of LA parameters meeting the requirements for the weakest events study was first introduced by Kitov [2026b] and tested in the recovery of the seismic process before the Sea of Okhotsk earthquake that occurred on May 24, 2013. There were no REB events for more than one year before this major earthquake. The WCC allowed for finding a sequence of weak earthquakes with an increasing magnitude right before the mainshock. Here, this set is accepted as successful for the purpose of weak seismicity recovery and analysis of the earthquake preparation process. The Kamchatka 2025 earthquakes had a history of seismicity detected by the IDC before the J20 and J29 major events. This allowed for assessing the performance of the set of LA thresholds and estimating their properties through the recurrence curves they produce. The REB and other bulletins cannot find the events that are most important for understanding the earthquake preparation process [Schaff et al., 2025]. The WCC approach focuses on events below the corner magnitude of the recurrence curves, between 2.0 and 3.0-3.4. The signals from these events are not detectable by analysts even on the best array stations with waveforms optimally filtered and beamed to the source hypocenter. Therefore, the set of LA thresholds was established without any reference to the REB or other bulletins. Instead, the thresholds were set from scratch, drawing from previous experience with XSELs. Due to numerous defining parameters in the LA processing, conducting a grid search through all of them with only one basic WCC detection list for the Sea of Okhotsk, containing a few hundred XSEL events at best, would not be feasible. The approach was simplified by the introduction of two LA versions, each with different sets of defining parameters and six cases per version allowing for the fine-tuning of statistical significance. These two versions needed to be sufficiently distinct in a statistical sense to avoid overlap between the cases. The strict version of the LA parameters has to be close to the corner magnitude of the recurrence curve for the region in order to provide a smooth transition from the XSEL to the REB. This version should not generate any XSEL events during quiet seismic periods, similar to the REB. The following LA parameters are used for this task: 1) the number of associated stations is 3. 2) The origin-time tolerance is a case dependent parameter. 3) The minimum total event weight is 2.5. 4) The weight of one of the best stations to be associated with any 3- to 5-station events is 0.855. 5) The minimum sums of SNRcc values for 3-, 4-, and 5-station events are 15.0, 18.5, and 22.0, respectively. 6) The lowest possible value for the minimum SNRcc at one of the top stations from 3) is 5.0. 7) The grid radius is 48 km, defined by 12 steps of 4 km. The event hypotheses beyond a radius of 43.2 km are rejected. This radius can be less than half the distance between neighboring MEs, but it is important to increase statistical significance by reducing the flexibility in location. On the opposite side of the XSEL sensitivity is the weak LA version. The defining parameters were guesstimated using the experience with LA processing in a number of previous studies and from the SNRcc curves in Figures 6 through 8, as well as similar curves for other involved stations. The parameters for the weak LA version are as follows: 1) the number of associated stations is 3. 2) The origin-time tolerance is a case dependent parameter. 3) The minimum total event weight is set at 1.8. 4) The weight of one of the top stations to be associated with any 3- to 5-station events is 0.80. 5) The minimum sums of SNRcc values for 3-, 4-, and 5-station events are 14.0, 17.5, and 21.0, respectively. 6) The lowest possible value for the minimum SNRcc at one of the top stations from 3) is 4.5. 7) The grid radius is 90 km, defined by 15 steps of 6 km. The event hypotheses beyond a radius of 81.0 km are rejected. There is a wide gap in statistical significance between the weak and strict versions. The task at hand is to accurately measure potentially subtle changes in the fluxes of extremely weak signals and events that may not be detected by other methods. An added flexibility to the versions is provided by changing the origin-time tolerance. This parameter directly impacts statistical significance by eliminating random detections in proportion to the width of the association window, which is twice tolerance. For signals related to the sought seismic activity, probability of rejection increases when narrowing the window, but the dispersion of arrival times relative to the average origin time depends on the quality of the signals defined by their position on the SNRcc curves. The valid signals tend to cluster closer together. After a brief test, six different origin-time tolerances, Δt, were introduced to determine their impact on the XSELs from the same detection lists: 5.0, 3.0, 2.0, 1.0, 0.5, and 0.25 seconds. These six tolerances create 12 version/case pairs. They can be aligned in a formal order: v1c1, ..., v1c6, v2c1,...,v2c6, where v1c1 corresponds to the weak LA version with Δt =5.0 s. The shortest Δt allows for practically only actual event hypotheses to be created. For detections randomly distributed in time and in SNRcc value, the probability of 3 or more of them at the best stations having origin times in a 0.5 s time window is extremely low, considering the observed detection rates of 30 to 40 per hour. The downside of having a shorter Δt is the higher likelihood of missing many weaker but valid XSEL event hypotheses, associating weaker signals with poor arrival-time estimates and larger travel-time residuals. The v2c6 pair should not be able to detect too many new XSEL events in addition to the REB. Overall, the XSEL events that match the REB events have to be of a higher quality related to the SNRcc values of the associated signals. The weak LA version with the narrowest origin-time window, v1c6, has to be focused on the new XSEL events with the best quality below the corner magnitude of the recurrence curve. These events are highly statistically significant, but can also include weaker WCC arrivals. The v1c1 pair has the highest resolution. It may contain many valid events and likely some false events, with both types formally matching the EDC. For an XSEL obtained with a given version and case pair, a formal statistical threshold can be defined to distinguishing between valid and false events as determined by the LA algorithm. Then, the strict and weak versions for the same case, Δt, define a specific range of event quality between their corresponding thresholds. The assumption behind introducing two versions and six cases was that the corner magnitude of the recurrence curve of the detected XSEL events depends on these thresholds of statistical significance. The potential influence of source mechanisms, as well as of the noise level at stations around the arrival times of all associated phases, is averaged as for the long-term REB recurrence curve. Formally, for pairs of vicj, we introduce quality boundaries Bij, where i=1,2 represents the version - weak or strict, and j=1,...,6 represents the tolerance case. By design, B1j ≤ B2j and Bij ≤ Bij+1. The quantitative meaning of these boundaries should be revealed by WCC calculations, with a decreasing number of event hypotheses generated as j increases for a given i. When the sought seismic activity from a completely quiet state reaches the lower boundary Bij, the number of weak events grows, while the number of strict events, which must have larger magnitudes and statistical significance, remains constant. The change in the ratio of the event numbers in the weak and strict XSEL versions, B1j/B2j, expresses the change in the seismic process within the range between two version and the same case, Δt. When the activity starts to grow from a quiet state, the B1j/B2j ratio also increases with the growing number of XSEL events above B1j. The activity may not reach its upper boundary, B2j, and then may start to fall back to the initial level. In some cases, the activity may reach the upper boundary and move above it, as happens after larger earthquakes. When the activity penetrates above the upper boundary B2j, the ratio starts to fall because of an increasing number of events above the upper boundary and a constant or decreasing number above the lower boundary. The larger earthquakes generate noise that masks the smaller events. In an aftershock sequence following the largest earthquakes, the boundaries B1j and B2j can be displaced to almost the same magnitude threshold above the corner magnitude of the REB recurrence curve. At that point, the B1j/B2j ratio may reach the lowest level, expressing the magnitude distribution of earthquakes according to the Gutenberg-Richter law. With the decaying post-seismic activity, the ratio grows again as the number of events above B1j has to decrease rapidly and the number above B2j decreases much slower. In conclusion, there are six quality ranges potentially related to magnitude to follow the seismic process before an earthquake. It is assumed that the XSEL events in these ranges span the magnitude range from the corner magnitude down to magnitude 2. The boundaries can be adjusted if they do not fit the assumptions. The recurrence curve for the low-magnitude events below the IDC detection threshold Recurrence curves for various seismic regions are estimated using long-term observations. They represent both the structure of the energy-emitting media, such as the zones of continental faults or subducting plates, and the external energy flux creating stresses in the zone that results in energy release in earthquakes of different sizes. The external energy flux can be considered almost constant, generated by tectonic processes lasting millions of years. Seismic energy release, as part of the Earth’s internal thermal energy dissipation, is a quasi-periodic process at a historical timescale of observations, but changes with the changing geological structures created and destroyed by tectonic forces. The recurrence curves are snapshots of long-term evolution and may change with changing tectonics and geological structures. At the same time, any recurrence curve is a cumulative observation with practically invariant properties, allowing for the prediction of important features such as seismic periodicity, activity, and the largest possible earthquakes. The short-term spatial and magnitude structure of the seismic process is much more variable than the overall recurrence curve for a given region obtained from decades of continuous observations. This is a well-known effect that poses a challenge to predicting large-scale events that endanger populations and infrastructure in various regions, with the Kamchatka Peninsula being one of the most vulnerable seismic hazard regions on Earth. The recurrence curves obtained from the IDC catalog for the studied region have to be depth-dependent because the magnitude estimates are subject to depth corrections. For near-surface events (0-40 km), the recurrence curve is likely the most relevant for the current analysis. The IDC has fixed the J29 mainshock depth to the free surface according to a procedure not to report the free-depth solution for events with poor depth estimates [Coyne et al., 2012]. Approximately 16,000 events out of ~26,500 within the area have depth estimates below 40 km, and almost 15,000 of them are fixed on the surface. Figure 15 demonstrates the recurrence curve for these near-surface events and its extrapolation to the lower magnitude range. The number of events missing from the IDC bulletin increases below the corner magnitude. At array stations, the WCC detector allows us to find many of the missed events, as the detection threshold is 5 to 10 times lower than for the standard beamforming. At 3-C stations, the gain is lower but still contributes to improving the bulletin. The actual WCC gain for arrays is difficult to estimate in standard threshold values, since the WCC detector uses a different time series. The WCC processing is accompanied by estimates of the standard SNR following the IDC rules. The arrival time of the WCC detection is determined by a peak in the SNRcc time series that is calculated using the CC-time series. The peak SNR value is taken in a 5.5 s window following the WCC arrival time and then used as the standard SNR. For a valid IDC signal, such a WCC-based SNR is close to the IDC estimates. When the IDC detection is absent, the SNR related to the WCC detection is taken from a series containing noise, and the peak SNR is a poor representative of the WCC signal amplitude for the magnitude estimates. This is a magnitude estimate representing the peak noise value. When using the RMS amplitude in the detection cross-correlation window as an amplitude approximation, the noise magnitude is smoothed but still represents noise rather than the corresponding WCC signal, which is often buried deep within the noise.

Figure 15. Recurrence curve for the depth range 0 km to 40 km. The approximated recurrence curve is extrapolated to lower magnitudes to show the deficit of event reported by the IDC.

To characterize the set of 12 version/case pairs, it is important to obtain recurrence curves with a corner value of statistical significance pertaining to each pair. The statistical significance of XSEL events cannot be calculated directly from the data, nor can the body-wave magnitude estimates. To present the results obtained for the 12 pairs reasonably, one has to find a relative scale that provides a reliable and clear functional dependence. This scale should serve as the magnitude in a standard recurrence curve. The number of events, N(m), above a specific magnitude larger than the corner one can be estimated by integrating the regression line in Figure 15: f(m) = 2.34‧108×10(-1.2‧m) , (1) where the decay constant b=2.736 is reduced to 1.20 for base 10, and the coefficient 9.0‧107 is corrected for a bin width of 0.2. For m=5.0, the predicted and observed number of events during the entire IDC observation period between January 2001 and December 2025 is 245. When extrapolated, relationship (1) allows for estimating the number of events above any magnitude below the corner value, including those missed in the IDC bulletin for various reasons. For a magnitude interval [m1,m2], the number of events for the whole studied period is as follows: dN = N(m1) - N(m2) = (2.34‧108/2.736)[exp(-2.736*m1) - exp(-2.736*m2)] (2) If we neglect the second term for magnitudes above 7, the total number above m1 is as follows: N(m1) = (2.34‧108/2.736)exp(-2.736*m1) (3) Relationship (3) has to be valid for any part of the recurrence curve above the corner magnitude and follow an exponential distribution. A reliable recurrence curve has to include a sufficient number of events in relatively narrow bins of 0.1 to 0.3 magnitude units to reduce the uncertainty of statistical estimates. This requires a longer observation time, even in a seismically active region like the Kamchatka Peninsula with the subducting Pacific plate. Shorter time intervals may not contain enough data, or the data may be biased. For example, the Kamchatka earthquake on July 29, 2025, generated thousands of aftershocks in a relatively small area. In the days following the mainshock, relatively large and smaller aftershocks can be under-represented in the recurrence curve. The highly elevated ambient seismic noise after large events masks the smaller ones. As a result, the decay constant can be shifted to lower values. This is likely the case under consideration, and the recurrence curve in Figure 15 does not necessary have to be the reference for the XSEL bulletin. Estimation of magnitude scale for the XSEL events The number of events in the 12 version/case pairs forms a sequence. When these pairs were introduced, there was no assumption of a specific magnitude threshold value related to each pair. The only assumption was that the number of events in a given version decreases with the case order number, meaning it decreases with a decreasing origin-time tolerance. The number of events in all cases of the weak version was not always expected to be higher than the numbers in all cases of the strict version. Ideally, the magnitude thresholds for the 12 pairs should form a sequence with a constant increment of Δm. Then, the corresponding numbers of XSEL events would follow an exponential law. To test the actual distribution of the magnitude thresholds in the 12 pairs, one can present the results of the XSEL calculations using the order number of the version/case instead of magnitude and estimate the difference between the ideal exponential curve and the observed curves. The order numbers range from 1 to 6 for the cases of the weak version and from 7 to 12 for the cases of the strict version. This representation is an important constraint on the technique used to estimate the change in the number of low-magnitude events in the range where no REB events are available. The time evolution of energy release from the smallest cracks to the level of IDC-detectable earthquakes during a rapid transition toward the mainshock is measured in narrow magnitude bins. The wave of events progresses through the bins and passes the stages of increase, peak, and possibly a subsequent decrease in the number per unit time as the wave progresses to larger events when approaching the coseismic phase. An example of aligning the version/case pairs by their order numbers is shown in Figure 16. It displays a black-dot curve for the XSEL event hypotheses created during the 10-day period after the J20 earthquake, including the day of July 29 but excluding the last hour with the J29 mainshock. The first pair (v1c1, weak LA version and Δt=5.0 s) has ~9000 XSEL event hypotheses, and the 12th pair (v2c6, strict LA version and Δt=0.25 s) generated ~1600 XSEL hypotheses. The numbers of XSEL events for all pairs are sufficient to generate reliable statistics. This period includes several hundred REB events, which are not enough to create a statistically reliable recurrence curve. The XSELs for these days have hypotheses matching almost all REB events, including those added to the REB by IDC analysts without seed events in the automatic bulletin SEL3. The sequence of the number of XSEL events the in 12 pairs represents a standard recurrence curve by the number of events above some threshold below the REB corner magnitude. Relationship (3) predicts an exponential decrease in this number for a constant step between the 12 magnitude thresholds. The black-dot recurrence curve in Figure 16 shows that the thresholds for the 12 pairs for the case of the 11-day period with active seismicity are distributed with an approximately constant magnitude increment as R2=0.995 indicates. However, the exponential decay constant, b=0.18, is much lower than that for the entire REB recurrence curve in Figure 15. Therefore, it is important to compare the black-dot XSEL curve in Figure 16 with the REB recurrence curve for the same period. Unfortunately, there are only 633 REB events in the aftershock sequence of the J20 earthquake. This is not enough to obtain a reliable recurrence curve. To improve these statistics, 779 REB events for 25 hours of after the J29 earthquake were added. The recurrence curve with 1412 events is shown in Figure 17. In addition, the recurrence curves for three different periods are shown: 1) the 5-day period between July 30 and August 3, 2025; 2) the aftershocks of J29 between July 29 and December 4, 2025; 3) all REB events in the area between January 1, 2001, and December 4, 2025.

Figure 16. Frequency distribution of XSEL event hypotheses as a function of the version/case order number for various time periods: blue dots represent the period between July 30 and August 3, 2025; black circles represent the period between July 20 (day 201 after the major earthquake) and July 29 (day 210); red signs represent two separate intervals between July 6 (187) and July 20 (201), as well as the entire periods.

These four REB recurrence curves were normalized to the corresponding total number of events. The obtained pdf's reveal significant differences in the decay constant between the frequency distribution of magnitudes in the short period between July 10 and July 29 (b=1.04) and that of the entire REB (b=2.62). For the period of the most intensive post-seismic activity between July 30 and August 3, 2025, b=1.91 and R2=0.993. For the aftershock sequence between July 29 and December 4, 2025, b=2.42 and R2=0.996. For the 11-day period characterized by non-peak post-seismic activity, the b-value is much lower than for a shorter period of an extremely high aftershock activity generated by the J29 event as well as for longer periods of observations. In all four curves, the REB events from all depths are included. The XSEL curves, which have a generic x-axis scale in Figure 16, can be converted into the standard mb form as shown in Figure 18. For example, the XSEL curve for the 2025201-2025210 period with a linear scale from 1 to 12 and b=0.18 can be reduced to mb scale by a simple multiplication factor of 0.1282 resulting in an actual b=1.0405. Figure 18 shows an example of such a conversion. Another issue with this conversion is the absolute mb value for the converted XSEL curve, as the methods to obtain the REB and the XSEL are different and the numbers are not directly compatible. The mb start point of the XSEL curve with b=1.04 is adjustable. In Figure 18, the REB and the converted XSEL curve intersect near the corner magnitude by adjusting the XSEL curve’s start point by 2 units of magnitude and the level by an amplitude factor of 2.5. This adjustment is arbitrary, and the XSEL curve can be moved closer to or further from the REB curve. However, the XSEL trend line extrapolated to larger values has to pass though the measured REB values. For the 2025201-2025210 period, the XSEL curve in Figure 18 covers the magnitude range from 2.1 to 3.5. This is a simple guesstimate of potential improvements in the event catalog using the WCC-based approach.

Figure 17. Four pdf calculated for the REB events in various periods: for the entire REB for the region with all depths included; for all aftershocks between the July 29 and December 4, 2025 earthquake (b=2.42, R2=0.996); for 5 days after the J29 (b=1.91, R2=0.993); for the 11-day period between July 20 and July 30, 2025. The XSEL for the 2025211-2025215 period is shown in Figure 18 to demonstrate that the XSEL scale conversions are case-dependent. In order to match the decay constant and the REB level, the following values were used: a magnitude scale factor of 0.05302, a start point shift of 3.0, and an amplitude factor of 1.5. The high level of post-seismic activity in the first days after the J29 makes it difficult to find low-magnitude events, and the XSEL curve covers only a narrow mb interval between 3.05 and 3.65. This is a guesstimate as well.

Figure 18. Scaling of the XSEL recurrence curve in Figure 16 to the REB for the same period of time. There are presented two examples of the order number conversion into magnitudes for the XSELs related to the 12 pairs with two versions of the LA setting and 6 different origin-time tolerances.

There are also different XSEL recurrence curves for the periods of lower seismic activity in Figure 16: 2025187-2025193, 2025193-2025201, and the joint period 2025193-2025201. The earthquakes from the REB for the period from 2025187 to 2025216 are shown in Figure 19. The XSEL curves cannot be directly compared to the REB recurrence curves for the same periods and then converted accordingly. Such a conversion is physically possible, because these XSELs represent actual seismicity below the corner magnitude of the local or global REB curves. Two examples of order-number conversion into magnitudes are presented for the XSELs related to the 12 pairs with two versions of the LA setting and 6 different origin time tolerances. There are also different XSEL recurrence curves for the periods of lower seismic activity in Figure 16: 2025187-2025193, 2025193-2025201, and the joint period 2025193-2025201. The earthquakes from the REB for the period from 2025187 to 2025216 are shown in Figure 19. The XSEL curves cannot be directly compared to the REB recurrence curves for the same periods and then converted accordingly. Such a conversion is physically possible, because these XSELs represent actual seismicity below the corner magnitude of the local or global REB curves. XSEL recurrence curves for the period of the highest seismic activity The Kamchatka earthquake on July 29, 2025, generated a record number of aftershocks per day detected by the IDC. There are 760 events in the REB for July 30. This makes one event per 114 seconds. During the first 6 hours of July 30, one event per 82 s was detected. An enormous number of smaller events were hidden in the noise generated by the very high-magnitude aftershocks, as Figure 19 shows. This effect has a negative impact on the recurrence curve for the whole region. The number of events closer to the corner magnitude is heavily underestimated, with the deficit increasing with a decreasing magnitude. The smaller, but above the corner magnitude, events can be and are found during periods of lower activity, participating in defining the recurrence curve, its slope, and corner magnitude. The latter values have to be biased, however, as the mid-size and larger earthquakes are counted accurately. A larger portion of these low-magnitude events are recovered in the WCC processing. At the same time, the number of new XSEL events, i.e., events not matching arrival(s) associated with any REB event at one or more IMS stations, is relatively low.

Figure 19. Magnitude of the REB events as a function of origin time for the period from July 4 to August 8, 2025. Three events with mb around 5.5 potentially affecting the XSELs are highlighted by red.

