Abstract
Waveform
cross-correlation (WCC) applied to data from seismic arrays allows for the reduction
of the detection threshold by approximately an order of magnitude. When applied
to the data of the International Monitoring System, the smallest WCC detected events
were by at least one magnitude unit lower than those reported by the
International Data Centre (IDC) and revealed that the pattern of low-magnitude
activity prior to the July 29, 2025, earthquake was similar to that prior to
the May 24, 2013, Sea of Okhotsk earthquake. The consistent increase in the
number of events with magnitudes approaching the corner value of the Kamchatka
recurrence curve can likely be used as a precursory indicator of a mega-earthquake
preparation. The WCC-based events are characterized by detections with a
signal-to-noise ratio below the IDC detection threshold and are often not
visible to analysts. This makes the statistical significance of the WCC event
hypotheses uncertain due to the absence of a random noise reference and the potential
side-sensitivity of the IMS arrays to high-amplitude signals from remote
sources. Both problems are addressed.
A computer-generated random noise is used to
calculate a WCC bulletin according to the same procedure as was used for the
actual data. This exercise shows a negligibly low number of WCC events
generated by random-noise waveforms and confirms the statistical significance
of the WCC-based events. The side-sensitivity is modelled using the March 11,
2011, Tohoku earthquake. When only master events (MEs) within the Kamchatka
region are used in the WCC processing, a large number of false events are
generated. When MEs from the Tohoku zone are added, all false events disappear
since the Tohoku MEs win the conflict resolution process.
The random noise added to the actual data can suppress false events created by
the Kamchatka MEs from Tohoku signals, but it also suppresses valid events in
the Kamchatka region. When the random noise is scaled to a small fraction of
the maximum amplitude within the processed interval, the WCC detection is
enhanced with more detections and WCC-based events created. This is an effect
similar to noise “whitening”, which makes the matched filter detector more
sensitive and closer to its optimal performance under stochastic noise
conditions. In the subsequent study, this stochastic noise effect will be used
to improve the WCC bulletins for the Kamchatka and Sea of Okhotsk
mega-earthquakes. A set of optimal random noise scaling factors was estimated
for further investigations.
Key words: waveform cross-correlation, Kamchatka megathrust earthquake, random
noise, seismic array, International Monitoring System, International Data
Centre
Introduction
Waveform cross-correlation (WCC) is an effective method to reduce the
detection threshold in various seismological tasks known since the beginning of
the progress of digital seismology [Israelsson, 1990; Joswig, 1990]. The gain
in the number of detected events can reach an order of magnitude for regional
and teleseismic networks [Schaff and Richards, 2004]. Another important feature
provided by WCC is the possibility of extremely accurate measurements of the
relative arrival time as achieved by synchronization of a template and sought
signals. The accurate arrival times are converted into a high location accuracy
of the sought events relative to the master event (ME), which is the source of
signals detected at the stations associated with this ME [Waldhauser and
Schaff, 2008; Selby, 2010]. These features lead to significant improvements in
the completeness, consistency, and accuracy of seismic catalogs and bulletins
[Bobrov et al,. 2014, 2016ab, 2017].
The WCC detector requires high-quality waveform
templates. Both actual signals and synthetic seismograms [Bobrov et al., 2016b] can be used as templates,
and the latter are more efficient in some cases [Kitov et al., 2016]. Between actual waveforms and synthetics lie semi-synthetic
templates generated from a large number of actual records processed by various
mathematical methods, from a simple SVD to modern AI. The areas with intense
seismicity, such as the Kamchatka region, provide a sufficient number of repeating
events to obtain the best possible set of representative MEs and their
templates.
Seismic phased arrays are like the magnifying glass in
the era of van
Leeuwenhoek that allows the visualization of
signals not detectable by three-component (3-C) stations. On average, the gain
in detection threshold for an array is proportional to the square root of the
number of individual sensors distributed within some area on the surface
[Schweitzer et al., 2012]. Arrays are
designed to magnify a signal, i.e. to increase the signal-to-noise ratio (SNR),
by noise suppression via the destructive interference when the signals from
individual channels are stacked. Time delays between arrivals at individual channels
for a given plane wave with a known apparent velocity vector can be calculated
from geographical positions of the sensors.
The accuracy of the time-delay prediction in the beamforming
method depends on the difference between the theoretical and the actual plane
wave’s apparent velocity. The larger the difference, the higher the beam-loss,
i.e., the power of the signal obtained with theoretical arrival times relative
to that which could be obtained with the actual arrival times [Schweitzer et al., 2012]. The WCC method
applied to seismic arrays possesses not only the advantage of the matched
filter detector [Turin, 1960] but also suffers no beam loss effect, as the
sought and template signals must be fully synchronized at individual sensors.
Any deviation from absolute synchronization must be due to the difference between
the master and sought events’ relative positions, and, thus, can be accurately
predicted across the channels.
The combination
of WCC and arrays provides the most efficient detection method used for
scientific research and applied purposes. The International Monitoring System
(IMS) includes a global seismological network of 170 stations (50 primary and
120 auxiliary) in its final configuration under the Comprehensive Nuclear-Test-Ban
Treaty (CTBT) provisions [CTBT, 1996]. Not all stations are in operation yet,
but there are already 34 working arrays. They were successfully used in various
studies from far-teleseismic to near-regional distances. One such study focused
on the May 24, 2013, Sea of Okhotsk mega-earthquake demonstrated the capability
of the WCC and arrays symbiosis in the detection of a large number of low-magnitude
earthquakes immediately prior to the mainshock. These events were not detected
by the International Data Centre (IDC) or any other seismological agency. At least, there are no records in the ISC
database.