One of the peculiarities of the 2025211-2025215 curve in Figure 16 is an abrupt fall in the number of XSEL events in the transition from the weak LA version to the strict one. There is no such effect in the 2025201-2025210 XSEL curve. A more detailed analysis of this phenomenon is presented in Figure 20. In the left panel, the J29 XSELs are presented. The second (2011.375) and fourth (2011.875) 6-hour-long intervals on July 30, with the highest recorded seismic activity, demonstrate not only an abrupt drop in XSEL numbers, but also that these numbers remain constant for all six cases of the same LA version. This suggests that the threshold magnitude of the XSELs for all cases of the same version is the same because the quality of arrivals is so high (large SNR and SNRcc values) that the scattering of origin (or travel) times is less than 0.25 s for at least 3 of them at the stations with the highest weights. The LA creates the same events except may be for a small difference observed as slight changes in the XSELs. The shift in the level between the weak and strict versions indicates a change in the threshold magnitude related to the required event statistical significance defined by several quality parameters, including the minimum weight for a valid XSEL event hypothesis.

Figure 20. Comparison of the 12 pairs’ performance in the periods of very high activity. Upper panel: aftershock sequence of the J29 in the even quarters (6 hours) of the day. Lower panel: Same for the J20 aftershocks. The curves are shown for every second 6-hour interval.

Since July 31, the number of XSEL events has started to decrease in correlation with the case number, eventually reaching a shape similar to those shown in the lower panel of Figure 20, where the XSEL curves are presented for the J20 aftershock sequence. Only during the first two days following the J20 event, a slight step between the weak and strict versions is observed. Then, the curve begins to resemble an exponential trend. Significant gaps in the XSEL numbers are observed between 2011.875 and 2012.375 as well as between 2014.375 and 2014.385. The difference between the curves within the groups separated by these gaps is much smaller. These gaps are interesting for understanding the process of post-seismic activity evolution. The J20 aftershock sequence does not demonstrate such gaps except for the difference between the first (201.375) and the second (201.875) curves, which is likely related to a natural decrease in seismic activity. The curves in Figure 20 for the period between July 20 and August 3 include many XSEL hypotheses matching the REB events. Figure 21 presents the number of matched REB events in the first four 6-hour intervals on July 30, 2025. For comparison, the number of SEL3 events (left panel) and REB events (right panel) are shown. The XSEL is an automatic bulletin that should be compared to the SEL3, but its primary objective is to match the REB. During the period of peak activity, the XSEL does not match all the SEL3 events that were used as seed events for the REB. The REB for the first 6 hours of July 30 lists 278 events in the studied area, with 198 in the SEL3. Several stations, such as PETK, KURK, and MKAR, have phases associated with almost all the REB events, making around 300 arrivals in 6 hours. The WCC detector is tuned to a lower level of seismic activity relevant to the earthquake preparation process and produces approximately 60 to 90 detections per hour. The strict version with a 2.0 s origin-time tolerance generates around 250 XSEL events, and the weak version generates ~400. This is the highest possible event rate for a given WCC configuration. It can be tuned to higher rates, however, in order to study the most active periods. This should be done to count the number of REB-ready low-magnitude events and to correct the overall recurrence curve for the region. In the current WCC version, the XSEL events for July 30, 2025, match a large number of purely REB events that are not based on the automatic seeds. This is an important observation to support the level of statistical significance of the XSEL events not matching any REB event. Retaining the same statistical constraints used in the WCC detection, LA, and Conflict Resolution processes guarantees a reliable link between the results obtained at different levels of seismic activity.

Figure 21. The number of XSEL events matching the SEL3 (upper panel) and the number of REB (lower panel) events for the same periods. The corresponding REB and SEL3 numbers are shown by red lines.

Brussels. Human Zoo

2026-05-08T17:50:09.554+02:00

Nevada Test Site seismicity from January 27 to February 2, 2026 recovered using waveform cross correlation and IMS data

2026-05-08T17:29:00.001+02:00

The week from jan 27 to Feb 2, 2026 is charaterized by a slighly higher seismicity than the previous 7 days. There were 36 events detected by waveform cross correlation (WCC) applied to seismic data of the International Monitoring System. Figur below shows their locations realtive to the NTS geographical center and 27 master events selected from the Reviwed Event Bulletin of the International Data Centre.

There is also an extended version of the WCC with an effective ambient noise suppression based on addition of stochastic noise. It takes more time to calculate and the result is coming soon. The extended method is focused on the central part of the NTS where the tests were conducted.

Figure. Locations of master events (red) and the events found by cross correlation (green). The NST center is shown by black circle.

Лихая мода, наш тиран, //Недуг новейших россиян

2026-05-08T16:14:00.002+02:00

Читайте "Евгений Онегин". Это и про нас.

Nevada Test Site seismicity from January 22 to January 26, 2026 recovered using waveform cross correlation

2026-05-07T19:18:00.001+02:00

This post follows teh same structure as the previous few on the Nevada Test Site seismic activity. Five days are presented. Figure below shows locations of 25 events found by waveform cross correlation. Catalog is below.

Figure. Locations of master events (red) and the events found by cross correlation (yellow). The NST center is shown by black circle.

Nevada Test Site seismicity on January 21, 2026 recovered using waveform cross correlation

2026-05-02T18:24:00.004+02:00

Following my previous posts on the recovery of seismic events at the Nevada Test Site on June 22, 2020 and around, it's to continue to trace the evolution of seismic regime at the NTS. Started with January 20, 2026 and we continue here with Jan 21. Figure below shows the locations of 27 master events and 9 events found by cross correlation. The corresponding bulletin (XSEL) is given below. (For details please see the previous post)

Figure. Locations of master events (red) and the events found by cross correlation (yellow). The NST center is shown by black circle.

# MASTER hh:mm:ss ot_stdev Lat Lon Depth Mb mb_stdev ndef NEW ORID SeisReg Ndef(SEL)

1 24060380 3:59: 30.28 1.47 36.761 -117.789 0.0 2.19 0.89 3 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 1.32 166.12 4: 0: 2.25 -0.626 32.67 25.15 5.4 2.8 -99.0 -3.121 0.110 10.00 3 -99.00

ELK 3.94 -152.66 4: 0: 41.80 1.969 69.32 62.30 3.9 2.2 -99.0 -1.700 0.014 9.00 2 -99.00

PDAR 8.26 230.76 4: 1: 38.33 -1.477 129.61 124.26 3.3 2.5 -99.0 -0.980 0.040 9.00 2 -99.00

2 10374180 4:15: 14.56 0.06 37.654 -115.255 0.0 2.02 0.76 3 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 2.60 106.97 4:15: 56.09 0.061 41.53 42.61 5.9 3.1 -99.0 -1.915 0.104 10.00 2 -99.00

ELK 3.04 -179.76 4:16: 4.00 0.021 49.50 48.86 11.5 3.1 -99.0 -1.713 0.086 9.00 2 -99.00

PDAR 6.62 221.99 4:16: 56.24 -0.082 101.89 100.59 4.8 2.8 -99.0 -0.222 0.042 9.00 4 -99.00

3 10374180 6:18: 22.81 1.22 37.890 -115.855 0.0 2.17 0.72 4 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 2.60 104.89 6:18: 53.95 -0.070 31.30 42.61 4.6 3.3 -99.0 -2.173 0.061 10.00 2 -99.00

ELK 3.04 -170.33 6:19: 10.43 0.734 46.79 48.86 3.4 2.8 -99.0 -1.377 0.034 9.00 1 -99.00

PDAR 6.62 221.99 6:20: 4.32 -1.896 103.63 100.59 3.8 3.3 -99.0 -0.713 0.079 9.00 3 -99.00

ILAR 32.94 129.85 6:24: 55.35 1.355 391.24 394.79 3.8 4.4 -99.0 -0.276 0.187 8.00 2 -99.00

4 24060380 8:28: 36.06 0.87 37.200 -117.294 0.0 4.14 0.29 5 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 1.32 146.73 8:29: 4.24 0.332 27.90 25.15 4.6 5.4 -99.0 -3.637 0.085 10.00 3 -99.00

ANMO 9.28 287.52 8:30: 50.70 0.224 134.45 137.52 3.6 4.6 -99.0 0.452 0.570 8.50 1 -99.00

ULM 20.27 238.38 8:33: 13.74 1.324 276.30 277.57 3.4 3.2 -99.0 -0.126 0.198 7.50 2 -99.00

YKA 25.34 185.53 8:34: 3.02 -1.096 328.09 327.80 3.5 3.3 -99.0 -0.323 0.075 8.00 4 -99.00

BVAR 89.83 6.34 8:41: 37.19 -0.840 781.96 781.67 4.3 6.9 -99.0 0.074 0.125 7.00 4 -99.00

5 11690187 8:31: 19.21 0.70 37.454 -117.159 0.0 3.88 0.46 5 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 1.53 136.87 8:31: 42.45 -0.686 23.98 27.82 6.6 292.5 -99.0 -2.295 0.095 10.00 3 -99.00

YBH 6.23 135.55 8:32: 52.81 1.266 92.12 94.62 3.5 3.4 -99.0 -0.994 0.292 8.30 3 -99.00

PDAR 8.15 228.98 8:33: 18.52 0.194 119.01 122.45 4.0 15.5 -99.0 -0.626 0.108 9.00 3 -99.00

YKA 25.43 184.93 8:36: 45.18 -0.411 326.31 329.17 3.8 4.8 -99.0 -0.874 0.158 8.00 3 -99.00

USRK 77.64 49.90 8:43: 15.41 -0.440 716.69 717.67 3.5 6.5 -99.0 0.195 0.178 5.50 4 -99.00

6 7564944 14: 4: 8.07 0.06 38.729 -116.120 0.0 1.27 0.85 3 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 1.49 79.36 14: 4: 40.70 0.043 32.65 28.03 6.7 6.8 -99.0 -2.572 0.060 10.00 2 -99.00

ELK 2.64 -161.14 14: 4: 48.12 -0.082 40.08 49.80 3.8 2.8 -99.0 -1.149 0.009 9.00 1 -99.00

PDAR 6.89 231.57 14: 6: 4.91 0.050 116.77 125.28 3.3 3.5 -99.0 -0.531 0.056 9.00 3 -99.00

7 19344894 22:38: 38.44 1.33 36.656 -117.175 0.0 3.93 0.17 5 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 2.10 152.89 22:39: 10.74 -0.896 33.30 35.58 5.0 6.7 -99.0 -3.009 0.105 10.00 3 -99.00

YBH 6.68 140.87 22:40: 21.77 1.982 101.14 101.59 3.9 2.2 -99.0 -0.398 0.189 8.30 1 -99.00

ULM 20.83 236.67 22:43: 18.10 1.062 278.60 282.32 3.8 3.0 -99.0 -0.429 0.208 7.50 1 -99.00

YKA 26.16 185.29 22:44: 12.81 -0.647 334.93 337.18 3.2 3.5 -99.0 -0.824 0.063 8.00 3 -99.00

KURK 92.18 12.87 22:51: 46.49 -1.609 789.64 790.50 3.6 3.5 -99.0 -0.523 0.089 7.00 5 -99.00

8 7564944 23: 0: 48.67 0.07 37.976 -116.613 0.0 1.18 0.87 3 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 1.49 108.31 23: 1: 15.04 0.024 26.43 28.03 5.1 5.0 -99.0 -2.487 0.085 10.00 4 -99.00

ELK 2.64 -158.57 23: 1: 44.70 0.066 55.94 49.80 3.6 16.2 -99.0 -1.667 0.034 9.00 5 -99.00

PDAR 6.89 231.57 23: 2: 59.35 -0.099 130.76 125.28 3.8 7.5 -99.0 -0.379 0.070 9.00 3 -99.00

9 24060380 23:55: 22.32 1.04 37.442 -117.985 0.0 3.70 0.39 6 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 1.32 165.62 23:55: 41.27 -0.421 19.48 25.15 4.5 3.2 -99.0 -3.256 0.017 10.00 3 -99.00

ELK 3.94 -146.30 23:56: 24.78 0.270 62.15 62.30 5.5 2.5 -99.0 -1.897 0.024 9.00 3 -99.00

YKA 25.34 185.53 0: 0: 48.78 0.364 326.17 327.80 3.8 5.7 -99.0 -0.101 0.074 8.00 3 -99.00

ILAR 32.57 133.47 0: 1: 52.88 0.314 390.28 392.67 3.0 6.3 -99.0 -0.140 0.199 8.00 2 -99.00

USRK 77.39 50.02 0: 7: 19.01 1.455 715.29 717.36 3.3 2.9 -99.0 0.161 0.213 5.50 2 -99.00

ZALV 87.14 17.72 0: 8: 7.13 -1.967 766.83 768.12 3.3 4.6 -99.0 -0.119 0.135 6.50 5 -99.00

Nevada Test Site seismicity on January 20, 2026 recovered using waveform cross correlation

2026-05-01T17:02:17.846+02:00

Following my previous post on the recovery of seismic events at the Nevada Test Site on June 22, 2020 and around, it's to continue to trace the evolution of seismic regime at the NTS. Start with January 20, 2026 and then continue at a daily basis. Figure below shows the locations of 27 master events and the events found ny cross correlation. The corresponding bulletin (XSEL) is given below. (For details please see the previous post)

Figure. Locations of master events (red) and the events found by cross correlation (yellow). The NST center is shown by black circle.

Bulletin.

# MASTER hh:mm:ss ot_stdev Lat Lon Depth Mb mb_stdev ndef NEW ORID SeisReg Ndef(SEL)

1 21946971 1:56: 35.54 0.02 36.949 -114.774 0.0 3.16 0.27 3 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 2.66 116.83 1:57: 27.29 0.025 51.67 44.12 8.9 596.1 -99.0 -0.226 0.039 10.00 2 -99.00

ELK 3.61 174.40 1:57: 35.36 -0.014 59.74 57.02 9.4 2.9 -99.0 0.157 0.062 9.00 2 -99.00

PDAR 7.18 220.33 1:58: 23.32 -0.011 107.71 109.35 8.4 3.3 -99.0 0.445 0.151 9.00 3 -99.00

2 19344894 2: 7: 26.32 1.64 35.978 -117.387 0.0 3.95 0.57 5 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 2.10 163.14 2: 8: 11.31 1.971 42.81 35.58 5.5 3.1 -99.0 -3.247 0.029 10.00 2 -99.00

PDAR 8.81 226.64 2: 9: 38.98 -1.904 134.70 131.12 3.8 3.3 -99.0 -1.477 0.072 9.00 2 -99.00

ANMO 9.10 282.50 2: 9: 41.12 1.886 132.78 134.44 3.7 2.2 -99.0 -0.423 0.139 8.50 2 -99.00

ZALV 87.95 17.84 2:20: 18.38 -1.070 773.22 771.07 3.2 3.7 -99.0 -0.093 0.155 6.50 3 -99.00

BVAR 90.66 6.35 2:20: 31.73 -1.079 786.56 784.47 3.2 3.0 -99.0 -0.092 0.139 7.00 2 -99.00

3 21946971 2:28: 5.08 1.12 37.244 -115.056 0.0 2.19 0.77 4 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 2.66 113.80 2:28: 52.38 0.630 46.63 44.12 5.6 7.6 -99.0 -1.648 0.090 10.00 2 -99.00

ELK 3.61 177.62 2:28: 58.81 -1.665 55.48 57.02 6.9 3.3 -99.0 -1.540 0.053 9.00 3 -99.00

PDAR 7.18 220.33 2:29: 52.69 1.314 106.13 109.35 3.1 2.2 -99.0 -0.309 0.054 9.00 3 -99.00

TXAR 12.50 311.49 2:31: 4.22 -0.308 179.43 181.06 3.8 3.9 -99.0 0.133 0.283 8.50 2 -99.00

4 15999493 8:20: 34.53 0.11 36.175 -116.262 0.0 2.95 0.44 4 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 3.30 143.60 8:21: 18.70 -0.003 44.15 52.36 7.3 97.9 -99.0 -1.562 0.072 10.00 2 -99.00

ELK 4.92 184.90 8:21: 44.90 -0.179 70.66 74.67 9.7 9.5 -99.0 -1.219 0.168 9.00 2 -99.00

PDAR 8.43 216.77 8:22: 39.78 0.125 125.10 125.77 6.4 4.8 -99.0 -0.939 0.097 9.00 3 -99.00

TXAR 12.07 305.55 8:23: 36.63 0.063 182.08 175.75 3.6 9.3 -99.0 -0.359 0.140 8.50 3 -99.00

5 24060380 14:42: 12.79 0.69 37.090 -118.120 0.0 3.27 0.79 5 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 1.32 173.77 14:42: 37.84 -0.552 25.67 25.15 5.5 3.1 -99.0 -3.356 0.095 10.00 4 -99.00

ELK 3.94 -147.56 14:43: 20.68 0.810 67.05 62.30 3.3 2.5 -99.0 -2.160 0.017 9.00 3 -99.00

YBH 5.99 136.76 14:43: 40.62 0.732 86.97 89.01 3.6 3.3 -99.0 -0.102 0.497 8.30 1 -99.00

YKA 25.34 185.53 14:47: 41.22 -0.937 329.45 327.80 3.7 4.4 -99.0 -0.298 0.110 8.00 3 -99.00

USRK 77.39 50.02 14:54: 8.99 -0.152 716.29 717.36 3.2 3.0 -99.0 0.139 0.274 5.50 2 -99.00

6 24060380 18:50: 11.13 1.02 37.507 -117.570 0.0 3.76 0.74 6 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 1.32 147.68 18:50: 30.25 -1.508 20.78 25.15 8.9 34.6 -99.0 -2.546 0.156 10.00 3 -99.00

ELK 3.94 -150.07 18:51: 11.61 1.219 59.09 62.30 4.5 3.1 -99.0 -1.487 0.098 9.00 1 -99.00

YBH 5.99 136.76 18:51: 38.97 1.345 86.27 89.01 3.3 5.1 -99.0 -0.000 0.391 8.30 1 -99.00

ANMO 9.28 287.52 18:52: 29.07 -0.322 138.26 137.52 3.3 3.6 -99.0 0.679 0.484 8.50 1 -99.00

TXAR 14.04 307.79 18:53: 34.98 -0.015 203.79 202.18 3.5 3.4 -99.0 0.034 0.090 8.50 4 -99.00

ULM 20.27 238.38 18:54: 45.85 -0.792 275.49 277.57 3.2 4.1 -99.0 0.019 0.313 7.50 2 -99.00

7 14628102 19:23: 13.12 0.07 36.476 -115.335 0.0 -1.39 0.50 3 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 2.49 128.75 19:24: 3.55 0.074 50.46 41.67 6.6 16.2 -99.0 -1.947 0.064 10.00 2 -99.00

ELK 4.04 188.61 19:24: 18.38 0.018 65.35 62.30 5.6 3.2 -99.0 -1.475 0.046 9.00 2 -99.00

PDAR 7.80 221.58 19:25: 8.15 -0.091 115.22 116.42 3.1 4.4 -99.0 -0.737 0.057 9.00 2 -99.00

8 24060380 19:24: 30.41 1.15 37.200 -117.598 0.0 3.72 0.53 5 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 1.32 155.38 19:24: 57.60 1.329 25.73 25.15 8.0 8.0 -99.0 -2.930 0.133 10.00 2 -99.00

ELK 3.94 -151.90 19:25: 32.87 -0.550 62.97 62.30 4.4 3.0 -99.0 -1.977 0.060 9.00 2 -99.00

YBH 5.99 136.76 19:25: 57.75 -1.870 89.28 89.01 3.3 3.9 -99.0 0.013 0.359 8.30 1 -99.00

ANMO 9.28 287.52 19:26: 48.34 0.174 137.70 137.52 3.3 2.8 -99.0 0.111 0.207 8.50 3 -99.00

PETK 58.33 69.01 19:34: 28.78 1.009 597.36 597.25 3.6 3.1 -99.0 0.230 0.183 7.00 2 -99.00

9 10374180 23:53: 1.92 0.01 37.654 -114.509 0.0 2.03 0.69 3 NEW 0 3

sta delta azim hh:mm:ss res,s travel time master TT SNRcc SNR SNRIDC dRM CC sta_weight filter tREBres

NVAR 2.60 103.38 23:53: 51.68 0.013 49.65 42.61 4.9 5.7 -99.0 -2.024 0.081 10.00 2 -99.00

ELK 3.04 169.40 23:53: 52.18 0.006 50.20 48.86 4.0 2.1 -99.0 -1.451 0.019 9.00 2 -99.00

PDAR 6.62 221.99 23:54: 38.98 -0.020 97.08 100.59 3.4 3.1 -99.0 -0.353 0.070 9.00 4 -99.00

Seismic noise suppression: array stations, waveform cross-correlation, and noise stochastization

2026-05-01T11:57:00.004+02:00

Full paper available on arXiv.org

([2604.21939] Seismic noise suppression: array stations, waveform cross-correlation, and noise stochastization)

Abstarct

Seismic noise with an amplitude higher than that of the sought signal is a challenge for detection. Several techniques have been developed to suppress the ambient noise and to reduce the detection threshold in order to find signals with the lowest possible amplitudes produced by events with the magnitudes significant for scientific research and technical applications. Seismic arrays were introduced in the late 1950s as a method for improving underground test monitoring, potentially reducing detection thresholds by fivefold or more by exploiting destructive interference effects of a quasi-random noise. The beamforming method is the backbone of data processing at the International Data Centre (IDC) with more than 30 array stations of the International Monitoring System (IMS) installed around the globe. The matched filter method allows for the suppression of noise incoherent to the sought signal. It employs waveform cross-correlation (WCC) with templates based on actual and simulated seismic signals to improve the signal-to-noise ratio estimates for similar signals. The performance of this method is significantly enhanced when it is applied to a seismic array. A novel technique combined with WCC, is the noise stochastization or the addition of scaled random noise to the actual data before calculating the cross-correlation coefficient. The stochastic component can easily be generated by a computer program. Alternatively, a regular signal propagating at an angle of around 90° to the plane of the sought signal can play a role of stochastic component at array stations. We demonstrate the separate and joint effects of these noise reduction techniques on the WCC performance, when applied to filtered data from selected IMS arrays and various waveform templates of historical events available at the IDC.