The evolution of
low-magnitude seismicity before mega-earthquakes is a potential indicator of the
approaching mainshock [Schaff et al.,
2025]. Both seismic arrays and WCC are mandatory ingredients of a successful
investigation into low-magnitude seismicity, but not all detected events can be
confirmed visually by IDC analysts as they are mainly deep in the ambient
noise. The WCC method can find very weak signals in line with the discrete
Fourier transform estimating amplitudes of high frequency harmonics orders of
magnitude lower than those of at lower frequencies. However, the event
hypotheses built in the WCC pipeline [Kitov, 2026d] are then missing one of the
principal sources of their statistical significance. In order to provide
sufficient information on the probability of an event hypothesis created in the
WCC pipeline of being valid, one has to present the case of random distribution
of arrivals as a reference.
The ambient
noise is not purely stochastic, as it created by a finite mixture of regular
seismic phases from various sources. This makes any experiment with the ambient
noise intended to represent a random process, limited in predictive power, as
the sought signals for a given template can be hidden in this very noise. A
computer generated random noise is a better choice, as it must fit several
principal requirements [Press et al.,
1986], but its actual properties are case-dependent. Stochastic noise generated by a computer program
is a tool to replace or suppress any actual signal to an infinitesimal level.
It is used in this study to mimic actual waveforms in the WCC pipeline to
produce a reference bulletin to compare with the actual cross-correlation
Standard Event List (XSEL), which is an automatic bulletin similar to Standard
Event List 3 produced by the IDC using the same IMS data [Coyne et al., 2012].
However, one can
use a random time series to suppress noise components coherent with the
templates [Adushkin et al., 2025].
The gain can be significant for both a relatively high SNR and the weakest
signals. This method was successfully applied to the WCC processing of the July
25, 2025, Kamchatka earthquake data during the hour following the mainshock
[Kitov et al., 2026]. Several aftershocks were detected during the
first ten minutes after the start of the coseismic phase. The first minutes
after megathrust events are well-known as a still period without any
aftershocks detected. The focused study of the WCC detector with added random
noise has shown high efficiency in cases where the ambient noise and the template
are coherent [Kitov, 2026c].
This study extends
the previous work on low-magnitude seismicity before the July 29, 2025,
Kamchatka earthquake [Kitov, 2026d] in three directions, all related to
stochastic noise. The first part is devoted to the simulation of actual
waveforms with random noise generated by the ran3 program [Press et al.,
1986]. The results of this simulation are compared with the results obtained by
the WCC pipeline for actual data. This comparison confirms the statistical significance
of the XSEL events used to reveal the growing low-magnitude seismic activity
potentially serving as a precursory variable for the earthquake prediction. The
second part is devoted to the investigation of the side-sensitivity of the WCC
applied to array stations in view of the possibility of some XSEL events be
false, as they are created from phases generated by strong sources outside of
the studied area. The random seismic noise is used here to vary the irrelevant
signals’ amplitude to estimate side-sensitivity. The third part encompasses the
advantages of the positive stochastic noise effect on the WCC pipeline. This is
a feasibility study to compare selected results of the previous work with new
results obtained with the WCC enhanced by random noise. A thorough testing of
various stochastic noise amplitudes had been accomplished before the optimal
value was estimated.
WCC
pipeline with stochastic noise as an actual waveform
Master events
The effect of
stochastic noise on the WCC processing starts from the selection of master
events (MEs) and signal templates at associated stations. There are thousands
of potential MEs in the studied region. For example, Figure 1 shows 6628 REB
events between July 20 and December 4, 2025. The 100 best MEs were selected by
[Kitov, 2026d] from the entire REB set from 2001 to 2023. The selection process
was based on the pair-wise cross-correlation of each event with all its neighbours.
The events that detected the largest number of neighbours were selected for the
MEs set. The selected MEs were distributed according to their positions to the
nodes of a regular Global Grid with an average spacing of approximately 1.25°
[Kitov et al., 2016]. From this
original global set consisting of approximately 42,000 MEs, the 100 best MEs
were selected for the WCC processing of the July 29, 2025, Kamchatka
earthquake.
Figure 1. Selected master events for the
Kamchatka (twenty MEs) and Tohoku (twelve MEs) regions. All 6,628 REB events in
the Kamchatka aftershock sequence from July to December 2025 are plotted. The
best 100 MEs are also shown to illustrate the distribution of the twenty MEs
used in this study.
The results of
the WCC processing revealed an increase in the low-magnitude earthquakes
activity prior to the mainshock, which is interpreted as a precursor to the
coseismic phase. One of the questions
raised in [Kitov, 2026d] was the statistical significance of the event
hypotheses created by the WCC pipeline. There is no direct way to measure it,
as the data set is not complete and the underlying statistical distributions
are not available. As an alternative, a stochastic distribution of detections
can be generated and used as an input to the Local Association (LA) and
Conflict Resolution (CR) processes described in [Kitov, 2026abc]. One of the
best ways to generate a stochastic detection set is to use a stochastic time
series instead of actual data in the WCC detection process. The choice of MEs
and the template signals at the IMS stations associated with them is crucial
for the evaluation of the random detection case. The number of MEs can be
limited, but their distribution has to correspond to the zone of aftershock
sequence of the J29 event shown in Figure 1. For this feasibility study, twenty
MEs were selected by their positions and the number of associated stations.