Key words: waveform cross correlation, seismic array, noise stochastization, filtering, International Monitoring System, International Data Centre

An example of regional seismicity recovery on June 22, 2020, using waveform cross-correlation. Nevada Test Site.

2026-04-30T17:37:00.008+02:00

Abstract

The monitoring regime for the Comprehensive Nuclear-Test-Ban Treaty includes seismic technologies based on data from the International Monitoring System (IMS), which is processed by the International Data Centre (IDC). High standards for data quality and the processing are mandatory to achieving the goals of the Treaty. The IDC bulletins and catalogues include only event hypotheses matching the established levels of statistical significance and reliability. The States Parties to the CTBT are flexible in applying the own methods of monitoring, focusing on specific regions and source types. The research community dealing with the scientific and technical issues related to the monitoring regime proposes, develops, and tests various techniques and methods to improve the resolution and sensitivity of the IMS network and to enhance processing. The waveform cross-correlation method (WCC) reduces the detection threshold and improves the accuracy of the principal parameters estimation. When applied to seismic activity at the Nevada Test Site, the WCC-based methods allow to find dozens of events not detected by the IDC. The monitoring regime of the NTS can be significantly improved by using the approach developed in this study.

Key words: CTBT, IMS, IDC, Nevada test site, waveform cross correlation

Introduction

The seismic network of the International Monitoring System (IMS) of the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) will include 50 primary and 120 auxiliary stations [CTBT, 1996]. As the CTBT has not yet entered into force, the seismic network has not been complete with a few more stations to be deployed and/or certified. Many State Parties, including the USA and China, have not yet ratified the CTBT, but they provide and process data of all technologies used by the CTBTO. The early ratification of the CTBT by Russia was revoked in order to return to equal position with the other two countries having the largest nuclear arsenals. The Treaty cannot come into effect without a few countries that have not signed it. Therefore, the Preliminary Technical Secretariat (PTS) of the CTBTO runs all the IMS networks and data processing in preparation mode. There is no obligation on any country to submit data to the International Data Centre (IDC) located in Vienna, Austria, before the CTBT comes into force. The same is applicable to onsite inspections - a powerful procedure of the CTBT monitoring regime.

Distribution of the IMS primary seismic stations over the globe was designed to provide a quasi-even distribution of detection threshold without any specific place to be monitored with a much higher sensitivity and resolution. By definition, seismic signals at primary stations define the statistical significance of the created event hypotheses with different inputs from arrays and three-component (3-C) stations [Coyne et al., 2012]. All statistical properties of a hypothesis are based on the measurements of travel time, slowness and azimuth of the detected signals. The residuals of these three parameters have to be within well calibrated tolerances that are specific to stations and seismic phases. The IMS auxiliary stations provide valuable information to improve the accuracy of the defining source parameters: hypocenter, origin time, and magnitudes, but they do not affect the event hypothesis statistics directly.

Larger seismic events tell for themselves and are easy to detect and to interpret. The smallest natural events and concentrated underground explosion has very specific features shaping the IMS network [Evernden et al., 1986]. All small events are very similar in terms of source function. An event with the body wave magnitude, m_b, of, say, 2.85 would have the size of emitting source or elastic radius of tens of meters. A 1 kt explosion in hard rock like granite or anhydrite has an elastic radius of approximately 100-120m, and the scaling law suggests that the radius is proportional to the cube root of the explosion yield. The source size of 50 m makes it effectively a point source as the length of generated P-waves observed at regional stations is of approximately 1 km (e.g., wavelength of the P_n-wave with apparent velocity of 8 km/s at 8 Hz). Moreover, the source duration is also a few thousandths of a second as the propagation velocity of the shock wave is more than 5 km/s and for the length of 50 m the propagation time is <0.01 s. The source function of any seismic event with magnitude of ~3.0 is a point source with δ-function as an emitted signal. There is no method to distinguish natural sources like earthquakes and underground explosions for such small magnitudes. The IDC has a rule not to apply the event screening procedure to the events with m_b below 3.5 as the generations of seismologists recommended [Coyne et al., 2012]. Any responsible statement of the explosion relevant features for an m_b 2.85 event has to be scientifically justified. An extensive statistics of successful identification/discrimination/ screening based on such features is a mandatory prerequisite for the monitoring community.

In the paper devoted to the Lop Nor test site during the period around the 22nd of June, 2020, we have processed the IMS data using waveform cross-correlation (WCC) to assess regional seismicity [Kitov, 2026a]. The WCC-based methods have been growing in number and capability since the early 2000s [Schaff, Richards, 2004; Gibbons, Ringdal, 2004, 2006; Gibbons et al., 2007, 2011]. At the IDC, WCC processing has been tested and introduced into a prototype pipeline since 2010s [Bobrov et al., 2014]. It showed excellent results in finding low-magnitude events missed in standard IDC processing. There were several exercises when experienced IDC analysts reviewed the cross correlation bulletin (XSEL) obtained for specific regions and time periods [Bobrov et al., 2014; Bobrov et al., 2016a, 2017]. The events created in these interactive reviews fully matched the IDC Event Definition Criteria [Coyne et al., 2012]. Since the Reviewed Event Bulletin (REB), the IDC final internal bulletin, cannot be changed after the interactive review is finished, these new events were added to a different database account and are available for further analysis. The share of these new REB-ready events was from 50% to 80% of that in the REB. This means that the IDC misses around 100% of low-magnitude events most relevant to the CTBT monitoring regime.

The WCC-based methods are also very useful for the CTBT monitoring regime as they allow for much more accurate location of explosions [Selby, 2010; Gibbons et al., 2017]. The smallest and weakest aftershocks of the announced DPRK underground tests are found at near-regional [Adushkin et al., 2017; Kitov, Sanina, 2022], regional, and teleseismic distances [Adushkin et al., 2025b]. The most recent improvements in the WCC capability to detect the weakest signals are based on the extensive use of arrays (e.g. IMS stations and "Mikhnevo" array (MHVAR) of the Institute of Geosphere Dynamics (IDG), Russian Academy of Sciences [Kitov et al., 2025]) and noise suppression by various techniques from mixing the processed waveforms with regular signals [Kitov, Sanina, 2025a; Kitov 2026d] to adding stochastic noise in order to induce destructive interference with the noise component coherent to the sought signal [Adushkin et al., 2025a; Kitov, 2026d]. Application of these new techniques to the IMS seismic data allows for detailed study of the physical processes before and after catastrophic earthquakes [Kitov, 2026b] and likely earthquake prediction [Schaff et al., 2025; Kitov, 2026c]. One can see the evolution of seismicity in time and space at the magnitude level not visible to standard methods.

For historic reasons, the NTS is characterized by the lowest detection threshold at the IDC with three IMS primary seismic arrays NVAR, PDAR and TXAR and a few auxiliary 3-C (e.g., ELK, ANMO, NEW, YBH) stations at regional distances. The detection threshold for the events within and close to the NTS can be even further reduced at the IDC using the new data processing techniques based on waveform cross correlation applied to IMS data [Bobrov et al., 2014, 2016ab, 2017; Adushkin et al., 2025a; Kitov et al., 2026; Kitov, 2026abc]. An example of such an analysis was presented for the Lop Nor in [Kitov, 2026a]. It's interesting to apply the same procedure to the NTS using the same approach to the IMS data for the same period as for Lop Nor. The low-magnitude seismic events can be generated by natural sources or by underground explosions, and not only by chemical ones.

Data and method

NTS seismicity, as per the IDC

The NTS is not characterized by a large magnitude seismic activity with smaller earthquakes detected by local, regional and global networks. There is a seismically active zone to the west of the NTS as Figure 1 shows. The approximate center of the NTS is presented by a red circle and has coordinates 37.15°N, 116.05°W. The size of the test site is of dozens of miles in each direction from the center. The IDC bulletin includes 58 events located within the rectangular area 114.0°W-117.2°W, 35.5°N-38.6°N and all of them are low-magnitude with the largest m_b(IDC) of 4.42 (Appendix 1). The number of associated phases, Nass (see Appendix 1), includes regional phases (P_g, P_n) at the same stations. Therefore, the number of associated stations is not large for all NTS earthquakes. Figure 2 presents the number of associated stations for all 389 events in Figure 1. At the closest stations NVAR, ELK, and PDAR, Nass is larger than the number of REB events. The most sensitive to the events within the NST are: near-regional (<4.5°) stations NVAR and ELK, regional stations PDAR, ANMO, TXAR, YKA, ILAR, YBH, ULM, NEW, teleseismic stations BVAR, KURK, and PETK. Array station PDYAR has been operating since 2023 and it is likely to be one of the most sensitive teleseismic stations to the NTS as associated with 20 from 23 REB events.

There were many underground explosions conducted within the NTS in the past. They are recorded by the IMS legacy stations with some waveforms available from the DARPA database. We do not use them in this study as the waveforms from smallest earthquakes would not be much different from that of the same-size explosions. For a point source with a δ-function as a signal shape, the solution does not depend on the nature as it's the Green's function of the event-station propagation path. The dependence of the signal amplitude on the azimuth for low-magnitude events is less important than the ambient noise at seismic stations. However, there is always a possibility to include historic records in the WCC processing as templates for a number of stations.

Figure 1. Seismic events from the REB from January 18, 2001 to October 31, 2025 for the area within and around the NTS. The REB events within the area confined by lines 114.0°W-117.2°W, 35.5°N-38.6°N are light blue circles, master events: red circles - for routine WCC processing, violet circles - for WCC processing with stochastic noise added.

Figure 2. Number of associated phases (P_g, P_n) at IMS stations for 389 REB events.

Master Events

Routine WCC processing is essentially the same as introduced in [Bobrov et al., 2014] for the first processing exercises followed by an interactive review conducted by experienced IDC analysts. It is based on the events from the IDC database called "master events" (ME) with their respective P-wave templates at all associated stations. (For regional stations, the P-wave templates can include the secondary phases.) Therefore, the MEs used in a given place are subject to replacement if better REB events appear in the growing IDC database. The ME selection process for various seismic regions depends on the availability of REB sources. Within the areas with an intensive seismicity and high REB event density, the best MEs have to detect the largest portion of the neighboring REB events. Corresponding calculations are conducted for all new REB events and the old MEs are replaced if the new ones are more efficient. For the areas with low event density and low quality of templates as defined by their signal-to-noise ratio (SNR), the best ME is selected by its weight equal to the sum of probabilities of the associated stations to participate in events in the area. For the places where only one of two events are available, they can be used as the ME(s) by default. All new unique events, e.g. the DPRK underground tests, are used as MEs when found and promoted to the REB. Finally, in the areas where natural and man-made events are absent in the REB, semi-synthetic and synthetic MEs are used [Bobrov et al., 2016b].

Seismic activity is high to the west of the studied NTS area. But these earthquakes are not representative for the NTS and are not used as MEs. There are 58 REB events more relevant to the task of NTS detailed monitoring shown in Figure 1. They are split in three categories. Seven violet circles present the events closest to the NTS centre and used as MEs for the WCC processing with stochastic noise. Twenty events shown by red circles are used for routine WCC processing and are at larger distances from the NTS central point. The other 31 REB events are shown by light blue circles and can be used as MEs when needed. They are located close to the events from the second category but have lower statistical significance and number of associated phases. The dark blue circles are the REB events not representing the NTS.

WCC detection

There are two approaches to WCC processing in this study. For the 20 light blue MEs in Figure 1, routine processing is used with the only enhancement by the "shaken, not stirred" technique applied to the traces of the cross correlation coefficient (CC) at array stations. The CC values can be shifted in the discrete time series relative to their real positions in time. Random shifts of individual CC time series by one or two counts before averaging over all channels. When applied a hundred times, the simultaneous shifts of all channels can create a configuration closer to the actual one and increases the signal-to-noise ratio (SNRcc) for the matched filter detector [Turin, 1960].

As an enhancement to the routine processing, a newly developed technique for ambient noise suppression using a stochastic time series [Adushkin et al., 2025a; Kitov et al., 2026; Kitov, 2026d] is able to reduce the detection threshold by up to a factor of 2 or more, depending on whether there is a coherent component in the ambient noise that matches the template. This method is thoroughly used in many wave processes to suppress noise. Its application to seismic data at array stations, which are phased antennas, is especially effective when used before the WCC-based detector is applied.

The WCC detector uses the CC time series calculated for the raw data filtered in five overlapping frequency bands between 0.5 Hz and 8 Hz. As the sough signal length above the noise is not known in advance, the WCC window width can vary from the shortest teleseismic signals of 3 s to 4 s to the longest near-regional signals of 120 s or more, which include all regional phases from P_g to R_g. Such wide windows make the CC estimates to be very sensitive to the difference in the apparent velocities of individual regular phases. The change in the sought event-station distance relative to that of the ME-station value effectively destroys the similarity of shapes as the secondary phases arrive earlier or later. For array stations, the change in event-station azimuth for even identical signals also destroys signal coherency resulting in lower CC values and non-detection.

For an array station, the individual CC time series are averaged over all channels without any time shift since the sought signal has to arrive at all sensors at the same relative times as in the multichannel template. The averaged CC time series is similar to the averaged trace created in the beamforming [Schweitzer et al., 2012]. The same ratio of short-term-average (STA) and long-term-average (LTA) can be used for detection. For an array beam, a detection is declared when the STA/LTA ratio reaches the predefined threshold. The maximum SNR of the detected signal and its peak amplitude are sought in a relatively short interval after the detection time. When the threshold in reached, the LTA is "frozen" not to allow the signal energy to affect the STA/LTA estimates.

The WCC detection is different as the sought and template signals have to be fully synchronized for the SNRcc has to reach its peak. The CC may start to rise when the tail of the template enters the initial part of the sough signal, however. These signals might be coherent throughout the whole length of the template. For the 120-second-long template and sought signals, the CC and thus SNRcc may start to grow tens of seconds before the signals finally coincide. At the same time, the detection threshold defined for the SNRcc has to be lower than the peak SNRcc value not to allow the increasing CC to be used in the LTA estimation. As a result, the detection window has to be at least as long as the template. The time of the peak SNRcc is considered as the arrival time. This is important station NVAR is at a distance of 3° to 4° from the NTS and has to detect long signals consisting of secondary seismic phases. For teleseismic distances, the sought signals are very short for low-magnitude events and the peak SNRcc is close to the first point where it reaches the detection threshold. The peak SNRcc value for a given time count is selected from the full set of filters and template lengths similar to the procedure in the beamforming detection [Coyne et al., 2012].

The detection thresholds have to be tuned to the expected signals and variations in the noise conditions. Station tuning is a mandatory task for the IMS/IDC optimal performance [Saragiotis, Kitov, 2020]. By varying the SNRcc threshold, one can obtain the desired rate of detections. Figure 3 presents pdf distributions of the SNRcc values for 6 hours on June 21, 2020, at three stations: NVAR - near regional, PDAR - regional, YKA - teleseismic. Two MEs (one for YKA) are shown for comparison of their performance. The detection threshold is set at two levels - low and high. For the high level no detection is possible since the SNRcc value for low-amplitude signals can never reach SNRcc=100. The low level is used for routine WCC processing and is tuned to generate from 30 to 80 detections per hour. The detection rate of approximately 1 per minute is an important constraint for the following phase association process with the travel time tolerance of 2 seconds. The difference between the low and high case is the presence of detections with SNRcc above 3.1-3.5 in the low detection threshold curves. These are the detections likely related to the sought signals from the NTS. For the high threshold case, there is a weak kink in the curves around 3.5. The absence of detections does not mean the absence of relevant signals, but the effect of long precursor in the CC trace described above suppresses the peak SNRcc values. At stations NVAR and YKA there are wide SNRcc peaks between 3.2 and 4.0. A part of sought signals from these peaks then associated with the event hypotheses. There is no such a peak at PDAR, but the pdf starts to deviate from the exponential trend approximately at SNRcc of 3.0-3.2 producing potentially valid signals.

The curves in Figure 3 demonstrate the features not observed in similar curves for standard SNR at the same stations. The SNRcc curves include only signals from the target area around the corresponding ME. For a fully quiet day in this target zone, the curves should have no signals and follow exponential trend. The SNR curves always have all sorts of local, regional and teleseismic signals from a multitude of physical sources. There are no really quiet days for a standard energy detector. This is one of the reasons why the SNRcc thresholds are lower than the SNR ones. The detection rate cannot be too high in order not to create to many false event hypotheses with randomly associated phases.

Figure 3. pdf distributions of SNRcc values at three stations: NVAR - near regional, PDAR - regional, YKA - teleseismic.

The matched filter is the optimal detector maximizing the SNRcc when the noise is stochastic and additive. For seismology, the ambient noise is almost always additive if to neglect resonance, liquefaction, and strong motions. But the ambient noise is almost never stochastic, because it consists of elastic signals generated by physical sources that are similar to the sources of the signals we are looking for. Then computer generated stochastic noise time series is added to the filtered waveforms before the WCC detector is applied, the noise component coherent to the template is suppressed more than the sough signal and the CC values decrease for the noise more than for the sought signal. The SNRcc increases respectively, with some values above the detection threshold. This is the mechanism at work and the first results fully support this approach for aftershocks of the Kamchatka July 29, 2025 earthquake [Kitov et al., 2026].

There are various ways to add time series to filtered data. The stochastic noise amplitude has to be tuned to the amplitude of the noise component to destroy. The target noise component is the one most coherent with the template. Constructive interference of this noise component mixed with the sought signal suppresses the WCC performance. The case when the ambient noise is almost fully coherent to the sought signals is the aftershocks right after a catastrophic earthquake. The sought signals are the same as noise and all detection methods fail to find even bigger aftershocks right after the mainshock. The addition of stochastic noise reduces the detection threshold even in such inferior conditions.

Since the amplitude of the target ambient noise component is not known, a set of stochastic noise amplitudes has to be used. The original random noise sequence obtained in the range [-1.0,+1.0] is scaled by the factor StochN before being mixed with real data. The simplest way is to globally scale to the peak amplitude of the real trace in the processed time interval. It is also possible to scale locally using the noise amplitude estimates like the STA and LTA. The best scaling method has to be evaluated before applied to the WCC processing of the data set under study. The STA occurred to be the choice for the NTS data. The factor StochN varies between 0 and 20 with 1.0 step. The calculation time increases by a factor of 21 as the CC has to be calculated for each StochN value separately and then the highest SNRcc is taken for a given time count. This is especially challenging for station NVAR where the template length varies from 10 s to 120 s. The CC computation for a given time count is done once for 120 s and the shorter windows are cut from the 120 s segment.

Local phase association and conflict resolution

After the WCC-based detection has been completed, individual lists of arrivals for the MEs are available for further processing. Each arrival is characterized by its principal parameters: arrival time, CC, SNRcc, standard SNR, and relative amplitude. The latter is the ratio of the RMS amplitudes of the sought signal and template in the detection configuration of the band-pass filter and the width of WCC window. The logarithm of this ratio is the relative magnitude of the sought signal with the known magnitude of the ME of the template. All these parameters are used in the following phase association.

For a ME, the event hypotheses have a very specific feature compared to the global association at the IDC or any other seismological agency. All hypotheses created by the detections for one ME must be close in space to it. Instead of using the global travel time curves, one can calculate the station-event hypotheses empirical travel time with a very high accuracy. This is a correction to the ME-station empirical travel time estimated from the hypotheses location relative to the ME and the empirical or theoretical slowness. Therefore, a grid search is an effective technique for the relative location of the event hypotheses within a small footprint of the ME. The relative location is the basis of local association (LA) of seismic phases with event hypotheses. The final set of hypotheses has to maximize the weights of events, i.e. the sum of probabilities of the stations to be associates with the events in the studied area. In addition to the quality requirements of the WCC-based processing [Kitov, 2026c], the quality of the created hypotheses has to match the Event Definition Criteria of the IDC. The most important IDC rule is that there have to be at least three IMS stations with P-wave arrivals. For all calculations in this study, the travel time residual for valid association is set to 2 s. All associated stations have to have origin times (the arrival time less the empirical travel time) within ±2 s of the averaged value defining the event origin time. The stations magnitude tolerance for standard WCC processing is 1.2. The magnitude estimates in this study are prone to large errors related to the low amplitude of the sought signals at the level of noise or even below it. The relative magnitudes of the event hypotheses can be biased significantly to larger values and cannot be used for further interpretation.