These MEs possess templates with the largest SNR values estimated by the IDC. Red circles in Figure 1 present the set of
twenty MEs. It is worth noting that the
deepest earthquakes are also presented in this set. Black dots represent the
set of twelve MEs for the March 11, 2011, Tohoku earthquakes. They are used to
study the side-sensitivity of the IMS array stations to large events far away
from the studied region of Kamchatka. The IDC parameters for all 32 MEs are
listed in Appendix 1.
From
Figure 1, it is clear that the 20 MEs may not perform as good as the best 100
MEs in terms of the number of event hypotheses in the XSEL. However, the
performance and general properties of the selected 20 MEs are compatible with
all other MEs used in the previous study [Kitov, 2026d] and in the prototype
WCC routine processing conducted by the IDC.
WCC detection with stochastic noise
A
stochastic time series is needed for the evaluation of the statistical
significance of the event hypotheses created in the WCC processing. An XSEL
obtained with a given set of defining parameters has to be compared with the
XSEL obtained in a “random” case. The latter includes a set of detections
randomly distributed over the processed interval and having SNRcc values
obtained from a random distribution in the range characteristic for the WCC
detections generated by a stochastic time series. For the WCC pipeline, the
best approach is to generate a stochastic time series and process it as an
actual data set in the same study.
Generation of a
stochastic time series without serial correlations is a case dependent problem
[Press et al., 1986]. The selection
of the ran3 Fortran code to generate
random numbers converted into a stochastic time series was dictated by the original
WCC pipeline code written in Fortran 77. It
guaranteed at least 2,000,000,000 random numbers matching the requirements of
the data at the IMS array stations and was sufficiently quick not to increase
the total calculation time. This random number generator was also used in [Adushkin et al.,
2025] to model stochastic noise added to the actual time series for the initial
assessment of the gain in the WCC detection threshold.
The
SNRcc frequency distributions obtained from a stochastic time series for
stations PETK, PDYAR, MKAR, KURK, and WRA are shown in Figure 2. The stochastic
time series was added to the actual data for the July 28, 2025 (jdate=2025209).
This was a day of relatively low seismic activity within the studied region,
and a day approximately 24 hours prior to the July 29 Kamchatka earthquake. The
stochastic waveform was scaled to the maximum amplitude of the actual time
series in a given hour for each channel and filter individually. The WCC
processing has an hourly rate, with an overlap with the next hour by six minutes
to provide a smooth transition to the next interval and avoid the edge effects
for the cross-correlation time windows (CCWW) and long-term average amplitude (LTA)
calculations. The last fifteen minutes of the processed hour are saved for the
next hour, and the total processing interval is 81 minutes long. The SNRcc values are estimated for each tome count
within the processed hour according to the WCC detection procedure with the
total number of samples equal to the sampling rate multiplies by 3,600 seconds.
The estimates for the full day of 24 hours are counted in 0.1-unit bins. The
obtained curves are shown for each of the 20 MEs, with lower numbers of MEs at
some stations due to the late start of operation or longer periods of upgrade
and maintenance.
For
station PETK in Figure 2a, all nineteen available MEs show nearly similar
behaviour with small deviations. There is a peak near 1.4 followed by a quasi-exponential
roll-off down to SNRcc level of 3. Then, some curves demonstrate low-amplitude
fluctuations, and all the curves except four do not reach the SNRcc level of 4.
There are four curves having SNRcc values above 4.0 but below 5.0. From the
REB, station PETK is associated with almost all events in the studied area
during its operational period. For the
Local Association process, is has the maximum event weight of 1.0, which represents
the highest probability of a station being associated with the event hypotheses
in the designated area. Station PETK is a major anchor for valid event
hypotheses. Figures 2b and 2c illustrate the curves similar to those for
station PETK. Stations PDYAR and MKAR are two small-aperture arrays. All other
small-aperture IMS arrays not shown here are characterized by similar SNRcc
frequency distributions, including the maximum SNRcc level below 5.
The full set of principal
Event Definition Criteria (EDC) used in the Local Association process defined
in [Kitov, 2026d] is listed in Appendix 2. They include the total event weight
determined as the sum of the weights of all associated stations. For the events with three to five associated
stations, one of these stations must have a weight above 0.855 for the strict
case and 0.8 for the weak case of the LA. Also, this mandatory station must
have SNRcc larger than 5.0 and 4.5, respectively. Therefore, the stochastic
time series practically never produces appropriate SNRcc values at station PETK
to match this minimal SNRcc criterion. PETK is practically excluded from the
event creation procedure, except for events with 9 or more associated phases
where the SNRcc restrictions are lifted.
The EDC are used
in the WCC pipeline, and the results of this processing depend on the version
of the defining parameters. Since these parameters are the same as in [Kitov,
2026d], all results are directly compatible. Any difference between the
original results and those obtained in this study can be considered related to
the new parameters such as StN and the
detection thresholds of 100 and 1000, or to the newly simulated stochastic waveforms.
The sets of EDC were estimated in [Kitov, 2026d] from the SNRcc frequency
distributions at the IMS arrays using quiet days without REB events and very
low numbers of XSEL events. In some cases, these curves are similar to those at
PETK.
The mid-aperture
array KURK reveals a feature potentially related to the WCC detection
algorithm. The curves at KURK have a peak slightly above the detection
threshold of 3.3. This is similar to the
pattern observed for the detections of the sought signals in the actual data.
However, the deep troughs at 3.2 are a new feature for the SNRcc curves. For
the actual detections, no troughs are observed. In any case, the SNRcc at KURK
are all below the 4.5 level, except for a few cases for IDC orid=21227220.