The MEs are closer to each other than the radius of their virtual location grid in order to cover the whole area without gaps. The adjacent MEs may create hypotheses for the same physical event with slightly different arrivals obtained by different templates at the same station. To resolve potential conflict between two of more hypotheses for the same physical source, the events' weights are used. If they are equal, the number of associated phases is compared. When both parameters are equal, the conflict resolution process is using the RMS travel time residual.

The final list of generated events hypotheses, XSEL, contains the events with associated stations. This is an automatic bulletin. Hence, it contains valid hypotheses ready to be promoted to the REB, valid hypotheses not promoted to the REB because of analysts experience with visible signal, and false hypotheses. The not promoted valid hypotheses are those with low SNR values and high SNRcc values. The signals are real but they are close to the noise level. Such detections are not allowed in IDC automatic processing since the energy detectors would generate enormous number of arrivals [Saragiotis, Kitov, 2020].

Results

The set of 20 MEs in Figure 1 was used to process data between June 18 and June 24, 2020. The detection lists for the MEs were processed by the LA program using two different settings corresponding to strict and weak requirements for the event hypotheses. The crucial difference is in the sum of the SNRcc values for the hypotheses with 3 to 5 associated stations. According to Figure 3, the probability of a detection falls almost exponentially as a function of SNRcc. An increase in SNRcc by 1.0 for each of the associated detections results in a dramatic spike in the statistical significance of the created hypothesis because the probability of the random association falls respectively. The statistical power of the created hypotheses is related to the capability of the XSEL to match the REB or the bulletin created by the IDC analysis from the XSEL. This exercises have demonstrated the extraordinary statistical power of the WCC-based bulletins [Kitov, Sanina, 2025b]. Another difference is the search area with the strict setting having the radius of 45 km while that for the weak one is 60 km. The third difference in the minimum event weight: 2.5 and 2.2 for the strict and weak setting respectively. The largest weight of 1.0 has station NVAR. Stations PDAR and ELK have the weight of 0.9, TXAR 0.85, and the other stations have weights of 0.8 and lower. This approach is similar to the weight calculation at the IDC based on the quality of stations and associated phases [Coyne et al., 2012].

Figure 4 presents the result of the WCC processing for the strict case. There were 31 event hypotheses created with the most of them concentrated near the high seismic activity area shown in Figure 1. Such distribution of the reliable XSEL hypotheses does not contradict the observed seismicity. The REB has not reported any event within this area. There are three XSEL events in different locations but they are also in the known seismic zones.

Figure 4. XSEL events for the strict LA setting

The strict LA setting may have too high thresholds for the defining parameters if to consider the detection rate at the involved IMS stations listed in Table 1. The total number of detections in the third column of Table 1 at a given station depends on the number of MEs associated with it and the processed period. Only NVAR has all 20 MEs associated and this is the reason for it 1.0 weight in the event hypotheses. The WCC processing is conducted at a daily basis, but the day length is 25 hours in order to allow arrivals from some events with origin time close to 00:00 in the next day. The hourly detection rates vary from 15 at USRK to 60 at KURK. The most sensitive station NVAR has detection rate of 39 per hour. These values are very low for the possibility of random association of 3 to 5 stations with an event hypothesis considering the origin time tolerance of 2 s.

The strict setting can reject some valid hypotheses and the weak setting may help to find some of them without a visible increase in the number of false hypotheses. Figure 5 depicts the distribution of 207 XSEL events obtained for the weak setting for the same 7 days as for the strict setting. The XSEL events concentrate in the same north-western zone, but many of them are found to the south and east of the NTS center. Appendix 2 lists the XSEL catalog for these events. The number of associated stations for a majority of events is 5. This number is important for the statistical significance of the hypotheses. There are several 3-station events consisting of the best stations and one 8-station event (#7 on June 23) with the weight 6.6. This XSEL can be compared to a local bulletin if the latter is available. The performance of 3-C stations of standard local/regional network can be less effective, however, than that of arrays. For a 16-instrument array, the detection threshold is by a factor of 4 lower on average than for the collocated 3-C station. The amplitude distance curve at near-regional distances decreases by a power law [Veith, Clawson, 1972] and the factor of 4 is converted into the lower detectable magnitude at the same distance or into a larger distance for the same magnitude threshold.

Table 1. June 18, 2020. Station detection rate for the routine WCC processing of 20 MEs

Station	Associated MEs	Total detections	Detections per ME	Detections per ME per hour
ANMO	11	10645	967	39
ARCES	3	2492	830	33
BVAR	4	3035	758	30
ELK	13	11006	846	34
FINES	6	3651	608	24
ILAR	14	7180	512	20
KURK	2	3007	1503	60
NVAR	20	19316	966	39
PDAR	19	12334	649	26
PETK	4	2868	717	29
TXAR	15	17199	1146	46
ULM	13	13883	1067	43
USRK	5	1874	374	15
YBH	8	6579	822	33
YKA	11	14542	1322	53
ZALV	6	7348	1224	49

The central part of the NTS lacks XSEL events as there are no MEs close to the central point in the 20 MEs set. There are seven ME closer to the NTS center. They are weaker than the MEs used for the routine WCC processing and have less associated IMS station - only those within the North America and station BVAR in Kazakhstan, which is characterized by very low-amplitude seismic noise and high sensitivity to the events within the NTS. In order to reduce the detection threshold for the central part of the NTS the stochastic noise component was added to the data before the WCC detection. Table 2 presents the average detection rates for the 22 June, 2020. The rates at stations TXAR and YKA increased dramatically - by a factor of 3. At the same time, all 3-C stations demonstrate the rates around 1 per hour. Station NVAR near the edge of the acceptable zone with 83 detections per hour for an average ME. The detection thresholds at YKA and TXAR should be tuned to the level of 80 if the elevated rates distort the LA process and generate too many event hypotheses.

Table 2. June 18, 2020. Station detection rate for WCC processing with stochastic noise

Station	ME	Total detections	Detections per ME	Detections per ME per hour
NVAR	7	7522	1074	83
BVAR	1	1064	1064	43
TXAR	6	10559	1759	135
PDAR	7	6248	892	69
ILAR	2	1357	678	52
YKA	5	9950	1990	153
ELK	3	100	33	3
ANMO	3	28	9	1
ULM	1	5	5	1
YBH	1	4	4	1

Figure 5. XSEL events for the weak LA setting.

Figure 6. Master events and 31 event hypotheses for the period between June 18 and June 24, 2020.

The results of the LA process for the 7 MEs, with StochN varying from 0 to 20, are presented in Figure 6 with the original data listed in Appendices 3 (XSEL catalog) and 4 (XSEL bulletin). There are 31 XSEL event hypotheses distributed near the MEs. The radius of virtual location grid is also 60 km and several XSEL events are tens of kilometers far from the corresponding MEs. There also hypotheses very close to the MEs. All XSEL hypotheses have 5 to 6 associated stations and the event weight above 40 as the evidence of their high statistical significance. The XSEL bulletin shows that stations YKA and TXAR have no extraordinary association rate due to the abundance of detections. Moreover, the low detection rate at 3-C stations does not prevent them to be an important contributor to the XSEL. This observation means that stations ANMO and ELK provide a larger share of valid detections.

On 21 June, 2020, there were three XSEL events and five on June 22, 2020. These events are weak and were not found neither by standard IDC processing (no REB events) nor by routine WCC processing. The WCC processing with stochastic noise allowed to create 31 XSEL event hypotheses with high statistical significance. Therefore, the NTS monitoring can be enhanced in the future.

Discussion

The IMS includes many legacy seismic stations historically focused on former nuclear test sites such as Nevada (NTS), Semipalatinsk (STS), Novaya Zemlya of Russia, Lop Nor of China, etc. Therefore, the final configuration of the IMS primary stations has some targets with lower detection threshold and some places with higher thresholds. By design, the number of primary stations located within continents have to be appropriate to provide the best detection capability of low-magnitude events. The focus on the known test sites makes the other territories to suffer higher detection thresholds.

This fact is even more negative to the CTBT monitoring regime when the possibility of various evasion scenarios are considered. The most efficient method to reduce the share of seismic energy emitted by an underground test is to conduct it in a large underground cavity [Latter et al., 1961]. This method is called cavity decoupling and is based on a physical phenomenon of much faster shock wave attenuation in air or vacuum than in solid rock. The shock wave energy is converted into heat in air, and into solid rock kinetic energy for tamped explosions. For a 1 kt explosion, radius of a spherical cavity in salt should be around 20 m to provide full or maximum possible seismic decoupling [Adushkin et al., 1993]. The radius increasing beyond that for the full decoupling does not affect the high-frequency wave generation and thus does not harm detection by IMS stations. The decoupling factor, i.e. the reduction in the seismic wave amplitude relative to the fully tamped explosion in the identical conditions, depends on rock type and cavity shape. However, the shape does not play a critical role and an elongated tunnel provides a decoupling factor close to the most efficient spherical case [Murphy et al., 1997].

The best places to construct a cavity for seismic decoupling as an evasion scenario are those where the products of detonation cannot reach the atmosphere. Salt deposits are perfect places for decoupling and they are usually far from the test site [Sykes, 1996]. For example, the Salmon/Sterling cavity decoupling experiment was conducted in Mississippi [Springer et al., 1968; Healy et al., 1971]. In the Soviet Union, a similar experiment was conducted in the pre-Caspian salt deposits [Adushkin et al., 1993]. This makes the station distribution around test sites not optimal as the focus is on the places where the efficient evasion methods are not applicable.

The CTBT monitoring regime has the seismic technology as the first source of information on the potential violation since the compression elastic waves in the earth are propagating at velocities above 8 km/s and arrive at IMS seismic stations within a few minutes after any event elsewhere. Prompt processing of the data from the IMS by the IDC allows quick assessment of the event potential importance for the Treaty. The IDC issues various internal and official products such as seismic bulletins and catalogues. The quality of these products matches the highest standard of statistical significance and reliability. This makes the products prone to potential incompleteness in the population of weak sources, which are difficult to find, assess their quality and interpret nature.

The States Parties to the CTBT are flexible in applying the own methods of monitoring, focusing on specific regions and source types. They can also announce their concern related to the potential violation of the Treaty by other Member State(s). The independent research community have conducted a lot of studies since the start of nuclear testing to provide the best methods for the Treaty monitoring. There was a invaluable scientific support for the understanding of the magnitude dependence on rock type when the violation of the Threshold Test Ban Treaty was discussed. The usage of NTS yield-magnitude curve for Semipalatinsk Test Site was a later admitted mistake. Seismic efficiency of explosions in dry alluvium and tuff is by almost an order of magnitude lower than that for the explosions in hard anhydrite.

The research community continue to develop and test various techniques and methods to improve the resolution and sensitivity of the IMS network and to enhance processing. The waveform cross-correlation method (WCC) reduces the detection threshold and improves the accuracy of the principal parameters estimation. When applied to seismic activity at the Nevada Test Site, the WCC-based methods allow to find dozens of events not detected by the IDC. The monitoring regime of the NTS can be significantly improved by using the approach developed in this study. The IMS data has to be used for further investigation of the local/regional seismicity in the areas of interest in order to be ready for potential changes in the testing policy.

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Trump, trap, Iran

2026-04-11T07:10:00.002+02:00

Trump announced an ultimate goal of the agreement with Iran - no bomb. This is a trap for Trump. Imagine, Iran signs such an agreement. Trump or any other POTUS in the future may denounce the signed agreement for own reasons. Trump has a major charateristic to be self-contradictory at least. Logically, then Iran gets the right to make what it has signed not to make as the agreement void.

EU dreams to be US

2026-04-07T09:54:00.002+02:00

The discussion of the veto in EU decision-making is of particular interest in defining any union. This was introduced to preserve the right of small powers when they are suppressed by large powers pursuing their own interests. To some extent, it follows the saying "government is not needed to build paradise, but to avoid hell on earth". Large powers like the United States are aiming to create paradise ( "to the glory of our Lord Christ") and are willing to create hell on Earth, as Trump has said. The European Union dreams of being a large one. Hellish

Излишняя материнская нежность (Н.С.Лесков)

2026-04-01T06:46:00.007+02:00

(Прежде чем жаловаться на интер нет)

В последнюю мою побывку в Москве знакомый букинист от Сухаревой башни доставил мне на просмотр несколько старых рукописей, в числе коих находилась и та, которую я нынче представляю вниманию читателей. Она была в старинном корешке, с оклеенными синею бумагою полями и не имела ни подписи, ни заглавия, также лишена была многих страниц с начала и в конце. Но, однако, и то, что в ней уцелело, на мой взгляд представляет немалый интерес как безыскусственное изображение событий, интересовавших в свое время какой-то, по-видимому весьма достопочтенный, оригинальный и серьезно настроенный общественный кружок. Засим я предлагаю в подлиннике заметки неизвестного летописца в том порядке и под теми же самыми частными заглавиями, под какими они записаны в полууничтоженной рукописи.

Излишняя материнская нежность

Асессорша, вдова, оставшись с малолетним сыном Игнатием при хороших средствах, все внимание на воспитание его обратила, сохраняя его от простуды и болезней, а также и от всяких бесед и слов несовместных, от которых ум детский растлевается и узнает о пороках. С той целию к ней в дом никто, ни один мужчина, кроме разносчика и булочника, не входил, да еще вхож был каждое первое число месяца для молебна и назидания духовник ее, отец Павел. Этот был роста высокого, острого понимания и в разговорах нередко шутлив. Он в обстоятельства сей своей почитательницы вникал и, оставаясь у нее после молебнов на чае и закуске, скромность и бережливость асессорши постоянно похвалил, но не одобрял, что она так Игнашу взаперти, при себе и одних домашних прислужницах, держит, до того, что он ничего мужескому полу сродного в характере не имел, а стал подобен как бы девчонке, или, лучше сказать, – ни к тем, ни к сем не относится. А Игнаше тогда шел уже шестнадцатый год, и он еще нигде не учился. Асессорша же, во всем отца Павла признавая, на этот счет его полезных советов не слушала и против его разных доказательств приводила примеры из своей прошлой жизни. Наичаще она вспоминала, что, состоя в браке с асессором, многое от него перенесла, ибо он имел такое обыкновение, что если с каким-либо просителем запирует, то несколько дней домой не возвращался, а удалялся по разным местам, пел и играл и под органную музыку разные танцевальные па представлял. Это танцевание асессорше столько в жизни огорчения сделало, и было понятно, что она опасалась, как бы и сын ее по стопам родителя своего не последовал. Отец же Павел, имея здравое суждение, говорил: «Сударыня, никакого плода дальше его лет не убережешь, а если убережешь, то выкинешь». И указывал ей, что может быть такой слепой случай, когда вдруг юноше нечто необычайное в жизни откроется, и тогда он хуже не узнает, как себя повести, и еще более пострадать может. Но недоумевшая асессорша стояла на своем и отцу Павлу не верила, и так благополучно сберегла Игнашу до двадцати лет и приучала его к хозяйству, водя его с собою всегда по саду и по амбарам, дабы минуты один не оставался. А между тем случай, которого она не допускала, подкрался в самой неожиданности и очень скоро обнаружился. У асессорши был брат, отставной бригадир и предводитель, с которым она редко видалась потому, что он жил за двести верст в своем имении слишком на кавалерскую ногу и приезда родственниц не хотел видеть, а присылал им дважды в год праздничные подарки холста и материй, по выбору проживавших у него посторонних вольнодомок. Но, как всему на свете бывает конец, то и бригадиру на семьдесят третьем году его жизни пришел черед умирать, и он в преддверии смерти вспомнил о сестре асессорше и прислал к ней нарочного сказать, что он умирает и желает с нею и с племянником проститься. Случай же, о возможности которого асессорше не раз намекал отец Павел, был настороже и устроил так, что перед этим самым временем она, перевешивая полотки на жердях сверху амбара, оступилась и упала с лестницы и столь сильно повихнула себе ногу, что лежала в постели и не могла двинуться, а потому ехать к умирающему брату не могла ни под каким видом. Между же тем она была домовита и вещелюбива и знала, что у брата, кроме недвижимого имения, коему уповала быть в своей доле наследницею, были еще многие драгоценности – часы и табакерки с портретами, камнями осыпанные и дареные ему за его храбрость из Кабинета. И асессорша опасалась, что он те вещи мог по своей слабости раздарить кому-либо из окружающих его женских угодниц его свободной жизни, которые к нему приласкались, или же они, в случае если брат умрет до ее приезда, то сами по алчности своей могут все это расхитить и после сказать: «Ничего не было», или: «Он нам подарил». В таком размышлении она провела всю ночь без сна, с стесненным сердцем, и к утру решилась послать к умирающему без себя Игнашу, с проживавшею у нее верною вдовою капральшею, чтобы он ехал и жил у дяди до самой его кончины и как можно прилежней к нему ласкался. Утром же велела скоро готовить бричку, а Игнаше с капральшею сбираться и вместе с тем послала просить отца Павла, чтобы прямо от обедни пожаловал отслужить «в путь шествующему» молебен и благословить Игнатия на дорогу. Отец Павел прибыл на приглашение асессорши и молебен в ее комнате отпел, так что и она в постели могла молиться; а когда затем здесь же на столе подали для отъезжающего на завтрак телячью печенку в сметане и пирожки, то отец Павел, кушая с Игнатием, делал ему по материной просьбе внушение, как ему себя весть у дяди. – Не будь, – говорил, – как дитя: на всякий шаг материного научения не ожидай, ибо ее с тобою не будет, а сам своим умом для себя полезное руководствуй: дядю ласкай, и руку ему целуй, и одеяло поправляй, и лекарство по часам лей и в ложке подноси; а вещей хороших и драгоценных смотри повсюду, где они есть, и их хвали и одобряй, чтобы он понимал, как они тебе нравятся. И про которую тебе вещь скажет: «Это тебе», – ты сейчас ему руку целуй, а вещь к себе уноси и запирай от слуг и вольнодомок. А мало спустя, как он опять в памяти покажется, ты прославляй его заслуги и храбрость, за которые он драгоценности получал в дар, и опять те вещи на вид ставь и хвали, пока скажет: «Бери себе и это». И так ласковым обхождением до самой его кончины обходись. А когда один останешься, то на других говори, чтобы он другим не доверял. Если же один быть не можешь, то встань, будто подушки поправить, и прошепчи. Так можешь все получить, даже и с остатком на мою долю, если совет мой оценить пожелаешь. И, преподав ему нравоучение, Игнашу благословил, и тот с капральшею поехал; но капральшу, выехав за градскую заставу, из брички ссадил и прислал назад, а сам понадеялся на себя и один поехал. После же кончины дяди он возвратился назад совсем благополучен и с довольными дарами в вещах и в части имения, но на две причины жаловался: первая, что покойный дядя его до нежной к себе ласковости ни разу не допускал и лекарства из его рук не пил, а вторая – мать заметила, что он теперь слабо спит, в постели мечется и во сне губами смокчет. И второй этой причины он матери не открывал, отчего это ему сделалось. Асессорша, с которою сын прежде был во всем откровенный, не раз даже со слезами просила его открыть: отчего ему стал такой беспокойный сон и смоктанье; но он что-то невнятно бормотал и ничего не открывал. Матери вздумалось, что не пристало ли это к нему что от покойника, или не сталось ли со страха, что смертный случай видел, или от досады, что грубый человек не мог, умирая, ласки его оценить, – и тогда, по всегдашней вере своей в отца Павла, асессорша и в этом случае призвала его к молебну и потом за закускою открыла, что «вот-де с Игнашею так и так, после езды его в одиночестве к дяде большая перемена: день невесел и задумчив, а ночью с вечера долго не спит, и в постели вертится, и губами смокчет»… – Знаю, – говорила асессорша, – что ныне даже и духовные волшебствам уже стали не верить. Однако же волшебница самого Самуила из гроба вызвала и Саулу тень пророка показывала, да и в книгах церковных недаром есть молитвы от злого очарования и на отогнания, а потому, так или так, – говорит, – вас прошу и даже уже своими руками вам из своего марселинового платья новый подрясник сюрпризом сшила, но возьмите вы Игнашу в свои руки и выведайте от него всю истину и помогите. Отец Павел сказал: «Хорошо!» и, приняв в одну руку завернутый в бумагу марселиновый подрясник, другою рукою взял за руку барчука Игнашу и пошел с ним в сад, как бы для осмотра нынешнего года урожая вишен. И тут, остановясь под одним сильно рясным деревом, стал указывать, как много воробьи ягод портят, и от этого вдруг со вздохом перешел к иной порче – как нравы повреждаются. – Налетит сверху, не знать откуда, словно птаха, и клюет доброе насаждение. Так, может быть, что-нибудь и с тобою сделано? Игнаша растрогался и от неожиданности только вопроса смутился. – Точно, – говорит, – отец Павел, было со мною плохое дело, и… может быть… и теперь что-нибудь осталось, и я за грех мой страдаю. А отец Павел покачал головою и говорит: – Сделаем-ка вот что: нарви-ка ты мне поскорее хороший лопушный лист вишен, которые позрелее, и особенно воробьиных оклевушков – они всего слаще, и подай. Тот мигом все исполнил, нарвал лучших вишен и оклевухов и подал их отцу Павлу на большом лопушном листе, как на дорогом блюде. Отец же Павел в траву под яблонею сел и рясу распахнул, а лопух с ягодами в колени поместил и говорит: – Ну вот, друг мой Игнатий Иваныч, хорошо, а теперь, как мы здесь только двое – ты да я, – и больше никого нет, а над нами бог всемогущий, от него же несть ничто неявленно или утаенно, то будем же мы с тобою как в раю откровенно разговаривать, и ты открой мне как на духу: что такое с тобою встретилось и о чем ты столь сокрушаешься, что даже и мать твою сокрушаешь: ибо она видит, как ты во дни невесел, а ночами беспокойно спишь и губами смокчешь. Я буду в траве сидеть и твоего срывания вишни есть, а ты мне свои тайности обнаруживай, и тебе легче станет. Игнаша отвечает: – Я и сам, батюшка, этого очень желаю, но только не хочу, чтобы маменька об этом узнала. – Она никогда и не узнает. Я тебе в том мое слово даю, а иерейскому слову сам закон без присяги верит. Я уже тебе вперед сказал, что речь твою я принимаю как исповедь, а что на исповеди сказано, то нам открывать никому не дозволено, кроме политического начальства. – Ну, если так, что маменька знать не будет, то я вам грех свой открою. – Открывай. – Ездил я к дяденьке, чтобы к нему перед смертью его приласкаться и получить вещей и наследство… – Ну, что же такое? Это долг родственности твой был, и в том нет никакого греха. – Да-с… Вещей я не много получил, а наследства сто душ с усадьбою… – Ну! Что же ты останавливаешься? Получил сто душ с усадьбою – и это не худо. И тут я никакого греха не вижу; если бы мне дали, то я и сам бы получить такое наследство готов был. – Вам нельзя, – говорит Игнаша, – духовные крестьян у себя в крепости держать не могут, а только одни дворяне. – Ну, это ничего не значит: я бы крестьян в шесть месяцев какому-нибудь дворянину за дешевую цену на переселение в безлюдные степи продал, а в усадьбе сам жить стал. Во всем этом греха нет: но вот я уже скоро все вишни поем, а ты мне еще одни, давно мне известные пустяки говоришь, а про грех утаиваешь. Тогда Игнатий, видя, что надо уже сделать окончание речи, сказал, что видел он у дяди большое стеснение от привитавших у него дам, которые были у него чужие из постоянных гостей, но бригадир их к себе приближал более, чем своих родственников, и из их рук лекарства принимал и их одних к себе сидеть близко у постели заставлял, а его отдалял и даже шутил над ним. При тех же дамах были и другие их родственницы, молодые и старые, и к одной приехала из Москвы молодая акушерница, или бабка-галандка, нрава веселого и смешливая, круглолицая, с бровью и с косым пробором на голове – совершенно как будто красивый мальчик. Эта молодая бабка-галандка при больном скучать не любила, а все отбегала в сад и Игнашу с собою туда звала и там заставляла его себя на качелях качать и горячий уголек ей на трубке для закуривания раздувать. – Когда же бригадир умер и Игнаша домой поехал, то на второй станции ему не дали лошадей потому, что большой разгон был, и он должен был на той станции заночевать. И едва он заснул в первый сон, как послышался шум, и в ту комнату, где он спал и кроме которой другой не было, вошла та же самая бабка-галандка, которая тоже домой ехала и за недачею ей лошадей тоже здесь до утра должна была остановиться. Тогда она, сняв с себя мантон и верхнее платье, легла спать на другом диване, в одном белом лифе, и закурила трубку. Игнатий же от нее оборотился к стене и усильно сдремал во второй сон очень недолго и опять к ней тихо оборотился, чтобы видеть – спит ли. Но она не спала и, глядев на него, рассмеялась и поцелуй ему губами сделала. Он же тогда скорее опять заворотился к стене и усильно искал, чтобы скорее заснуть в третий сон, но не мог этого сделать, ибо слышал, как она, посмеиваясь, губами вроде поцелуев чмокала до самого утра. А когда утром он проснулся, чтобы ехать дальше, то ее уже не было, а он этак же, как она, губами чмокал и доселе с той привычкой остался. Прослушав такой сказ, отец Павел спросил: не было ли ему все это во сне? Но Игнатий выражал свое твердое уверение, что все то с ним было наяву. Тогда отец Павел, докушав последние вишни, стряхнул с лопуха приставшие к нему некоторые выплюнутые косточки, а лопух положил Игнатию на голову и, прихлопнув по нем ладонью, сказал: – Молодчина ты – похваляю! И в этот раз ты вышел чист и безгрешен. А теперь держи ты этот лист покрепче на голове и походи с ним, погуляй по аллейке, пока из тебя выйдут последние помышления, а я вернусь к твоей матери и тайны твоей ей не открою, а успокою ее и скажу, как ей тебя от сего избавить, чтобы ты по-прежнему спал крепко и в первый сон, как во второй и в третий. И, пустив Игнашу ходить под лопухом по аллее, отец Павел пришел к асессорше и говорит: – Ничтоже вам и сыну вашему, которого вы при себе воспитали. Я его совесть испытал и никакой вины в нем не нашел. Асессорша перекрестилась и хотела любопытствовать, но отец Павел ей всего открывать не стал. – Я, – говорит, – это Игнатию обещал, да и по службе не могу, потому что открытое нам по тайности навсегда ото всех в тайне должно и оставаться, разве как перед одним политическим начальством. Но помочь я вам для успокоения ваших материнских чувств могу и полезный совет вам дам. Асессорша говорит: – Сделайте, батюшка, милость. Я вам к Покрову богородицы гарусный пояс цветами вышью. – Хорошо, – говорит, – только вы слушайте и все точно исполните. – Слушаю, батюшка, слушаю и непременно исполню. – Встаньте вы сами рано утром на заре, когда еще роса на травах не высохла… – Встану, – говорит, – отец Павел, даже до зари встану. – Да; и возьмите вы с собою новый серп, такой, которым еще никто не жал. – Есть у меня в кладовой два серпа новые. – И выйдите вы с ним одна в сад, и оглядите такую яблоньку, которая кудрявее и чтобы на ней были плоды румяные. – Есть у меня такая, есть. – И нажните вы своими материнскими чистыми руками вокруг нее травы, и высушите из нее на солнце пуд сена. – Все так сделаю. – И пусть он этот пуд сена съест. – Кто это? – Разумеется, он, сын ваш Игнатий. Асессорша изумилась. – Как же это так: разве, – говорит, – он у меня конь? А отец Павел отвечал: – Конь-то он у тебя действительно не конь, но осел преизрядный.

Подробнее на livelib.ru:

https://www.livelib.ru/book/159197/read-zametki-neizvestnogo-nikolaj-leskov

Now on arXiv.org: Spatio-temporal evolution of low-magnitude seismicity before the May 24, 2013, Sea of Okhotsk earthquake recovered by waveform cross correlation. Is it an earthquake prediction case?

2026-03-31T07:05:00.002+02:00

Now my paper

Spatio-temporal evolution of low-magnitude seismicity before the May 24, 2013, Sea of Okhotsk earthquake recovered by waveform cross correlation. Is it an earthquake prediction case?

is available in pdf format on arXiv.org: http://arxiv.org/abs/2603.26717

I am working on the Kamchatka 2025, Kamchatka 2006, Tohoku 2011, and Sumatra 2004 events. Papers are in preparation. Just one Figure from Kamchatka to illustrate that the immediate evolution of low-magnitude seismicity is similar to the Sea of Okhotsk earthquake described in the published paper.

Figure. Growth in the low-magnitude seismicity from July 24 (day 205) to July 29 (day 210), 2025. A peak is observed just before the mainshock as for the Sea of Okhotsk, 2013 deep earthquake.

Spatio-temporal evolution of low-magnitude seismicity before the May 24, 2013, Sea of Okhotsk earthquake recovered by waveform cross correlation. Is it an earthquake prediction case?

2026-03-23T09:10:00.000+01:00

Abstract

According to the International Data Centre (IDC), the Sea of Okhotsk earthquake occurred at 05:44:49.7 on May 24, 2013, had coordinates 54.89°N,153.31°E, m_b=6.27, and depth of 604 km. The USGS moment magnitude is 8.3. The previous event detected by the IDC in the surrounding volume 53°N-57°N, 151°E-155°E, depth from 400 to 700 km occurred on February 6, 2012. Using the same seismic data from the stations of the International Monitoring System together with detection and phase association methods based on waveform cross correlation, a series of low-magnitude earthquakes was recovered immediately before this major earthquake. More than 200 events obeying the Event Definition Criteria adapted by the IDC were found between May 13 and the mainshock, with a sudden increase in their occurrence rate starting on the afternoon May 19. The evolution of the numbers of these low-magnitude earthquakes in various ranges of statistical significance within the source volume demonstrates some features, which can be related to the approaching initiation of the Sea of Okhotsk earthquake.

Key words: Sea of Okhotsk earthquake 2013, earthquake prediction, IDC, IMS, waveform cross correlation

Introduction

The Sea of Okhotsk is a well-known area of deep earthquakes. The subducting Pacific plate reaches here the boundary between the upper and lower mantle with the deepest earthquakes located at ~700 km as reported by the International Data Centre (IDC) using data from seismic stations of the International Monitoring System (IMS). The deepest earthquakes are of higher interest not only because of their seismic features but also they provide valuable data for other geophysical fields. The evolution of seismicity at the depths of 400 to 700 km may differ from that near the surface as related to temperature, lithostatic pressure, rheology, chemical and mineralogical structure of the plate relative to the surrounding mantle, etc.

The IMS provides continuous seismic data to the IDC since 2001. It includes seismic arrays which are characterized by much higher sensitivity and resolution than collocated three-component (3-C) stations. The usage of arrays allows to reduce the detection threshold worldwide and to detect earthquakes with much lower magnitudes than with the 3-C networks. Dense regional seismic networks of 3-C stations can detect events with lower magnitudes, but within the remote regions such as the Sea of Okhotsk there are no possibility to install enough bottom seismic stations just for the deep earthquakes study. With the array stations, the IMS is the best instrument to observe the evolution of seismicity in remote regions of the earth and the IDC provides a quality list of reliable event hypotheses as defined by the adapted version of Event Definition Criteria [Coyne et al., 2012]. The interactive analysis serves as a quality filter for the Reviewed Event Bulletin (REB) - the IDC final internal product of data processing. The REB contains up to 40% of events added by analysts, which have no counterpart in the automatically generated standard event lists (SELs) of the IDC.

The natural seismic process is characterized by repeatability of events in location and size. The magnitude distribution of repeating earthquakes is well described by recurrence curves introduced in [Gutenberg, Richter, 1936,1945]. As the time sequence of earthquakes in a given area is characterized by close locations one can effectively use not only the arrival times of the signals from them to find new events, but also the full waveform [Schaff, Richards, 2025]. This allows for finding many more events with much lower magnitudes in the vicinity of well-defined historical sources [Israelsson, 1990; Joswig, 1990; Schaff, Richards, 2004; Gibbons, Ringdal, 2004, 2006; Gibbons et al., 2007, 2011, 2017; Waldhauser, Schaff, 2008; Adushkin et al., 2015, 2017, Kitov, Sanina, 2022]. The matched filter is an optimal detector for signals similar in shape [Turin, 1960] and it uses waveform cross correlation (WCC) to maximize the signal-to-noise ratio. When applied to deep earthquakes, the WCC-based detection and phase association techniques may recover the seismic events missed by standard IDC processing of the IMS data.

The main objective of this study is to recover the low-magnitude seismic events during eleven days before the May 24, 2013 earthquake in the Sea of Okhotsk and three days after it. According to the IDC, this earthquake occurred at 05:44:49.7 on May 24, 2013, had coordinates 54.89°N,153.31°E, m_b=6.27, and depth of 604 km. The USGS moment magnitude is 8.3. There was no events detected by the IDC in the surrounding area 53°N-57°N, 151°E-155°E since February 6, 2012. The same seismic data from the stations of the IMS is used together with detection and phase association methods based on WCC. The recovered events are studied additionally in various magnitude ranges in order to estimate the evolution of the size distribution just before the mainshock. The sequence of mechanical effects before the mainshock may be revealed as the evolution from micro-cracking to the final rupture runs over increasing sizes of fracturing.

Data and method

Data sources and general features

The IMS seismic network consists of arrays and 3-C stations. There are IMS primary stations defining the statistical significance of the created event hypotheses matching the EDC and auxiliary stations assisting in location and magnitude estimation of the valid hypotheses [Coyne et al., 2012]. This division is prescribed by the Comprehensive Nuclear-Test-Ban Treaty (CTBT) as providing uniform distribution of detection threshold worldwide. The civilian applications of the IMS data are not constrained by this rule and all stations are treated according to their performance in the statistical sense. The IMS data is available via virtual Data Exploitation Centre (vDEC) of the CTBT Organization (CTBTO) [vDEC, 2026].

As only the IMS data is used in this study, the REB is a natural source of events and associated detections used for comparison with the result of WCC processing. For the purposes of WCC processing, the REB provides event locations (epicenters and depths), magnitudes m_b and M_s, origin times as well as arrival times at IMS stations with a 0.001 s precision, and signal-to-noise ratio (SNR) for the associated signals. Selected properties of the deep seismicity in the Sea of Okhotsk region are also obtained from the REB. Figure 1 shows the recurrence curve for the region 42°N-65°N, 140°E-165°E and depth>410 km obtained from the REB. This curve uses the data from 2001 to the end of 2025 with the total number of approximately 1000 events. The corner seismic magnitude is in the range between 3.0 and 3.4. The regression line is extended beyond the corner magnitude to demonstrate the increasing deficit of low-magnitude earthquakes, which can be partially recovered by WCC.

For the purposes of WCC processing, the signals associated with a set of REB events are used as waveform templates. At 3-C stations, the templates may have one- or three components depending on seismic phase and the station-event distance. For the IMS arrays, multichannel templates are used, with only vertical channels involved. Cross correlation coefficient, CC, is a common measure of the angle between two data vectors representing digital time series of a template and a sought signal. As a measure of similarity, this angle is calculated by a textbook dot product of two data vectors. The CC is not the best variable for detection purposes, however, as it depends on signal spectrum and duration. In the presence of ambient seismic noise, both the template and the sought signal may differ significantly even being identical in their unique source.

The search for a similar signal with a high-quality template, i.e. using a signal with large SNR, meets the noise as an important obstacle. By definition, the matched filter is an optimal detector maximizing SNR only in presence of stochastic and additive noise [Turin, 1960]. On average, such theoretical noise has the minimum CC value with any regular signal. In practice, there is no such actual noise realization, which could be considered as stochastic and allowing for perfect detection conditions. Any ambient noise realization can have a component that is coherent with any real signal, from very low similarities up to a fully identical case. The latter case is related to the search of a signal from an aftershock of a catastrophic earthquake, as a multitude of other aftershocks in the same area simultaneously generate almost identical signals. As a result, the immediate aftershocks of large-magnitude earthquakes are difficult to find.

Figure 1. Recurrence curve for the region 42°N-65°N, 140°E-165°E and depth>410 km. The trend line extended below the corner magnitude of 3.0 to 3.4 indicates the number of potentially missed events. A portion of them can be recovered from the IMS data using WCC.

Deep earthquakes are different in the post-seismic activity form shallow events. There are only 33 aftershocks of the M8.3 Sea of Okhotsk earthquake observed during the first 60 hours as Figure 2 shows. The decay of event magnitude with time during the initial 4 hours is a common feature of the major earthquakes. There is an effect of elevated noise as related to the mainshock wavefield, which likely prohibits to find aftershocks with lower magnitudes. The time gap between the mainshock and the first aftershock is approximately 18 minutes. It is longer than for the Tohoku March 11, 2011, and the Kamchatka July 29, 2025 earthquakes with moment magnitudes closer to 9.0. The second aftershock was found ~11 minutes after the first one. As well known from practice, deep earthquakes generate short impulsive signals not usual for near-surface sources except explosions. This effect may impact the performance of WCC detector. The signals from deep events are very similar to each other and are characterized by an almost vertical incidence angle at the closest station. In that sense, they are not coherent to signals from the shallow sources, which are by far the main contributors to the ambient noise.

Figure 2. Magnitudes (black dots) and depths (red dots) of the mainshock and 33 aftershocks as a function of the elapsed time.

In this retrospective analysis, the aftershocks of the May 24, 2013 earthquake can serve as master events (MEs) with corresponding templates at IMS stations together with other REB events found before and after the mainshock. Figure 3 demonstrates the distribution of 70 selected MEs and their catalog is listed in Appendix 1. The biggest earthquakes are less effective in detection of the smallest ones as their signals differ in shapes as related to their spectral content. However, after band-pass filtering the templates from the m_b>5.5 events are useful as they have very large SNR compared to the low-magnitude MEs.

Altogether, the IMS data set and the IDC bulletin provide a set of waveforms, events and detections/templates for an analysis of deep seismicity in the remote Sea of Okhotsk region. The IMS array stations allow to reduce the detection threshold in standard IDC processing by a factor of 3 to 5 [Schweitzer et al., 2012]. The WCC-based processing allows for another 3 to 5 times reduction in detection threshold and finding of 60% to 100% of new events matching the REB requirements for a valid hypothesis [Bobrov et al., 2014; Bobrov et al., 2016ab; Bobrov et al., 2017; Kitov, Rozhkov, 2024; Kitov, Sanina, 2025b].

WCC-based detection

In accordance with the matched filter approach, the WCC-based detection procedure uses the signal-to-noise ratio technique applied to the CC time series. Not to be confused with the standard SNR, this ratio is known as SNRcc. A set of CC time series is calculated using various template lengths or cross correlation window widths (CCWW). Waveform filtering is a standard procedure, and at the IDC it is realized in routine processing as a comb of band-pass filters [Coyne et al., 2012] covering the range of the expected signals related to the CTBTO monitoring mandate. The same procedure is applied to the IMS data before the CC is calculated in a given CCWW [Bobrov et al., 2014]. The number of CC time series is equal to the product of the numbers of CCW and filters.

The CCWWs and the comb of band filters are both varied to make the WCC procedure reliable as there is no a priory information on the sought signal length and spectrum above the ambient noise. It is mandatory to cover the entire spectrum of interest for the first P-phases used in the current WCC version adapted to low-magnitude events: from 0.75 Hz to 8 Hz. The potential signal lengths are between a few seconds for impulsive P-phases and up to 100-120 seconds for regional sequence of signals from P_g/P_n to L_g. The length step depends on source type (shallow and deep earthquakes, volcano eruption, landslide, explosions, quarry blasts, other artificial sources), station-source distance, and properties of the propagation path.

Figure 3. Distribution of 70 MEs. For more information see Appendix 1.

For the Sea of Okhotsk mainshock and its aftershocks, Figure 4 presents examples of templates at IMS stations PETK (epicentral distance ~3°) and MKAR (~45°). At PETK, the mainshock (the upper trace) creates a long wave-train (the original record is clipped) related to the source size and propagation path. Several aftershocks of various magnitude (see scales for relative sizes) also demonstrate long signals filtered between 0.6 Hz and 4.5 Hz. The CCWW set is adapted to the observed wave-pattern. At MKAR, the signals from the mainshock (and likely its immediate aftershocks hidden in the self-generated noise) are also lengthy, but the aftershocks, which are different from those at PETK, are characterized by impulsive and high-frequency first arrivals (3.0-6.0 Hz band filter is applied). Since our goal is to find the weakest possible signals like the aftershocks in Figure 4, the best at the level of the ambient noise, the low-magnitude aftershocks of the Sea of Okhotsk earthquake could be the optimal choice to be used as MEs. The initial segment of the mainshock signal is not similar to the sought signals and would be appropriate to find only the biggest events in the area.

Figure 4. Examples of waveform templates at stations a) PETK (filtered in 0.6-4.5 Hz band), b) MKAR (filtered in 3.0-6.0 Hz band). The scales on the left show their relative amplitudes.

The detection thresholds at IMS stations have to be tuned to optimal fluxes of valid and false arrivals [Saragiotis, Kitov, 2020]. Statistical significance of the created event hypotheses depends on the probability of associated phases not to be randomly generated but rather to be related to a set of seismic sources to find. Therefore, the frequency distribution of SNRcc values determines the reliability of the created event hypotheses, their statistical significance and power. A detection list consists of the signals having SNRcc above the predefined threshold, but also matching a few additional quality parameters, with the main being the standard SNR threshold. By varying the SNRcc threshold one can control the detection flux. A reasonable value is 60 detections per hour with possible scattering ±30 for different MEs and time intervals. For quiet days, as defined by the absence of REB events in the studied area, the most of these detections are likely to be false in terms of relation to the used MEs. In some cases, such detection can be the result of the side sensitivity of the WCC detector to very intensive sources like the Tohoku earthquake. A spontaneous above the threshold SNRcc is also possible due to data problems like zeroes or spikes. The quality check is able to suppress such cases by the requirement of a tight sequence of SNRcc values above the threshold. There is also a possibility to use adaptive thresholds in order to adjust to the current valid events flux and noise level. Such adaptive thresholds are useful in tune WCC routine processing to low and high seismicity periods.