Figure 2e
displays the SNRcc curves for the mid-aperture station WRA. It also serves as
an illustration of troughs before the peaks above the detection threshold of
3.3. These troughs are much deeper than at KURK and reach a level of 1 for one
of the MEs. All mid-aperture IMS arrays, except for ILAR, demonstrate this
feature and no small-aperture arrays show any significant troughs in the SNRcc curves
before the detections. The peaks in the SNRcc curves are related to the
detection algorithm freezing the LTA when the SNRcc reaches the threshold
value. For a stochastic waveform, the SNRcc values calculated without above-the-threshold
procedure or with extremely high threshold can be higher of lower than the
detection level. The frozen LTA may increase or decrease them relative to their
stochastic levels. The effect would be the troughs and the peaks. Figure 3
demonstrates the effect of the detection threshold set at 100 at station CMAR.
The peaks and troughs observed for the routine detection threshold of 3.2
disappear. The curves for the routine processing are extended by the detection
algorithm to the level above 5.0 for three MEs. The other MEs are limited by
the maximum SNRcc of 5. Station CMAR has a relatively low weight and cannon
serve as a mandatory contributing station.
The evolution of the SNRcc frequency
distribution with StN and the detection threshold is shown in Figure 4
for the large-aperture station NOA. This is the largest IMS array designed for
far-teleseismic signals. It fails to process regional and near-teleseismic
signals using all 42 channels. For regional distances, only one out of seven
groups of 6 sensors are used. For teleseismic signals, there are
source-specific arrival time corrections to be used instead of theoretical time
delays in order to avoid beam-loss. Otherwise, the signals cannot be stacked
synchronously. The WCC has no such problem,
as the cross-correlation at an individual channel does not depend on the other
channels and channel staking has zero time-delay.
Figure
4a shows the setting with the StN=100 and the routine detection
threshold 3.2. The troughs and peaks are as well developed as those at the
mid-aperture IMS arrays. Figure 4b presents the Figure 4a case but with StN=1000.
The peaks and troughs are almost the same, as is the overall shape. The absence
of any difference between the cases with StN=100
and StN=1000 confirms the consistency
of the assumption that the waveform is stochastic. Figure 4c presents the case
with StN=1000 and a threshold of 100.
The corresponding SNRcc curves have no peaks and troughs, as the threshold is
so high that no SNRcc value can reach it. These SNRcc curves are truly
stochastic, but a comparison with the original XSEL with StN=0 requires retaining identical thresholds.
a) a) Station
PETK
b) b) Station PDYAR
c) c) Station
MKAR
d) d) Station
KURK
e) e) Station
WRA
Figure 2. Frequency distribution of SNRcc values at four stations (PETK, PDAR, MKAR, KURK, and WRA) on July 28, 2025. Twenty master events are used. Station may miss some of the MEs due to maintenance works, upgrade, or late start of operation.
a)
b)
Figure 3. Comparison of the SNRcc
frequency distributions with detection threshold 3.1 (a) and 100 (b). Stations
CMAR. The effect of threshold and detection procedure is significant.
a)
b)
c)
Figure 4. Frequency distributions of
SNRcc at station NOA. Three cases: a) StN=100,
detection threshold 3.2. b) StN=1000,
detection threshold 3.2. c) StN=1000,
detection threshold 100.
The principal features of the SNRcc
curves generated using stochastic waveforms and shown in Figures 2 through 4
for further phase association are related to the EDC adopted for valid events. Hypotheses with the number of
associated stations between 3 and 5 must include a highly reliable station (weight
above 0.855 or 0.80) with the SNRcc value above 5.0 (4.5). There is also a
requirement for the sum of the SNRcc values of all associated stations. For a
three-station event, it must be above 15 (14), and the sum increases by 3.5 for
with each additional station.
The rule of a
minimal SNRcc of 5 (4.5) at one out of a few best stations is applied to the 3-
to 5-station events. For 6- to 9-station events, the station with the high
SNRcc is not restricted to the best set. For 10- or more station events, no
minimal SNRcc rule is applied. The SNRcc curves for all small-aperture stations
have a maximum SNRcc for the best ME below 5.0, with a majority of the 20 MEs
generating SNRcc values below 4.5. The
mid– and large-aperture arrays generate SNRcc values below 5.5. They also
generate an excess of SNRcc values near the detection threshold used in the WCC
processing of actual waveforms.
By design, the
EDC are intended to prohibit the creation of random events. The SNRcc curves
for quiet days were used to estimate the thresholds in the LA to guarantee very
low probability of a random event being created. The performance of these
preliminary thresholds is tested in the LA and CR processing.
WCC Local Association and Conflict
Resolution with stochastic noise
Stochastic
waveforms with various scaling factors StN
were processed at all the IMS stations participating in the study of the July
29, 2025, Kamchatka earthquake. Several days were processed in order to
understand potential variations in the corresponding XSEL bulletins depending
on the seismic activity reported by the IDC. The subsequent procedures of the
WCC pipeline were executed to obtain the XSELs – namely, Local Association and Conflict
Resolution. There were 20 MEs in this case (see Figure 1), and the CR procedure
plays a significant role in determining the quality of the final XSEL bulletin.
In
line with the original study of the Kamchatka 2025 megathrust earthquake
[Kitov, 2026d], twelve different LA settings were created to cover various
magnitude ranges of the XSEL events. There are two LA versions described in
Appendix 2 – “weak” and “strict”. Each version has six cases defined by the
origin time tolerances: 5.0 s, 3.0 s, 2.0 s, 1.0 s, 0.5 s and 0.25 s. This
makes twelve version-case pairs arranged in a matrix sequence. Index 1 belongs to the weak version with a 5.0 s origin
time tolerance, and index 12 corresponds to the strict version with a 0.25 s
tolerance. The first version-case set is aimed at the detection of the weakest
seismic events with magnitudes 2.0 and lower. The twelfth set is designed to
detect events near the corner magnitude of the recurrence curve obtained from
the REB for the studied area. The task is to estimate the XSELs for the stochastic
waveforms for all twelve version-case pairs.
Table
1 presents the results of the WCC processing of three sequential days – July
28, 29, and 30, 2025. These three days include almost two days prior to the
July 29, 2025, Kamchatka megathrust earthquake, which occurred at 23:24 UTC,
and July 30 – the day of the most intense post-seismic activity. Prior to the
mainshock, seismic activity was not high, as one can judge from the number of
REB events: 7 (two of them pure REB) on July 28 and 8 (2 pure REB) for the 23
hours between 0:00 and 23:00 UTC on July 29. This represents a slightly
elevated daily rate in the tail of the aftershock sequence generated by the
July 20, 2025, M7.4 earthquake that occurred in the vicinity of the July 29
earthquake. The first six hours on July 30, 2025, likely represented the period
of the highest seismic activity measured by the IDC, with 278 REB events within
the studied area.
Table 1. The numbers of XSEL events for
days 2025209, 20025210, and 2025211. Twelve LA sets (see Appendix 2) and five StN
values.
|
2025209 |
2025210 (0h-22h) |
2025211 (0h-5h) |
|||||||||||||
|
index |
StN |
StN |
StN |
||||||||||||
|
0 |
1 |
5 |
10 |
100 |
0 |
1 |
5 |
10 |
100 |
0 |
1 |
5 |
10 |
100 |
|
|
1 |
245 |
68 |
6 |
4 |
3 |
281 |
96 |
11 |
14 |
10 |
282 |
98 |
17 |
7 |
9 |
|
2 |
181 |
54 |
2 |
1 |
1 |
232 |
78 |
4 |
3 |
3 |
298 |
102 |
16 |
4 |
5 |
|
3 |
160 |
53 |
2 |
0 |
0 |
217 |
65 |
3 |
1 |
2 |
305 |
106 |
12 |
4 |
2 |
|
4 |
128 |
45 |
2 |
0 |
0 |
164 |
53 |
2 |
1 |
1 |
294 |
105 |
12 |
2 |
2 |
|
5 |
83 |
32 |
2 |
0 |
0 |
114 |
40 |
2 |
1 |
1 |
279 |
99 |
11 |
2 |
0 |
|
6 |
55 |
27 |
2 |
0 |
0 |
76 |
33 |
2 |
1 |
1 |
251 |
80 |
8 |
0 |
0 |
|
7 |
55 |
20 |
1 |
0 |
0 |
60 |
26 |
1 |
1 |
0 |
148 |
43 |
7 |
0 |
0 |
|
8 |
46 |
19 |
1 |
0 |
0 |
51 |
17 |
0 |
0 |
0 |
146 |
46 |
6 |
0 |
0 |
|
9 |
38 |
18 |
1 |
0 |
0 |
51 |
14 |
0 |
0 |
0 |
146 |
44 |
5 |
0 |
0 |
|
10 |
25 |
14 |
0 |
0 |
0 |
29 |
13 |
0 |
0 |
0 |
142 |
45 |
6 |
0 |
0 |
|
11 |
17 |
7 |
0 |
0 |
0 |
22 |
11 |
0 |
0 |
0 |
124 |
41 |
5 |
0 |
0 |
|
12 |
9 |
5 |
0 |
0 |
0 |
17 |
7 |
0 |
0 |
0 |
111 |
39 |
3 |
0 |
0 |
The results of
the WCC processing in Table 1 demonstrate variations in the twelve XSELs
depending on the noise scaling factor StN. These XSELs are obtained in
the LA and CR processes applied to the detection lists generated by random
waveforms with the respective StN values. In the StN=0 case, only
the actual data were used. This is a reference case to be compared with the
results obtained with a random time series added. For the zero StN case, the first pair - the one with the least restrictive EDC
and the widest origin time tolerance of 5.0 s - has a total number of XSEL
events ranging from 245 on July 28 to 282 for the first six hours of July 30. This
first pair’s XSEL for the first six hours of July 30 has likely reached the
largest possible number of events per an ME for the current WCC setting of the
detection, LA, and CR requirements.
This can be the
result of the detection thresholds and the rules governing the minimal allowed
spacing between subsequent arrivals in the WCC detection process. The hourly
detection rate is bounded from above by 120 and from below by 30 per hour. Such
rates are sufficient for the creation of around 50 events per hour or 300 per
six hours. A similar saturation limit is likely reached in the IDC automatic
processing based on its EDC and processing requirements. A total of 196 out of
278 REB events have seed events in the automatic SEL3 bulletin, and 82 REB
events are added by IDC analysts. There are many more actual events occurring
during this time period, but they cannot be detected due to the high amplitude
seismic noise and the limit on the number of detections at a station.
For the 20 MEs,
this number can be larger, but the CR process effectively eliminates the
multiple solutions for the same physical events and the aftershock zone
actually belongs to a few out of the 20 MEs. This effect can be illustrated by
the numbers of events in the final XSEL for individual MEs compared to the
numbers generated in the LA process before the CR is applied listed in Table 2.