A quasi-random SNRcc distribution for a given station can be generated within the WCC processing when the threshold is very high, say 500. In this case, detection fails and all SNRcc values represent noise. For an hour processing interval, the number of SNRcc values should be 3600 times the sampling rate. The IMS stations have sampling rates from 20 Hz (e.g., ASAR, BRTR, CMAR, ILAR, KSRS) to 100 Hz (FINES, but it was 40 Hz in 2013) with a majority of IMS seismic stations working at 40 samples per second. For a random SNRcc generation case during quiet time periods without detected signals similar to a given template, the frequency distribution is expected to be quasi-exponential. Any deviation from this basic case would reveal the presence of valid detections as the template reacts to the presence of similar signals in data. The SNRcc level where this deviation starts may be used as the detection threshold.

Figure 5 shows several SNRcc frequency distributions for IMS stations PETK and MKAR. Station PETK is the closest to the mainshock, and station MKAR is the second most sensitive to deep events in the Sea of Okhotsk as per the REB. Four MEs were selected from the top of template quality list as defined by SNR values of corresponding template signals. Two detection thresholds are used: 3.1 and 500. There are three cases appropriate for the comparison. Firstly, a 6-hour interval on jdate=2013133 (May 13, 2013) with a zero total number of events in the cross-correlation standard event list (XSEL) - an analog of the final automatic standard event list of the IDC (SEL3), as obtained in this study, represents the most quiet time period. Secondly, a 6-hour interval after the start of visible increase in seismic activity found by WCC on 2013139 (May 19, 2013). There were no REB events found in this interval, but 45 new XSEL events were detected. The third time interval starts with the mainshock and also lasts 6 hours. There were 31 aftershock with only 20 (65%) of them having seeds in the SEL3. Other (pure) REB events are added by IDC analysts using different sources of information and procedures. The XSEL includes 51 new events, and matches 26 REB events, including 18 with seeds from SEL3 and 8 from the pure REB subset.

Figure 5. Frequency distribution (0.1 bin width) of SNRcc at PETK and MKAR for three days. Four MEs are shown with two different detection thresholds: 3.1 and 500. The difference between the quiet (133) day and the days with only hidden (139) and IDC detected (144) activity is significant. The patterns also differ between stations.

The earthquake preparation process has to include the growth in the sizes of the sources emitting the observed signals. At the same time, the noise at the recording stations from the increasing seismic emission includes the very same signals from all sources in the zone of the mainshock preparation. When beamforming is used as a detection technique [Schweitzer et al., 2012], this noise may mask the smaller events at array stations as the suppression is based on the assumption of destructive interference. The same effect is observed for the WCC-based methods, but there is a possibility to improve the array resolution by adding numerically generated random time series to real data [Adushkin et al., 2025]. In this study, we applied this method and found several aftershocks missed by the IDC in the first 30 minutes after the mainshock.

When interpreting the curves in Figure 5, it is important to understand what does mean a valid signal with SNRcc above the predefined detection threshold. A sought signal can generate a long sequence of relatively large SNRcc values even below the threshold (e.g., 500). When correlated, a template and a sought signal create a sequence of CC values higher than those obtained by correlation with the pre-signal noise with a length compared to the CCWW. This sequence of CC values transforms into a sequence of SNRcc values above those created by the noise. This is similar to standard STA/LTA detector where a signal above noise generates a sequence of elevated SNR values.

When a signal is detected, the LTA has to be frozen in order not to add the signal energy to the SNR or SNRcc. This makes a longer sequence of higher SNR values. For the WCC detector, the effect of frozen LTA is approximately the CCWW. In any case, the presence of sought signals create longer sequences of higher SNRcc values, as one can observe in Figure 5. However, there is only one of all the SNRcc in a given sequence to be used to characterize the detected signal, which is called "arrival" after it passes quality checks. For the arrivals, many parameters are calculated such as arrival time, amplitude, period, SNRcc, SNR, and CC. When detection failed, the sequence of higher SNR and SNRcc is shorter and their values are lower as the LTA is not frozen. To tune a detection threshold a special procedure has to be implemented [Saragiotis, Kitov, 2020], which balances the detection rate and the portion of the generated arrivals associated with valid event hypotheses in the final bulletin (SEL or REB).

In this study, the detection thresholds at individual IMS stations were estimated to retain the total number of arrivals below the predefined tolerance level. They were tuned in a series of test calculations and then are fixed thought the calculations. This makes the following phase association procedure to be unbiased in terms of the arrival lists quality over the studied period. The MEs are selected from the REB and have different numbers of associated stations and quality of corresponding templates. There are places where only relatively poor REB events with just a few associated stations are available. Therefore, the detection rate at individual stations and the total number of detections produced by a given ME vary in a wide range. This effect may create some disproportions in the MEs input to the final XSEL. This is a normal situation for an automatic bulletin. For example, SEL3 has many seed events at ranges of 90° to 180° from the final REB solutions. An automatic bulletin has to be approved in an interactive analysis or compared to a high quality bulletin for the same area. Fortunately, the REB can be used as a reference for the XSEL for the studied region. A direct comparison of arrivals associated with the events in both bulletins is possible at the same IMS stations by their arrival times. Such a comparison needs only 1 common arrival within the allowed retiming window (±10s) to match an XSEL and REB event. Such a procedure is often used by the IDC for comparison with alternative solutions.

Local association

The WCC arrival list consists of individual lists for each of the 70 MEs (see Figure 3). These individual lists do not intersect but may contain arrivals corresponding to the same physical signals. By design, all templates of a given ME are able to find only signals from other events within a small footprint around its epicenter. For the sought events within 1/4 of the signal wavelength, CC can be between 0.95 and 0.99 if the noise is negligible [Arrowsmith et al., 2006; Baisch et al., 2008]. Such a situation was observed for the signals from the DPRK announced underground tests [Selby, 2010; Kitov et al., 2025]. For very high CC and SNRcc values, the arrival time precision for the sought signal can be as low as 0.001 to 0.005 s. As a result, the RMS travel time residuals for the sought event located using the WCC arrivals can be of the same magnitude of 0.005 to 0.01 s. In terms of spatial location accuracy, it corresponds to 40-80 meters for the apparent wave velocity of 8 km/s, e.g., P_n-phase. This is the accuracy of relative location and the absolute location accuracy of the sought event is practically the same as for the corresponding ME. The relative location using all the associated phases (stations) and confined to a small area around a ME is called Local Association (LA). The LA version used in this study is well described in [Bobrov et al., 2014; Bobrov et al., 2016ab; Kitov, Sanina, 2025b].

The CC and SNRcc values rapidly fall with distance from a given ME and with the amplitude of the sought signal relative to the noise level. For an array station, a virtual event location moved over the LA grid may change the scalar slowness and the azimuth in the arriving plane wave, which can improve or suppress the multi-channel cross correlation with a template. The change in actual event location may also affect the source function of the sought event and the difference in propagation paths may disturb the sought signal shape.

The search area for a given ME is defined by the degradation of correlation with distance and by the presence of different MEs. For the MEs in Figure 3, the search area of 40 to 90 km in radius is appropriate as the MEs also have confidence ellipses of from one digit to tens of km and some intersection of the search areas would be helpful. For such an area, a grid search is a natural choice as any position within the search radius can be tested for the sought event location without extensive calculations. For example, a grid with 35 nodes and 2 km step in both directions from a ME can be used. The depth of the sought event is fixed to that of the ME as the depth sensitivity is very low and thus increases uncertainty. To accommodate the depth dependence into the WCC processing, MEs in 40 km depth intervals are independently selected where available.

The grid search for valid event hypotheses is based on the origin times for virtual solutions related to the nodes of the grid. A virtual event origin time in the (0,0) node can be calculated as the WCC arrival times less the empirical ME-station travel times as obtained from the REB. For the other nodes, the travel times have to be corrected for the dot product of the vector to the node and the vector slowness of the signal at the related station. This is a very accurate time correction as the node vector is a predefined value and the slowness vector for a given station does not change much between the nodes of a small grid search area compared to the ME-station distances.

For a valid event hypothesis, the origin times for three or more associated arrivals (stations) have to be within the predefined tolerance. At the IDC, the allowed travel time residual relative to the theoretical time is 2 s for the first P-phases, and 2.2 s for the P_g- and P_n- waves. These residuals correspond to the desired statistical significance of the REB events as adapted in the EDC. At least three first P phases at different stations have to be associated with a valid event. These rules are used in the WCC processing to match the IDC approach [Coyne et al., 2012]. As the XSEL arrivals potentially have higher relative arrival time accuracy, the origin time tolerance can be much lower than for the IDC without a significant loss in performance efficiency expressed in the number of valid (i.e., matching REB) events. For automatic IDC bulletins (e.g., SEL3), the allowed travel time tolerance is much larger than 2 s and can reach 5 to 7 s. The WCC-processing, despite being automatic, strictly follows the entire list of the REB requirements, except the division into the primary and auxiliary stations.

Three or more arrivals with origin times within ±2 s interval from their average value are not a guarantee of a reliable event hypothesis. There are many arrivals at many stations and the event hypotheses have an additional degree of freedom - varying location. The REB provides valuable information on the IMS station performance for the historical events in any given seismic region. There are stations which contribute to almost all REB events is a specific area as Australian stations WRA and ASAR to the events within Australia. Thus, an event hypothesis within Australia without these stations, when they are operational, would be rather false despite other parameters may match the EDC. There are also IMS stations contributing only to the largest events in this region or not contributing at all. The difference between the most sensitive and the ineffective stations can be described by their participation rates in the REB events. Such rates are calculated for each IMS station for all regions with repeating seismic events including the Sea of Okhotsk. For example, the first P phases detected by PETK have the highest probability to be associated with the events in the studied area and can be characterized by a station weight (or probability) of 1.0. Stations MKAR has a weight of ~0.9. Other stations have weighs less than 0.85. To create a statistically significant event hypothesis having three associated stations, with PETK and MKAR included, one can define the minimum event weight, i.e. the sum of all associated station weights, of 2.7. Then there will be just a few valid three-station configurations.

With the increasing number of associated stations, the requirement of total event weight plays lower and lower role as the probability of many random arrivals to be within a narrow origin time interval rapidly decreases. An important parameter for the statistical significance of an event hypothesis is the requirement of large SNRcc at one or two best stations. According to Figure 5, random arrivals with SNRcc>5 are almost excluded on quiet days. A similar approach to the event quality using the arrival probabilities is the sum of individual SNRcc values. This parameter introduces a series of thresholds for 3- to 7-station event hypotheses. For example, for a 3-station event the sum of SNRcc is set to the level of 12.0. One of these stations has to have SNRcc above 5.0 and the other two have to add at least 7.0 in any combination. A 4-station event has a threshold of 15.5. With the increasing number of stations above 5, the threshold increases by a constant predefined step.

All in all, the most important LA parameters are as follows: origin time tolerance, total event weight, weight of the best station, number of associated stations, sum of SNRcc values of all associated arrivals, and the minimum SNRcc for one of the best stations. The grid radius and spacing between nodes are also important for the final XSEL. There are less influential parameters, which are retained unchanged through all calculations after tuned in the test calculations.

Conflict resolution

There can be dozens or even thousands of MEs in WCC processing. The global coverage in routine processing includes more than 42,000 MEs. Each of the MEs generates an individual arrival list and an XSEL. Two or more neighboring MEs can find the same physical event, i.e. they can detect the same physical signals and use them to create similar hypotheses. But a unique physical signal must belong to one and only one XSEL event. A similar conflict of interests exists in any seismological agency including the IDC. To resolve such a conflict a special procedure is developed and applied [Coyne et al., 2012]. In automatic processing, Conflict Resolution between the event hypotheses competing for one arrival is based on an assumption that the event with a larger number of associated phases wins. If this number is equal between the competing events, the event weight comes into play. After the CR procedure is finished, the arrival is associated with a stronger event hypothesis and all competing event hypotheses lose this arrival. Then, the losing hypotheses are checked for the EDC match and can be rejected if not meeting the requirements.

The IDC event weight includes the input of associated phases. Each phase can add a specific value related to the residuals of arrival time, azimuth and slowness. These values depend on phase and station type (array or 3-C). For a secondary phase to add to the event weight, it has to be the first P-wave associated at the same station. The sum of individual values related to all associated phases at primary IMS stations defines the event weight and the threshold weight defines the statistical significance of the event. This threshold is tuned to the level than only the event hypotheses with 3 or more primary stations with associated first P-phases can be promoted to the REB.

The number of conflicts in the final XSEL creation is much higher as several MEs usually conflict for the same arrivals at many stations. Following the IDC approach and the event weight definition used in the WCC processing, all conflicts are resolved in favor of the event with the highest weight, then follows the number of associated phases. If these two parameters do not resolve the conflict, the RMS residual origin time is used. The final XSEL contains only one arrival per a unique physical signal.

An event hypothesis losing one or more arrivals is checked against the EDC related to the WCC processing. If it does not match any of them it is rejected. The loss of an associated phase does not preclude this hypotheses to exist if it still matches the EDC. There are a few cases of earthquake doublets close in time and space which are difficult to distinguish and potential mis-association of phases from different source with one out of the two. The SEL3 gives some examples of "joint" (arrivals from two different events are associated with a single event) and "split" (one event is split into two different events) events. Such events are mainly belong to the aftershock sequences of the largest earthquakes when secondary phases can be mis-associated and the arrival times are not accurate. These are the problems for the automatic WCC processing as well.

Measuring the growing activity with increasing event magnitudes before the mainshock

For routine WCC processing, a permanent set of LA parameters is determined in a tuning procedure. This set has to generate the XSEL with the largest number of matched REB events and the lowest number of false event hypotheses. A few experiments of interactive review of the automatic XSEL according to the IDC rules made it possible to conclude that the REB misses 50% to 100% of REB-ready events. And these newly found events are weak, but fully comply with the EDC. These smallest events are the principal objective of the CTBT compliance. The biggest events tell for themselves.

The study of the Sea of Okhotsk earthquake is different from the principles of the IDC operation with well established thresholds, as the seismicity before the mainshock has to be found and characterized according to the mechanics of earthquake preparation process. The IDC has to limit the event magnitude by 2.0 as one can observe from Figure 1, where no events are observed below this threshold. There is no limit to the WCC processing resolution except the requirement that the XSEL should include valid events according to the adapted EDC.

The mantle convection drives the plate tectonics with the solid plates subducting under the continents to a depth of 700 km and likely deeper. The deformations and stresses in the plate play defining role in the near surface tectonics and seismicity. With increasing depth, the earthquake mechanism may change as the impulsive character of the observed signals indicates. There are various scenarios proposed and the correct one has to rely on actual observations of the seismic process it describes. One of the possibilities to look into the details of this seismic process is opened by the use of WCC-based processing.

The evolution of seismic process before major seismic events should be the same as in laboratory experiments from the point of view of increasing sizes of smaller events before the mainshock. For shallow earthquakes, small cracks in the very beginning evolve through small faults to the level of main rupture. For deep earthquakes, there are three major mechanisms proposed: transformational faulting, dehydration embrittlement, and thermal runaway. Their combination in a unique event is also possible. Physical models of the preparation process need observations before such deep events in order to tune their defining parameters.

In order to recover the seismic process before the Sea of Okhotsk earthquake, the WCC-based processing was split into several cases with different resolution and sensitivity. In the most sensitive case, the XSEL has to include the weakest event hypotheses allowing to find the earlier signs of the start of the earthquake preparation process. In the most strict case, the XSEL has to be tuned up to the level where it can find and match the most of the REB events in the aftershock process. This allows to prove the statistical power of the entire procedure. In this case, the number of XSEL events extra to the REB should be within the range of 50% to 100%, as observed in the previous interactive exercises. Below this strict XSEL level on the way to the weakest set of XSEL defining parameters, the same number or more REB events can be matched and the number of XSEL events may grow. The increasing number of XSEL events may include those which cannot be approved in an interactive review as the analysts have to have visual confirmation of the signals. Nevertheless, these XSEL events can be valid as radar applications without human interference prove. The signals deep below the noise level can be safely detected and used.

Before the Sea of Okhotsk earthquake, seismic activity may progress up from the weakest events around magnitude 2.0 in Figure 1 to the events which can be potentially detected by the IDC. Therefore, various cases of WCC-processing have to focus on specific parts of the recurrence curve from below 2.0 to 3.0-3.4 in order to detect and describe the pre-seismic process evolution. There is no reliable quantitative information on the uncertainty of the magnitude estimates for the WCC detections near the noise. One can only judge on the sensitivity of a given WCC processing scenario by the number of XSEL events built in the predefined time intervals. The full set of the WCC scenarios is based on two limit versions - strict and weak. The strict version has the search radius of 43 km, the best station minimum weight of 0.855, total event weight of 2.5, the SNRcc sum thresholds of 15.0, 18.5, 22.0 for 3-, 4-, and 5-station events, respectively, and the SNRcc threshold of 5.0 for one of the best (with weight > 0.855) associated stations. The weak version has the search radius of 80 km, the best station minimum weight of 0.8, total event weight of 1.8, the SNRcc sum thresholds of 14.0, 17.5, 21.0, and the best station SNRcc threshold of 4.5. All other parameters are the same. The statistical significance of XSEL events in each version is additionally controlled by six values of the origin time tolerance, Δt: 0.25, 0.5, 1.0, 2.0, 3.0, and 5.0 seconds. There are 12 version/case pairs: v₁c₁, ...v₁c₆, v₂c₁,...,v₂c₆. The narrowest origin time window allows practically only actual event hypotheses to be created as the probability of 3 or more random detections at the best stations to occur in a 0.5 s time window is extremely low considering the limit on the detection rate of 60±30 per hour. On the other hand, the narrowest window may potentially miss many valid XSEL events consisting of weaker signals with poorer arrival time estimates as related by the noise influence. The v₁c₁ pair should not be able to detect too many new XSEL events extra to the REB. Overall, the XSEL events matching the REB events have to be of a higher quality related to the SNR values of the associated signals.

The weak WCC version with the shortest origin time window, v₂c₁, has to be focused on the new XSEL events with the best quality just below the corner magnitude of the recurrence curve. These events are of high statistical significance and may include weak WCC arrivals. The v₂c₆ pair has the highest resolution below magnitude 2.0. It may contain many valid events and likely some false events, with both types formally matching the EDC. The strict and the weak versions with the same Δt are focused on a specific event quality range, which depends on event magnitude and mechanism as well as on the noise level at stations around the arrival times of all associated phases. Formally, for pairs v_ic_j, we introduce quality boundaries Bⁱ_j, where i=1,2 is the version - weak or strict, and j=1,...,6 is the tolerance case. By design, B¹_j≤ B²_j and Bⁱ_j+1≤ Bⁱ_j. The quantitative meaning of these boundaries is revealed by WCC calculations with an increasing number of event hypotheses generated with increasing j for a given i. When the sought seismic activity from the quiet state reaches the lower boundary Bⁱ_j the number of weak events grow and the number of strict events, which must have larger magnitudes and statistical significance, stays still. The change in the ratio of the event numbers in the weak and strict XSEL versions, B²_j/B¹_j, expresses the change of seismic process in this range. When the activity starts to grow from a quiet state, the B²_j/B¹_j ratio also increases with the growing number of XSEL events above B²_j. The activity may not reach its upper boundary B¹_j and start to fall to the initial level. In some cases, the activity may reach the upper boundary and move above it as, for example, happens after larger earthquakes. Then the ratio may fall because of large number of events above the upper boundary and constant or decreasing number above the lower boundary. The larger earthquakes may generate noise masking the smaller events. In an aftershock sequence of the largest earthquakes, the B²_j/B¹_j ratios in the magnitude ranges much below the corner magnitude may reach the lowermost levels and express the distribution of earthquakes in the recurrence curve. With the decaying post-seismic activity, the ratio grows again as the number of events above B¹_j has to decrease fast and the number above B²_j decreases much slower. All in all, there are six quality, potentially related to magnitude, ranges to follow the seismic process before the earthquake.

Results

Statistical power. Aftershocks and new XSEL events

The mainshock at 5:44:50 on May 24, 2013 is a reference for all calculations. Initially, the recovered seismicity was analyzed at a daily rate. The processing period was 25 hours per day, with 1 hour in the next day serving to find the events in the processed data day but with associated arrivals in the next day. Such an overlap is used to make processing continuous. The revealed evolution of seismic activity made it more appropriate to present data in 6-hour intervals in order to better determine the start of the change in the rate of the event occurrence and the evolution of the aftershock sequence since its principal phase lasted only 12 hours.

There was no aftershock before 6:02:45, i.e. ~18 minutes after the mainshock. Such a still period is observed after the major earthquakes and can be related to the absence of any large magnitude post-seismic activity or to a much higher noise level hiding the immediate aftershocks. The latter problem can be resolved with the coherent noise suppression based on the added stochastic noise [Kitov et al., 2026]. In total, there were 40 aftershocks between 06:00 and 18:00 on May 24. Then, the postseismic activity stopped. From these 40 aftershocks, 27 had SEL3 seeds and 13 (33%) were built by IDC analysts. Table 1 lists the numbers of events in the XSELs for all 12 versions/cases used in WCC processing for two 6-hour intervals within the 12-hour period between 6:00 and 18:00. The best strict WCC version (Δt=3.0 s ) finds almost all (19 out of 20 for the interval 6:00-12:00, and 7 out of 7 for the 12:00-18:00) REB events with SEL3 seeds. For the pure REB events, the best result is in the Δt=3.0 s case - 8 out of 11 for the first interval and 1 of 2 in the second. In total, there were 27 out of 31 REB events matched in the Δt=3.0 s case of the strict version.

For the v₁c₁, the XSEL has matched 25 REB events, i.e. practically the same proportion of the total as in the best case v₁c₅. The number of new XSEL events, not matching the REB, in the 12-hour segment increases with Δt from 23 for 0.25 s to 74 for 5.0 s. For the v₁c₁, the number of new XSEL event hypotheses corresponds to the experience with the XSEL interactive analysis. These are the events that match the IDC rules and could be confirmed in interactive analysis. The v₁c₆ contains all the new events found by the v₁c₁, but they have more associated stations as the origin time residuals between 0.25 s and 5.0 s cannot be included in the latter case. Statistical significance of the v₁c₆ may suffer the probability fall related to the larger tolerance, but this fall is partially or fully compensated by the number of associated arrivals. The number of added stations is from 0 to 4. When no stations are added, the XSEL solutions for the v₁c₁ and v₁c₆ are identical. The importance of additional arrivals is in the change of event location and magnitude.

There are many additional to the v₁c₁ events created by v₁c₆. Formally, they all match the EDC and the quality criteria of WCC processing. Most of them have to be valid as their statistical significance similar or even larger (e.g., larger event weight, more associated stations, lower RMS origin time residual) to the XSEL events matching the REB events on May 24. The overall WCC performance for the Sea of Okhotsk aftershock sequence demonstrates high statistical power of the XSEL events confirmed by the REB match. This conclusion on the statistical power of the XSEL events is important for the analysis of the events missed in the REB. The XSEL events have the same statistical significance through the whole study, and thus, the same statistical power as that during the aftershock period.

A special question is the quality of the REB events not matched in the XSEL. The REB may contain some poor solutions often related to the higher noise level after the mainshock forcing phase mis-timing and mis-interpretation/association [Kitov, Sanina, 2025b]. Appendix 2 lists bulletins (only P-phases) for those six REB events which were not matched in the v₁c₁. The SNR values of associated phases are predominantly below the IDC detection threshold. These arrivals were added manually. Low SNR values indicate poor quality of these arrivals - the reason they were not detected in automatic processing. The arrivals with SNR between 1.0 and 2.0 in Appendix 2 are rather a challenge for visual identification. Two out of these six not-matched events consist only of such poor arrivals, one event has just one arrival above the automatic detection threshold. Five out of the six not-matched events occurred during the hour of the most intensive aftershock activity when the detection rate was the highest due to many aftershocks and very high number of secondary phases coherent to valid first P phases. These events are poor and are likely unreliable. Therefore, the XSEL may fail to create similar hypotheses. An extended study is needed with more powerful detection method based on WCC with noise stochatization [Adushkin et al., 2025].

Table 1. Statistics of WCC performance between 6:00 and 18:00, May 24, 2013.

Δt - origin time tolerance; Start, End - start and end hour of 6-hour intervals; SEL - number of REB events with SEL3 seeds; REB - number of pure REB events, SEL/Total - share of REB events with SEL3 seeds in the REB. For Strict and Weak, SEL and REB - number of matched REB(SEL3) and pure REB. Total REB - total number of matched REB. Total XSEL - total number of XSEL events. NEW - number of XSEL events new to the REB.

Finding the aftershocks in the still using noise suppression

The still period between 5:45 and 6:03 was processed together with a noise suppression technique based on a stochastic noise component of varying amplitude added to the filtered waveforms. This technique has shown high efficiency and allowed to find several aftershocks in the still period after the Kamchatka July 29, 2025, earthquake [Kitov et al., 2026]. The WCC processing is essentially the same except the stochastic component destroying the template coherent noise to a larger extent than the sought signal. The ambient noise after the major earthquakes mainly consists of the signals from the aftershocks, i.e. the events with lower than the mainshock magnitudes but similar source functions and propagation paths to IMS stations. This component of the ambient noise is well correlated with any template from the aftershock area and thus generates higher CC values than the usual seismic noise consisting of signals from a multitude of sources with various magnitudes and at different distances, not mentioning the wind and human activity as noise sources.

These higher CC values generate higher LTA at the CC-traces. Therefore, the sought signal has to have higher amplitudes in order to generate elevated CC values that can be detected at the same threshold level. An SNRcc value of 2.5 means that the STA is 2.5 times larger than LTA. By adding a stochastic noise component equal to the actual LTA one can reduce the CC level and thus the new LTA by a factor larger than 2.0, as numerous test calculations show [Adushkin et al., 2025; Kitov et al., 2026]. For the sought signal, the STA for the new CC-trace may lose just a small portion of around 20%. Then a conservative estimate of the new SNRcc will be (STA*0.8)/(LTA*0.5) = 4.0. The SNRcc gain is 60%. As the amplitude of the coherent noise component is not known in advance, by varying the stochastic noise amplitude in a wide range one can reach the almost maximum possible gain in SNRcc. This procedure needs extensive calculations and is most effective in finding the weakest signals in the noise coherent to the template and the sought signal. The basic version of WCC processing is efficient enough for different cases when hidden seismicity has to be recovered in a usual noise realizations.

There are many ways to add stochastic noise to real data. The simplest is to scale it to the maximum amplitude of the signal in a given time interval, which can be from several minutes to a day. In this study, one hour intervals are used with a 20-minute overlap with the next interval, which covers the travel times for all first P-wave phases. As the sought signal amplitudes can span over a few orders of magnitude, the number of various stochastic noise factors, StN, covering the whole range can be very large. The stochastic noise amplitude scaling might be more flexible with standard STA and LTA playing the role of local original noise amplitude to suppress. The standard STA and LTA time series are calculated first and then used stochastic noise scaling. For the LTA case, the product of a LTA estimate, a random number between 0.0 and 1.0 and StN is calculated for each time count and then added to the original trace for further WCC processing. For the STA case, a similar procedure is applied to each time count where standard STA/LTA is below a predefined threshold, which is not the detection threshold but a tuned parameter. When the STA/LTA ratio reaches the threshold, the LTA value for this count is used instead of STA for generation of the stochastic noise component. The length of fixed LTA window is defined by the STA/(fixed LTA) above the threshold rule.

The simplest approach with scaling of the maximum amplitude in the interval is used. The range of StN is from 0 to 20. The first value corresponds to the basic WCC progressing as an alternative to the noise suppression technique. The WCC processing is applied to each StN value in the range separately and the maximum SNRcc value is taken for each count. This is similar to standard detection procedure [Coyne et al., 2012]. Two 1-hour time intervals between 5:00 and 7:00 were processed at all involved IMS stations and the results for the pre-mainshock and the after-mainshock still periods are presented in Table 2. No events are in the REB except the mainshock which is excluded from the list. All 12 version/case pairs were used, but Table 2 presents only the limit pairs StN_v₁c₁, StN_v₁c₆, StN_v₂c₁, StN_v₂c₆. As a reference, the basic pair 0_v₂c₂ is listed. There were 13 XSEL events found by the StN_v₂c₆ pair before the mainshock with magnitudes from 2.64 (±0.46) to 3.45 (±0.47). The number of associated stations, Nass, varies from 5 to 12. The other three version/case pairs found from zero (StN_v₁c₁) to 4 (StN_v₁c₆) out of the 13 events. The 0_v₂c₆ pair detected 5 out of 13 events, but also added one event hypothesis not found by the StN_v₂c₆. This 0_v₂c₆ event (highlighted bold) at 5:10:43 was very close to the 5:11:04 event in the v₂c₆ and could be missed due to the CR rules. These numbers demonstrate that the technique using stochastic time series to suppress the ambient noise can find 2 to 3 times more events than the basic WCC processing despite the latter is able to find many events not detected in standard processing.

Table 2. Event hypotheses for the period 05:00-06:02, May 24, 2013. The still period is between 5:44:50 and 6.02:45.

In the 18-minute interval between the mainshock and the first aftershock, the StN_v₂c₆ pair found 3 events and the 0_v₂c₆pair found an event different from these 3 events at 5:59:01 (highlighted bold), which is again close to the 5:58:41 event. The first aftershocks at 5:56:20 is confirmed by all pairs but with different number of associated stations and m_b values. There is still a gap between 5:45 and 5:56 without aftershocks. Unlike the Kamchatka July 29, 2025, earthquake, the stochastic noise technique did not demonstrate a better performance than the basic WCC processing during the high-noise period. The source functions of the deep aftershocks might be too impulsive and the noise created by the such events in a relatively small volume is rather a sequence of impulses with varying amplitude at array stations where all secondary phases with higher slowness are effectively suppressed if also impulsive. In any case, further analysis is needed with various scaling of stochastic noise.

The evolution of seismic activity since May 19 recovered by WCC

The main results of the WCC processing for two weeks between May 13 and May 26, 2013 are shown in Figure 6. The weak (a) and strict (b) versions are presented separately, but each version includes all six origin time tolerance cases. There was revealed a significant rise in the number of found XSEL events for all twelve v_ic_j pairs. The ratio of the number of new XSEL strict events during the fourth quarter of 2013139 and the average number in the twenty six 6-hour intervals between the Q1/2013133 and the Q4/2013139 varies from 6 (52/9) for v₁c₆ to 37 (37/1) for v₁c₁. The latter value is especially important as these 37 new XSEL events in a narrow 6-hour interval are likely the most statistically significant among all cases. For the weak version, the same ratios decreased to 4 and 25 for v₁c₆ and v₁c₁, respectively. As a function Δt, these ratios practically follow a power law with the exponent of -0.67 (R²=0.97) for the strict version and -0.59 (R²=0.97) for the weak version. By all means, the spike from 1 to 37 per 6 hours is outstanding. No of these events were found by the IDC, but one can consider the Q4/2013139 as a start of the mainshock preparation process. Then the behavior of the seismic activity in various event quality bins Bⁱ_j may reflect the evolution of the earthquake preparation process. The number of events in the 6-hour interval after the mainshock was increased to the level of 45 for v₁c₁ to 83 for v₁c₆. For the weak version, ratio is 47/108. These events include the REB matched by the XSEL and new XSEL events.

Figure 6. Comparison of the number of detected events in 6-hour intervals using six different origin time tolerances and two versions of phase association parameters: a) strict; b) weak. Vertical red line - Q4/2013139, black line - mainshock.

In Figure 7, the evolution of seismic activity between 2013133 and 2013146 is presented by a) depth and b) event weight for the v₁c₄ pair. The origin time residual of 2 s corresponds to the threshold adapted by the IDC for the REB and the strict version likely gives events more reliable from statistical point of view. The depths of XSEL events are equal to the depths of the ME winning the potential CR. Therefore, the best MEs generate XSEL sequences with constant depths. Before Q4/2013139, the XSEL events In Figure 7a have lower depths on average and after the start of activity the events move to the depths where the most of aftershocks reside together with the mainshock. The event weights are lower in the low seismicity interval and grow significantly with the start of increased activity. On average, the XSEL events matching the REB events have larger weights but there are many events, mainly pure REB, which have the weights between 4.0 and 6.0 as the events in the pre-mainshock interval.

Figure 7. Depth a), event weight b), and the number of associated stations c) as a function of time for the v₁c₄ XSEL events. The start of seismic activity and the mainshock are presented by red and black vertical lines, respectively. The XSEL event matching aftershocks in the REB are highlighted by red circles.

Relative location of the XSEL events for v₁c₄ and v₂c₄ is shown in Figure 8. For the strict version the footprint is smaller than for the weak one as defined by the search radii. There are three different periods: Q1/2013133-Q3/2013139, Q4/2013149-Q1/2013144, and Q2/2013144-Q4/2013146. Overall, the ME are to the south of the mainshock and there are not too many XSEL events above 55° N despite the search area covers this part of the observed seismicity and some immediate aftershocks also were located in this part of the plate. The events before the mainshock do not reveal any specific gravity points with very high density, but their density within the area occupied by the northern MEs is relatively low during the pre-mainshock period for both strict and weak versions. The pure XSEL events after the mainshock also dispersed over the search area, but those matching the REB are close to them and concentrate near the northern MEs and the mainshock.

Figure 8. Locations of the XSEL events for v₁c₄ and v₂c₄ pairs.

Accurate location of the XSEL events is not the main objective because the low-magnitude events usually have large confidence ellipses and their absolute locations are not reliable. Statistical significance and power are essential for a reliable estimate of the seismicity evolution before the mainshock. For a more strict set of the LA defining parameters, including a smaller search area, one could obtain a tighter XSEL distribution with a lower number of events. The statistics of the event flux would change as a result, however. At the same time, even if to admit that a part of the XSEL events are false according to some strict rule, their presence is definitely the result of an elevated flux of signals similar to templates as Figure 5 demonstrates. In that sense, even the potentially false events, e.g., generated by valid first P-phases and some secondary phases created by reflections from the plate boundaries, support the observation of the increasing seismic energy generation started in the third or fourth quarter of May 19.

After the sharp peak in Q4/2013139 there were four peaks in the XSEL events number in 6h intervals with decreasing amplitude before the mainshock. The observed variations in relatively short time intervals partially mask the pattern of increasing/decreasing activity before the mainshock. Figure 9 shows the curves in Figure 6 smoothed by a simple moving sum of the four 6-hour intervals, MS(4), to retain the causality principle with no data from the future. A downward trend starts in the first quarter of 2013142, but for the weak version it is less significant, especially for larger Δt values. Seismic activity in the strict version after 2013133 is characterized by 3 groups with close figures: for Δ of 3.0 and 5.0 s, 1.0 and 2.0 s, and 0.25 and 0.5 s. The gap between these groups is larger than the distance between them in their pairs. On 2013138 the curve Δ=0.5 s diverts to the second group and the Δ=0.25 s curve stays alone despite it also starts to grow. For the weak version, all curves almost all time are separate and do not group for long. This is an important observation since the set of Bⁱ_j was constructed to reveal variations in the ratio of the events in the strict and weak versions. The B²_j/B¹_jratio should reveal the upcoming activity in various quality ranges defined by the origin time tolerance. The larger the case j, the earlier the signs of activity should be observed.

Figure 9. Same as in Figure 6 smoothes by a moving sum MS(4) applied. The start time of the occurrence rate growth in shown by vertical red line.

Figure 10 presents the weak-to-strict number ratio for all the six Δ values. Before Q3/2013139, these ratios are varying in a wide range and do not reveal any coherent behavior since the numbers of new XSEL event in the strict version are relatively low and demonstrate strong variation (see Figure 6). In Q4/2013139, the curves start to evolve almost in sync and the numbers of new events in the strict and weal versions rise significantly. After approximately two days of low variations, the curves start to grow, with those with the larger Δ starting earlier than for the Δ=0.25 s and Δ=0.5 s cases. The Δ=2.0 s and Δ=5.0 s curves reach their peak values first among all cases, with the curves Δ=3.0 s and Δ=1.0 s reaching their peaks immediately after. The Δ=0.5 s curve grows slowly to Q3/2013143 and then jumps to its peak on Q1/2013144. The Δ=0.5 s curve is approximately constant to Q3/2013143 and then also increases by almost a factor of 2 to its peak on Q1/2013144. Figure 11 shows this behavior in details with the only difference that not only new XSEL events are counted in, but the XSEL events matching the REB are also included. Therefore, these curves present "total" numbers, which are identical with "new" before the mainshock. The curves with Δ>1.0 s slowly fall to their minimum level in Q2/2013144 practically ignoring the mainshock. The other three curves also fall from Q1/2013144 to their respective minima in Q2/2013144. For the Δ=0.25 s case, this minimum is close to 1.0. When the IDC aftershock sequence stops, the curve start to diverge again.

Figure 10. The ratio of the number of new XSEL events in weak and strict versions in Figure 9.

The described behavior of the weak/strict ratios follows the expected scenario of the low-magnitude seismicity related to the earthquake preparation progressing from the smallest to the largest sizes or emitted seismic energies. The whole process of the Sea of Okhotsk earthquake preparation spans over 4.5 days. In takes 2.5 days of synchronized higher seismicity in all six event quality bins between Q4/2013139 and Q1/2013142 (see Figure 9). Then the seismic activity reaches its peaks in the lower quality bins without significant changes in the higher quality bins with Δ=0.25 s and Δ=0.5 s. In the final preparation stage, seismic activity reaches the top quality bin signaling the readiness to the mainshock initiation.

Figure 11. The ratio of the total (new and REB matching) number of XSEL events in weak and strict versions for the period between 2013139 and 2013146.

This qualitative description of the observed seismicity evolution is one of possible explanations. A comprehensive WCC processing over the entire dataset since 2001 has to be fulfilled to prove that this example is a case specific and there are no other similar seismic activity sessions without catastrophic earthquakes. Alternatively, other major earthquakes can be analyzed by the same WCC procedure in order to evaluate the evolution of pre-event seismicity in the same or different quality bins. The Sea of Okhotsk earthquake is a unique one. The source volume is isolated with no seismic events detected by the IDC foe more than one year. This makes any seismic activity within this volume to be directly related to the major event. Such earthquakes as the Tohoku and the July 29, 2025 Kamchatka occur in the extremely tectonically and seismically active environment. In some sense, this makes them random cases with unpredictable rupture trajectory and generated seismic energy. For example, the July 20, 2025 Kamchatka earthquake was very close to the July 29 event in time and space but failed to progress along the same rapture path. These and other major events have to be studied in a procedure similar that developed in this study.

Discussion

The WCC-based detection and phase association methods allow to reduce the detection threshold by almost an order of magnitude, create statistically significant event hypotheses of very weak sources, and to improve the estimates of relative and absolute location of these low-magnitude seismic events. The usage of array stations provides additional advantages to the WCC detection and estimation of azimuth and scalar slowness of valid arrivals. The primary IMS seismic network includes almost 30 arrays together with 6 arrays of the auxiliary network. The quality of the REB used in the CTBT monitoring and many civilian applications is mainly defined by the global distribution of array stations. When applied to the IMS seismic data, the WCC processing found additional 50% to 100% of new events in the studied areas, all confirmed by IDC analysts and promoted to lebview database account of the IDC as REB-ready events.

No events were detected by the IDC in the studied area of the May 24, 2013, Sea of Okhotsk earthquake for more than 14 months before it occurred. More than 200 events extra to the REB were found between May 13, and the mainshock of the Sea of Okhotsk earthquake using data from the IMS seismic stations and the WCC-based methods of detection and phase association. A sudden increase in the occurrence rate of the low-magnitude events was detected on the afternoon May 19th. The absence of events found by standard detection and phase association methods is an evidence of the problem in the study of the earthquake preparation processes. The relevant events occur below the detection threshold even when they are not hidden in the surrounding seismicity. More sensitive methods are needed.

The transition to the elevated seismicity at an ultra-low-magnitude level is likely related to the change in mechanical state of the volume of the following major earthquake as well as the change in other geophysical fields relevant to the deep earthquakes. The evolution of the numbers of these events in various magnitude ranges within the source volume may demonstrate some features, which can be related to the physical processes leading to the Okhotsk Sea earthquake. The observed pattern corresponds to the propagation of seismic activity from the lowest magnitudes and sizes to those compatible with the smallest detected aftershocks. This study is mostly focused on the solution of general methodological problems related to detection and phase association. A trial-and-error method was thoroughly used to obtain the first results demonstrating the potential of the WCC-based methods. Further studies are needed to adjust the set of defining parameters to the optimal resolution of the ultra-low-magnitude seismicity.

The final stage of the preparation started from 18 to 12 hours before the mainshock when concentration of the found events started to increase near the lower boundary of the strict LA version with the origin time tolerance of 0.25 s. This was a signal of the readiness to start. If to presume that the preparation processes before major earthquakes follow the same sequence a special attention has to be focused on the search for similar features of seismic activity below standard detection thresholds of global seismic networks. The study of a few major earthquakes has been started and the first results are promising.

The Sea of Okhotsk earthquake is a specific, almost laboratory, case since the source volume is almost fully isolated and its seismic activity is very low between the larger events. These features allow for very low-amplitude signals to be detected using the WCC-based methods. There is a possibility even to reduce the detection threshold by noise stochastization also called noise "whitening" as was demonstrated for the aftershocks of the Kamchatka July 29, 2025 earthquake and in this study. This method can be effectively used in noisy environment in seismically active areas.

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Appendix 1.