The ME with the IDC orid=23689063 generated 444 event hypotheses, the highest number
among all the 20MEs, and 73 of them were promoted to the final XSEL. The second
best ME generated 389 event hypotheses in the LA and 42 appeared in the final
XSEL. The other 18 MEs were not so effective for various reasons from a
geographical position relative to the most intense part of the aftershock
sequence to the lower numbers of the associated templates. The ME with the IDC
orid=21227220 generated 177 hypotheses after the LA and
no events were promoted to the XSEL. The ME with the IDC orid=22605238
generated no hypotheses in the LA although it was a good ME during the
pre-seismic period. The extraordinarily high ambient noise consisting of
signals coherent with
the templates can be the reason for such behaviour. Only the closest station PETK
generated a detection list for this ME.
Table 2. Comparison of the individual
XSELs for the 20MEs obtained in the LA process and the final XSEL after the CR.
StN=0.
|
orid |
23689063 |
23329683 |
23316512 |
22605238 |
21227220 |
20280472 |
18683607 |
18517208 |
18425349 |
17328560 |
16438469 |
16313833 |
16007199 |
14686581 |
12688414 |
12618922 |
11231455 |
7220668 |
5376373 |
5050040 |
|
LA |
444 |
335 |
401 |
0 |
177 |
300 |
270 |
226 |
292 |
298 |
327 |
393 |
361 |
211 |
229 |
389 |
66 |
268 |
107 |
306 |
|
CR |
73 |
6 |
16 |
0 |
0 |
5 |
4 |
6 |
4 |
14 |
15 |
17 |
19 |
4 |
12 |
42 |
8 |
16 |
6 |
14 |
The decrease in
the number of XSEL events for all the LA version-case from index 1 to index 12
is well illustrated in Table 1. The
increase in StN from 0 to 1 leads to a dramatic two- to four-fold
decline in the XSEL numbers. The effect of the random noise with the maximum
amplitude equal to the maximum amplitude of the one-hour interval of the actual
waveform in a given channel-filter configuration demonstrates that it likely
contains no components coherent to the templates. In the case of a high noise and
template coherence, the effect of the equal amplitudes is devastating to the
XSEL [Kitov, 2026c].
For the StN=5,
the XSEL numbers drop to the level below 5% to 10% of those of the StN=0.
For the pre-seismic period, the XSELs for the indices from index 10 to index 12
are characterized by the absence of event hypotheses. For the post-seismic
period, the numbers are above zero for all the indices. This has to be the
effect of the signals from the large-magnitude aftershocks coherent with the
template in the high-amplitude random noise. The matched filter detector is
based on this assumption. It can find similar signals deep in the random noise.
The results for StN=10 and 100 are very similar and demonstrate the
absence of XSEL events in all tolerance cases of the strict LA version. For the
weak LA version, there are a few XSEL events generated with their number
decreasing with the origin time tolerance. They are likely related to the
random and thus noise-amplitude independent generation of detections and event
hypotheses. They do not depend on the templates but can fluctuate with the
random noise realizations.
The XSELs for
the strict LA version always have zero random events for StN=100. The statistical significance of the XSEL events for this
version is very high as the random generation is prohibited. For the weak LA
version, there is a probability of a random event being created, but it is less
than 5% and does not affect the uncertainty of the precursory parameters used
in [Kitov, 2026d]. The source of false event hypotheses is not only random
noise but also the side-sensitivity of the WCC detector at array stations to
the high-amplitude signals from the events not related to the studied area.
Table 2 confirms the potentially significant input from such sources with the
MEs far from the aftershock zone of the 2025 Kamchatka mega-earthquake. They
create event hypotheses close to their own positions but far away from their
real physical hypocenters. This effect
deserves a special investigation to evaluate its influence on the results in
[Kitov, 2026d].
Overall, the WCC
detector inherently generates false detections from the stochastic waveforms.
The distribution of the SNRcc values in Figure 4c, obtained in the case of StN=1000 and the detection threshold of
100, demonstrates that the quasi-exponential roll-off ends at the maximum
values of approximately 4.0. The LA requirement of the SNRcc to be above 5.0
for the strict and above 4.5 for the weak version would prohibit the creation
of any XSEL event hypotheses. The real thresholds are much lower and the WCC
detection procedure with a frozen LTA extends the SNRcc distribution to the
level of 5.0 for the stochastic time series. There can be an extremely rare
chance when a specific realization of stochastic time series can produce an
event hypothesis with the number of associated stations less than 10.
Otherwise, all generated hypotheses must have 10 or more associated stations, when
the requirement of the minimal SNRcc of 5.0 or 4.5 is lifted. The probability
of such events for a given LA version directly depends on the origin time
tolerance. As a result, no XSEL event hypotheses are produced for the
stochastic waveforms generated with StN>10
by the strict LA version with the tolerances below 3.0 s. For the weak version, there are insignificant
numbers of XSEL events generated for the tolerances below 2.0 s. The results
reported in [Kitov, 2026bd] are not biased by the random false detections.
Distance-dependent efficiency of MEs
Table 2
illustrates the relatively lower efficiency of the MEs outside the aftershock
area. The distance between an ME and a sought event is crucial for the shape
similarity of the template and the sought signals at array stations. The
template-sought signal cross-correlation coefficient (CC) decreases with distance relative to that for the ambient noise
[Arrowsmith and Eisner,
2006; Baisch et al., 2008].