Table 1A. List of 70 master events

ORID (IDC)	epoch time, s	lat, deg	lon, deg	Nass	mb	depth, km
10135295	1380598702.792	53.168	152.861	222	5.78	582.31
9813664	1369374289.657	54.886	153.312	163	6.27	604.236
5761403	1260412253.013	53.448	152.746	163	5.35	660.977
9853071	1370948198.355	54.175	152.882	122	4.24	636.182
9824827	1369731519.192	54.258	153.314	89	3.84	629.503
9813875	1369380725.728	54.942	153.55	72	3.58	614.955
17205602	1554592969.038	53.327	153.648	63	3.4	514.569
5066131	1228431005.988	53.078	152.769	61	3.65	572.169
7135786	1297181407.808	53.181	153.345	58	3.78	518.525
4826051	1215223924.014	53.905	153.028	58	5.85	627.028
9813345	1369518064.658	53.61	153.426	56	3.56	539.297
23854429	1680745370.046	53.204	153.505	50	3.2	510.653
9884947	1372297849.439	54.151	153.47	50	3.58	635.21
21500256	1639353003.391	53.308	153.183	48	3.49	543.782
9813788	1369379233.433	54.641	153.26	47	3.28	616.858
9810781	1369441175.714	54.567	153.129	45	3.66	620.434
10168383	1381576364.328	54.425	153.153	38	3.28	613.307
9841029	1370474984.910	54.212	153.31	38	3.19	631.664
3230677	1115676914.851	53.31	153.481	35	3.59	501.793
14489716	1496701706.135	53.083	152.718	34	3.22	547.991
9820186	1369572061.070	54.869	153.089	33	3.21	620.501
9813674	1369406005.282	54.164	153.452	32	3.27	637.238
10721708	1396757164.906	53.153	153.228	31	3.24	515.628
9810966	1369381262.379	54.56	153.149	29	3.07	617.183
8369312	1328497880.060	53.702	153.743	29	3.11	500.868
4055723	1170136677.811	53.098	153.366	29	3.35	511.446
9811200	1369377323.512	54.345	153.366	28	3.25	627.911
9813886	1369403385.967	54.219	153.175	26	2.97	626.165
9813792	1369376719.598	54.382	153.041	26	3.66	628.772
9813791	1369379662.599	54.176	153.509	25	2.86	633.172
9811242	1369398901.028	54.524	153.163	24	3.05	618.703
9811209	1369377661.761	54.27	153.028	24	2.97	624.959
9809264	1369377742.847	53.161	153.169	22	2.98	511.99
2699433	1092728752.311	53.639	153.856	22	3.23	522.065
9811104	1369421983.175	54.558	153.103	20	2.83	616.142
9810705	1369377079.908	55.131	153.765	19	3.23	603.144
24428519	1690114315.736	53.204	153.673	18	2.8	503.885
10886687	1400716754.619	54.463	153.322	17	2.88	613.972
7572355	1304827534.681	53.368	153.5	17	2.8	506.299
3088584	1109401670.402	53.491	153.694	17	3.02	501.396
1972498	1067433219.035	53.344	153.554	17	3.27	514.242
9810611	1369390865.824	54.827	153.532	16	2.63	620.625
9809372	1369382410.885	54.184	153.365	16	2.75	633.731
29423659	1764193387.507	53.475	153.836	15	3.04	510.526
28634412	1753832718.971	55.927	152.869	15	3.8	585.023
12375814	1441527964.074	53.186	153.509	15	2.79	508.303
9822022	1369557714.879	53.543	153.734	15	2.88	508.593
9813031	1369385141.779	54.437	153.511	15	2.84	616.076
9809262	1369382861.729	54.649	153.85	15	2.78	567.235
10234531	1383401230.684	54.276	153.045	14	2.7	622.781
4429214	1193146082.919	54.006	153.95	14	3.13	509.094
9813147	1369387000.640	54.05	153.364	13	2.62	627.19
9812995	1369385016.762	54.129	153.365	13	2.68	633.355
9811489	1369377821.856	54.531	153.235	13	2.81	609.585
9811181	1369377279.646	54.18	153.506	13	3.16	641.86
9821981	1369545820.709	54.901	153.316	12	2.65	565.503
9811284	1369375365.180	55.282	154.02	12	3.93	606.697
24970171	1698470745.129	53.003	152.641	11	2.84	540.441
9887080	1372297878.828	54.934	152.816	11	2.73	699.052
9857445	1371270785.773	54.847	153.268	11	2.72	614.875
9853538	1371015355.260	54.752	153.587	11	2.85	599.315
9811275	1369411887.652	54.863	153.404	11	2.71	620.76
9811250	1369400392.260	54.109	152.842	11	2.63	628.53
9811178	1369377204.923	54.262	153.127	11	3.14	638.519
3175041	1112732892.358	53.267	153.544	11	2.76	508.515
22386776	1655810590.838	53.833	154.078	10	2.98	507.946
9826638	1369989297.098	54.425	153.371	10	2.53	612.616
9820010	1369507278.262	54.707	152.895	10	2.43	627.294
9813299	1369389498.103	54.794	153.197	10	2.5	608.356
9813000	1369385056.226	54.176	153.144	10	2.57	626.751

Appendix 2.

Table. The not-found REB events for the strict version and Δt=0.25 s

Lost internet connection to the CTBTO web site

2026-03-23T08:16:00.003+01:00

Russia is a State Signatory of the CTBT since 1996. There are many Russians working at the CTBTO since 2001. Communication with the CTBTO is important for many researchers and public. I cannot reach the CTBTO web site to check the IMS map. It looks like CTBTO is a threat to Russia.

Stopped AI at W11. i9 works much better now

2026-03-20T07:27:00.002+01:00

I am not sure that AI does not help to the majority of people working with W11. It's possible that it may be of service for simple operations repeated every day. I do intensive calcuations using my own Fortran program which AI considideres as dangerous. They are not in its knowledge system as it did not exist when it was trained. After I have switched AI off - all dozens of simultaneous processes at my i9 core are stable and stationary. As an additional remedy the internet connection was stopped as well. Big relief.

Low-magnitude seismic activity between the Kamchatka July 20 and July 29, 2025, earthquakes. Spatio-temporal evolution recovered using waveform cross-correlation

2026-03-19T07:49:00.002+01:00

ARXIV.ORG https://arxiv.org/abs/2601.15302

Low-magnitude seismic activity between the Kamchatka July 20 and July 29, 2025, earthquakes. Spatio-temporal evolution recovered using waveform cross-correlation

Ivan O. Kitov

The M8.8 Kamchatka earthquake on July 29, 2025 was one of the largest in the first quarter of the 21st century. It deserves a thorough analysis including the preparation process. A smaller M7.4 earthquake occurred on July 20 with its epicenter within the confidence ellipse for the July 29 event. The aftershock sequence of the July 20 earthquake and the evolution of seismicity within the Kamchatka Peninsula region during 10 days period before the July 29 event may provide important information on the earthquake preparation and initiation processes. The CTBTO's International Monitoring System is one of the most sensitive global seismic networks comprising high-resolution array stations with enhanced sensitivity relative to three-component stations at the same locations. The International Data Centre of the CTBTO processes IMS data automatically and interactively to create a Reviewed Event Bulletin (REB), which serves as a source of information for the International Seismological Centre. Waveform cross-correlation (WCC) allows for additional detection capabilities to the IMS data and IDC processing when repeated seismicity is analyzed. The aftershock sequence of the July 20 earthquake is recovered using the WCC-based detection and phase association techniques as applied to the IMS data in order to accurately describe the spatio-temporal evolution of seismic process just before the July 29 event. With the reduced detection threshold, smaller events are found in the zones where the REB has no located sources. This finding opens up the possibility for a more detailed study of seismic and mechanical processes before the July 29 mainshock.

An example of regional seismicity recovery on June 22, 2020, using waveform cross-correlation

2026-03-18T17:06:00.000+01:00

Full paper version is available on arxiv.org - [2603.00094] An example of regional seismicity recovery on June 22, 2020, using waveform cross-correlation

Research Square

Abstract

June 22nd, 2020 was an important day for nuclear test monitoring. The US undersecretary, Thomas DiNanno, made an official claim that a secret nuclear test was conducted at the Lop Nor testing site on that day. However, the Provisional Technical Secretariat (PTS) of the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) reported that there were no seismic events consistent with a nuclear explosion on that date. This means that the event was either hidden under the threshold of the international monitoring system (IMS), or it was missed by the international data center (IDC). Alternatively, no event occurred. All scenarios are of interest to the scientific community. The routine processing of seismic data by the IDC is well documented in open sources. The threshold for detection is not uniform across the globe, especially in continental areas. Additionally, it is not low enough to detect weapon-sized explosions using the cavity decoupling method. There are methods to lower this threshold using waveform cross-correlation (WCC) techniques. On June 22th, 2020, the IDC ran a preliminary pipeline for processing seismic data from the IMS. This was done in a testing mode. Since 2020, the development of WCC methods has allowed for revisiting cases and obtaining high-quality reports on events that were not reported five years ago.

Key words: CTBTO, IMS, IDC, waveform cross correlation, cavity decoupling

Spatio-temporal evolution of low-magnitude seismicity before the May 24, 2013, Sea of Okhotsk earthquake recovered by waveform cross correlation. Is it an earthquake prediction case?

2026-03-18T16:52:00.001+01:00

Abstract

Key words: Sea of Okhotsk earthquake 2013, earthquake prediction, IDC, IMS, waveform cross correlation

Trump has won the miltidimentional war

2026-03-16T14:33:00.005+01:00

Nuclear materials buried very deep. Oil cost is high and pours money into the oil(!) billionairs pockets (not others). NATO is dismissed as worthless. No obliagtions, no oil for allies (actually the worst enemies as T does not trusts them), industries run to the US for cheap everything, money run from arab countries to the US for safety, weapon producers are full of new orders (no limit) ... Why someone thinks that T's lost?

P.S. This is also the solution for Greenland. This group of cowards and traitors is not a problem. Ignore as nothing.

AI in Windows 11 is a danger for my work on earthquake prediction

2026-03-16T13:53:00.003+01:00

Today switched off AI in Windows 11. It declares my own Fortran programs a danger for safety and stops them. It takes time to mitigate the risks and harms made by MS AI and I am busy with calcualtions of potential algorithm to predeict earthquakes. AI should help MS to organize their work.

The risks of neighboring US military bases was heavily underestimated. New balance to be found

2026-03-14T09:15:00.002+01:00

A US base is the point of power projection. The risk of escalation was much much underestimated by financial guru recommended huge investments near the US protecting bases. There are more than 800 such points worlwide with the underestimated risks for any investment and even development. The new profit/risk balance depends on how much the investors lose in the months to come. Unimaginable task for the next decades of declining US power as its economy shrinks in relative terms.

Мусоргский - Ночь на Лысой горе

2025-11-18T10:14:09.091+01:00

современная музыка. каждая нота и все вместе

В Европе опять сошли с ума или самообманываются. Видят N-лучи.

2025-10-06T19:47:00.000+02:00

Ситуация с различными дронами и истребителями в Европе, которые видят все, напомнила мне замечательный случай из позорной истории французской науки. Он замечателен тем, что десятки, если не сотни французских, как и несколько ученых из соседних стран, вдруг увидели N-лучи. После X-лучей все хотели сделать великое открытие. Были написаны десятки статей, выданы французские высокие степени и премии. Американский физик Роберт Вуд разоблачил этот научный подлог и сумасшедший фарс самым тривиальным способом.

Вот как это описано в книге Сибрука "Роберт Вильямс Вуд". Кстати, издана в Ленинграде в 1946 году под редакцией С.И. Вавилова!

Вот рассказ самого Вуда о том, что было, по всей вероятности, величайшим научным заблуждением нашей эпохи. "Поздней осенью 1903 года профессор Р. Блондло, глава Физического отделения в университете в Нанси, член Французской Академии, широко известный исследователь, провозгласил открытие новых лучей, которые он назвал N-лучами, со свойствами, далеко превосходящими лучи Рентгена. Прочитав о его экспериментах с этими лучами в Comptes Rendus Академии, основном научном журнале Франции, я попытался повторить его наблюдения, но мне ничего не удалось, хотя я потратил на это целое утро. Согласно Блондло, лучи излучались спонтанно многими металлами. Как детектор можно было употреблять очень слабо освещенный лист бумаги, ибо -- чудо из чудес -- когда N-лучи попадали в глаз, они усиливали его способность видеть предметы в почти темной комнате. Огонь открытия, зажженный Блондло, теперь ярко разгорелся, и его раздувало десятка два других исследователей. О них было помещено в Comptes Rendus двенадцать статей до конца года. А. Шарпантье, зна-менитый своими фантастическими опытами с гипнозом, утверждал, что N-лучи исходят из мускулов, нервов и мозга, и его авторитетные заявления были опубликованы в Comptes Rendus с полным подтверждением д'Арсонваля -- первого авторитета Франции по электричеству и магнетизму. Затем Блондло объявил, что он сконструировал спектроскоп с алюминиевыми линзами и призмой из того же металла и получил спектр из линий, разделенных темными интервалами, показывающих, что имеются N-лучи разной преломляемости и длины волны. Он измерил их длины волн. Пламя исследования N-лучей разгорелось в целый пожар. Жан Беккерель, сын Анри Беккереля, который открытием излучения урана положил основу для открытия радия Кюри, утверждал, что N-лучи можно передавать по проводу, так же, как свет передается по изогнутой стеклянной палочке благодаря внутреннему отражению. Один конец проволоки около слабо светящегося "детектора" вызывал колебание его интенсивности, в то время как другой конец проволоки водили по черепу живого человека. Если человека усыпляли эфиром, N-лучи от его мозга сначала усиливались, а потом слабели, по мере того, как он крепче засыпал. Он утверждал, что металлы можно "анестезировать" эфиром, хлороформом или спиртом, после чего они переставали испускать и передавать N-лучи. Биологи, физиологи, психологи, химики, ботаники и геологи присоединились к этой веселой компании. Нервные центры позвоночника изучались в связи с болезнями. или повреждениями, по их излучению N-лучей. "Обнаружилось", что лучи испускались растущими растениями, овощами и даже трупом человека. Шарпантье нашел, что слух и обоняние также обострялись под их влиянием, как и зрение. Колеблющийся камертон испускал сильные N-лучи. В начале лета Блондло опубликовал двадцать статей, Шарпантье -- тоже двадцать, и Ж. Беккерель -- десять, все с описанием новых свойств и источников N-лучей. Около ста статей о N-лучах были опубликованы в Comptes Rendus в первой половине 1904 года. N-лучи поляризовали, намагничивали, гипнотизировали и мучили всеми способами, какие можно было выдумать по аналогии со светом, но все явления были способны наблюдать только французы. Ученые во всех других странах держали себя открыто скептически и смеялись над фантастическими измышлениями. Но Французская Академия увенчала работу Блондло своим признанием, присудив ему премию Лаланда в 20 000 франков и золотую медаль -- "За открытие N-лучей". В то лето мы жили в Бег-Мей, в Бретани, и я потерял связь с научными фокусами в Нанси, но в сентябре я поехал в Кембридж на собрание Британской Ассоциации Наук. После сессии некоторые из нас собрались для обсуждения вопроса: что же делать с N-лучами. Из нашей группы особенно яростно был настроен профессор Рубенс из Берлина, с которым я был тесно связан, еще будучи студентом. Он особенно возмущался, так как кайзер приказал ему приехать в Потсдам и продемонстрировать лучи. Потратив попусту две недели на попытки воспроизвести опыты французов, он был очень смущен необходимостью признаться кайзеру в своих неудачах. Он повернулся ко мне и сказал: "Профессор Вуд, а не могли бы вы теперь поехать в Нанси и проверить их эксперименты?" -- "Да, да", -- поддержали его все англичане, -- "это -- идея! Поезжайте!" Я предложил, чтобы поехал сам Рубенс, как главная жертва, но он сказал, что Блондло крайне любезно ответил на все его письма, сообщив все малейшие детали своей работы, и что будет очень неудобно, если он поедет разоблачать его. "Кроме этого, -- добавил он, -- вы ведь американец, а американцы умеют делать все..." Итак, прежде чем присоединиться к своей семье в Париже, я посетил Нанси и встретился с Блондло, по его приглашению, в его лаборатории ранним вечером. Он не говорил по-английски, и я избрал средством разговора немецкий, чтобы он чувствовал себя свободно и мог говорить конфиденциально со своим ассистентом, который, невидимому, был главным ассистентом лаборатории. Сперва он показал мне лист картона, на котором. было нарисовано светящейся краской несколько кругов. Он пригасил газовое освещение и просил меня обратить внимание на увеличение интенсивности их свечения, после того, как на них направили N-лучи. Я сказал, что ничего не замечаю. Он ответил, что мои глаза недостаточно чувствительны, и это ничего не доказывает. Я спросил его, можно ли мне ставить и убирать на пути лучей непрозрачный свинцовый экран, в то время как он наблюдает флуктуации на экране. Он ошибался почти на 100 процентов, и говорил, что интенсивность меняется, когда я ничего не двигал, и это уже доказывало кое-что, но я держал язык за зубами. Затем он показал мне слабо освещенные часы на стене и пытался убедить меня, что он может различить их стрелки, если держит над глазами большой плоский напильник. Я спросил его, можно ли мне подержать напильник у него над глазами, так как я заметил на его столе плоскую деревянную линейку, и вспомнил, что дерево было как раз одним из немногих веществ, которые никогда не излучали N-лучи. Он согласился. Я нащупал в темноте линейку и держал ее перед его лицом. О, да -- он прекрасно видел стрелки. Это тоже кое-что мне доказало. Но решительная и главная проверка была еще впереди. В сопровождении его ассистента, который уже бросал на меня довольно враждебные взгляды, мы прошли в комнату, где стоял спектроскоп с алюминиевой призмой и линзами. Вместо окуляра, этот прибор имел вертикальную нить, окрашенную светящейся краской, которую можно было передвигать вдоль той области, где предполагалось наличие спектра N-лучей, поворачивая круг с градуировкой по краю. Этот круг вращал горизонтальный винт с подвижной гайкой, на которой и была установлена нить. Блондло сел перед прибором и стал медленно вращать круг. Предполагалось, что нить, пересекая невидимые линии спектра N-лучей, начинает ярче светиться. Он называл мне деления шкалы для ряда линий, читая их при свете слабого фотографического красного фонаря. Этот опыт убеждал некоторых скептических посетителей, так как он повторял свои измерения в их присутствии и всегда получал те же числа. Он утверждал, что смещение нити на 0,1 мм было уже достаточно, чтобы ее яркость изменилась. Когда я сказал, что это невероятно, так как щель спектроскопа имела ширину 2 миллиметра, он ответил, что это -- одно из необъяснимых свойств N-лучей. Я попросил его повторить измерение, потянулся в темноте и снял со спектроскопа алюминиевую призму. Он стал кружить круг, отсчитывая опять те же числа. Прежде чем включили свет, я поставил призму на место. Блондло сказал своему ассистенту, что его глаза устали. Ассистент стал уже вполне очевидно подозрительным и просил Блондло дать ему самому повторить опыт для меня. Прежде, чем он потушил свет, я заметил, что он очень точно поставил призму на ее маленькую подставку, углами как раз на краю металлического диска. Как только свет погас, я двинулся по направлению к прибору, сделав шаг с некоторым шумом -- но ничего не тронул. Ассистент начал вращать круг, и вдруг сказал Блондло быстро по-французски: "Я ничего не вижу. Спектра нет. Я думаю, что американец что-нибудь сдвинул" -- после чего сразу же зажег свет и внимательно осмотрел призму. Он уставился на меня, но я не выдавал своих мыслей. Этим сеанс окончился, и я сел в вечерний поезд и отправился в Париж. На следующее утро я послал письмо в Nature. Журнал подробно изложил мои наблюдения, опустив, однако, сообщение о двух инцидентах в конце вечера и обозначив лабораторию просто как ту, где было выполнено большинство опытов с N-лучами. La Revue Scientifique, французский полупопулярный научный журнал, опубликовал перевод моего письма и начал анкету, прося французских ученых высказать свое мнение о реальности N-лучей. В последующих номерах было напечатано до сорока писем, и только полдюжины из них защищали Блондло. Наиболее агрессивным было письмо Ле-Беля, который говорил: "Какое зрелище представляет собой французская наука, если один из ее значительных представителей измеряет положение спектральных линий, в то время как призма спектроскопа покоится в кармане его американского коллеги!" Только две статьи о N-лучах появились после этого в Comptes Rendus. Должно быть, это были запоздавшие. На ежегодном заседании Академии в декабре, где была вручена премия и медаль, провозгласили, что она присуждается Блондло "за его долголетние труды в науке". Трагическое разоблачение в конце концов привело к сумасшествию и смерти Блондло. Он был вполне искренний и большой человек, у которого "зашел ум за разум", возможно, в результате самогипноза или чрезмерного зрительного воображения после многих лет работы с приборами в темноте. То, что сделал Вуд, против собственного желания, но с научной беспощадностью, было для него coup de grace. Развязку охарактеризовал А.А. Кемпбелл Свинтон, член Королевского Общества, в Westminster Gazette: "...высшая ученая инстанция Франции признала его, и все, казалось бы, шло хорошо, пока американский профессор физики Р. В. Вуд из Балтиморы, теперь -- иностранный член Лондонского Королевского Общества -- не взорвал полностью и навсегда все открытие, показав, что Блондло продолжал видеть спектр, которого никак не могло получиться, даже если бы он и был перед этим!"