Consequently, the WCC detection probability decays with distance, ceteris paribus. However, the increase
in the standard SNR of the sought signal, i.e.,
the increase in the sought event magnitude, can compensate for the
distance–dependent CC decrease. This
is the WCC detector’s side-sensitivity when the CC increases at a few random channels in sync with that of the
template and the sought signal CC,
with the others retaining low CC
values. As a result, the average CC
trace generates false WCC detections at many stations. The differential arrival
times at the stations associated with a given ME deviate progressively more
with the ME-sought event distance, and the LA may use these false detections to
produce false event hypotheses far away from the physical positions of the
sough events.
Therefore, the
MEs outside the zone of the most intense post-seismic activity can generate many
event hypotheses in the LA process as their templates have lower but still
sufficient similarity with the signals from this seismically active area. These
hypotheses have lower statistical significance and lose in the CR to the
hypotheses within or closer to the area. However, these remote MEs can generate
winning valid events in the zones of their responsibility. There exists a
distance range where the CR process has to select between two MEs with very
close defining parameters such as SNRcc, which are intrinsically prone to
measurement uncertainty. For such hypotheses in the gray zone, the CR process
may result in a wrong choice. Consequently, the XSEL may lose a valid event
matching the REB without any change in the total number of events. As a result,
the REB match statistics before the CR is also a useful parameter to evaluate
the WCC overall performance. Such erroneous CR decisions can also be mitigated
by the addition of new MEs in the gray zone. This requires more computer power
or longer processing time. There are around 1000 MEs in the studied area of the
2025 Kamchatka earthquake in the prototype routine WCC processing at the
IDC.
For a given StN value, the number of XSEL events decreases from index 1 to
index 12. This is the main feature of the twelve version-case pairs. They
define the increasing lower magnitude boundaries for the corresponding XSELs
leading to a decrease in the number of XSEL event hypotheses. For a short
period of a few days, the dependence of the number of events across the twelve
XSELs can be locally biased by the underrepresentation of events in the
corresponding samples. In the original study [Kitov, 2026d], for longer periods
of weeks or more, these curves demonstrate an exponential decay with coefficients
of determination up to 0.99, and thus, the version-case index can be converted
into a linear magnitude scale. Figure 5 presents the number of XSEL events as a
function of the index for StN=0.
Overall, the exponential regression lines for the pre-seismic period are characterized
by high coefficients of determination. The post-seismic period immediately
after the mainshock is characterized by a step between two versions and almost
constant XSEL numbers within the same version [Kitov, 2026bd].
Figure 5. Number of XSEL events as a
function of the index of the version-case pair. StN=0.
Such behaviour
indicates that for the highest rate of aftershocks in a relatively small area
the origin time tolerance window does not affect the XSEL much. For these aftershocks,
the actual magnitude boundaries for all tolerance cases of a given LA version
are larger than the corner magnitude of the respective recurrence curve. For
the WCC processing, the XSEL magnitude boundaries are defined by this actual
magnitude threshold and the smaller events are almost fully suppressed. For a given version, all XSELs are
approximately equal. The difference between the two versions is expressed in
the difference in the share of actual events matching the EDC for the WCC.
The XSEL statistics for the REB-matching
events and the number of new XSEL events
The results of the
random generation of detections and XSEL event hypotheses in the WCC processing
have to be reflected in the statistics of matched REB events. The latter are generated in the interactive
review by IDC analysts. The term “match” means the fact that the XSEL and REB
detections are within 20 s of each other. This rule
follows from the retiming interval allowed by the IDC rules for an automatic
detection without the creation of a new detection. This value follows from the
statistics of arrival time difference between the SEL3 and REB for the same
physical signals when the former were also associated with the REB events
[Saragiotis and Kitov, 2020]. The station-to-station XSEL-REB comparison is a
natural operation since they both use the same IMS stations but different
detection lists.
For an REB event
to be matched by an XSEL event, one REB-matched P-phase is sufficient, as
adopted by the IDC for the comparison of the automatic SEL3 bulletin and the
REB. The XSEL uses only P-phases for the cross-correlation calculations, but
the length of templates can be sufficient to include many secondary phases. The
template length is an important parameter because the difference in the group
and phase velocities between various secondary phases results in a rapid change
in the wavefield. The change in the shape of the evolving sought signal puts stringent
restrictions on the relative position of the respective sought event. The level
of cross-correlation with the template drops as rapidly as the sough signal
changes its shape.
It is important to stress that the matching XSEL and the
matched REB events do not have to be close in space, as the IDC has a strict
rule to fix the events with a high uncertainty of depth estimates to the
surface. Consequently, a significant bias up to 10° can be introduced in the
respective IDC hypocenter locations. The locations of the XSEL events
are close to their respective MEs. False XSEL events can also match REB events.
Therefore, the number of false XSEL events has to be minimized to the greatest
extent possible. The match statistics are important for the demonstration of
statistical power of the XSEL events and the reliability of the WCC
processing.
The statistics of new XSEL events, which are
not matching any of REB events, are important for the evaluation of the random
events input. The number of random events has to change with the origin time
tolerance case for a given version, as Table 1 illustrates. The total number of
new XSEL events has to decrease with the tolerance case when the magnitude
boundary is not elevated by high seismic activity. In that case, the number of
new XSEL events does not depend on the tolerance and differs
between versions.
Table 3 presents extensive statistics of the
XSELs for StN=0 as obtained during
the period between July 28 and July 30, 2025. There are two relatively quiet
days of July 28 and 29 (23 hours). July 30 is a day of the highest seismic
activity. The last hour of July 29 is not processed. The quiet days are
processed as one interval. July 30 is split into four 6h intervals with a
decaying activity – from a total of 278 REB events in the first interval to 160
events in the last one. Two configurations with of 20 MEs and 100 MEs are used.
The latter is the set of the best 100 MEs used in [Kitov, 2026d], as shown in
Figure 1. This allows for the evaluation of the effect of the MEs density on
the statistics.
Column “REB/SEL”
in Table 3 displays the total number of events and the number of events built
starting from the SEL3 seed events. The difference between these two numbers is
the number of pure REB events built by IDC analysts. This is a measure of the
IDC automatic processing efficiency. For example, on July 30 the ratio of the
number of the pure REB to the SEL3 seeds is 0.42, 0.26, 0.27, and 0.33 for the
four subsequent 6h periods.
The XSEL match
statistics are shown for all twelve version-case indices. The first number in
the cells is the number of matched REB events, the second number corresponds to
the matched pure REB events, and the third number is the new XSEL events. For
the two quiet days, the match rate for all versions-cases-configurations is from
70% (5 out of 7) 100%. The total number of XSEL events and the number of new
events decrease with the version-case index. The difference between the 100 MEs
and 20 MEs configurations is from twofold for the weak version to fivefold
(18/4) for index 12. This is important for the statistical reliability of the
ratios of the number of XSEL events between the weak and strict versions for
the same origin time tolerance used in [Kitov, 2026bd] as a precursory variable
of the 2013 Sea of Okhotsk and 2025 Kamchatka mega-earthquakes. The configuration
of 20 MEs is too sparse to be used for these purposes. The weakest XSEL events
have to be much closer to the MEs which can detect them.
Table 3. Statistics of the REB matches
and new XSEL events during the period between July 28 and July 30, 2025.
For
July 30, 2025, the number of the matched REB events depends on the MEs
configuration, LA version, and origin time tolerance. For the first 6h
interval, the match result for index 1 is not the highest for the 20 MEs
configuration. This is the consequence of the largest tolerance forcing an
increase in the number of phases for the CR process. Index 2 maximizes both the
total number of matched REB events (a total of 204 out of 278) and the number
of pure REB events matched by the XSEL (39 out of 82). The former number is larger than the
corresponding number for the SEL3 and includes many pure REB events. The WCC
processing version for the current study was adjusted to lower detection rates
pertaining to the earthquake preparation process. There is a version with
reduced spacing between consecutive detections to process the intense aftershock
activity, but the focus of this study is to assess the performance of the
low-seismicity version.
The
respective numbers for the 100 MEs configuration are always higher with the
best match rate of 244 out of 278 REB event matched for index 1. The match for
pure REB events stays at 55 out of 82. The REB match rate in both categories
decreases with the index, but stays high even for index 12 –161 and 21,
respectively. These results confirm high statistical power of the XSEL events –
most of them are real as the REB match suggests.
The
new XSEL events are the only ones to be potentially related to the random
detections and related event hypotheses.
For the quiet days, their number for the twelve indices follows the
exponential roll-off as was shown in [Kitov, 2026d]. It is a prominent feature
for the recurrence curves. This
exponential decay is also a characteristic of the random detection
distribution. The total numbers of the XSELs events are much higher than in the
random case listed in Table 1. For the strict version, the number of new XSEL
events is always above zero, i.e.,
they are not randomly generated. A very specific feature of July 30 seismic
activity is an almost case-independent total number of XSEL events for a given
version. The new XSEL events also follow this behaviour, except maybe the
shortest tolerance of 0.25 s. For the random case, this number would decrease
rapidly with the tolerance decreasing from 5.0 s to 0.25 s.
The
statistical estimates in Table 3 do not contradict the assumption that the
random generation of XSEL events does not affect both the number of matched REB
events and the number of new XSEL events. The effect of random detection is
negligible and the statistical significance of the XSEL hypotheses is high
enough to be used in the seismological and geophysical research.
Side-sensitivity
of the WCC at array stations
The
effect of high-amplitude noise generated by a mega-earthquake and its
aftershocks on the WCC detection process was studied in detail in [Kitov et al., 2026; Kitov, 2026c]. This type
of noise consisting of high-amplitude regular phases can be an extremely
powerful obstacle to WCC detection when it is coherent with the sought signal.
For array stations, however, there are situations when such noise becomes
quasi-stochastic and improves detections conditions [Kitov, 2026c]. Therefore,
it may serve as a quasi-stochastic noise sample when the plane wavefronts of
its constituent regular phases are orthogonal to the template and sought
signals at an array. The March 11, 2011, Tohoku earthquake was used to simulate
this high-amplitude noise in the previous studies and serves as the best case
of remote but not too far away sources of very high-amplitude signals at the IMS
stations most important for the XSEL events – PETK, MKAR, KURK, and TXAR. A
very important station PDYAR started in 2023 and did not participate in the
Tohoku WCC processing.
For
the current study, our principal objective is to estimate the capability of
remote seismicity to affect the XSELs obtained for the days before and after
the July 29, 2025, Kamchatka mega-earthquake. The set of 20 MEs was extended by
12 MEs covering the Tohoku aftershock zone, as presented in Figure 1. This
allows for the investigation of the direct influence of the Tohoku aftershock
sequence on the XSEL bulletins for the Kamchatka region and for the separate
performance of the 20 Kamchatka MEs and 12 Tohoku MEs.
The first problem
to address is how large the remote earthquakes’ effect is on the Kamchatka
XSELs generated with 20 MEs? Furthermore,
we must address whether we can suppress this effect using stochastic noise
added to the actual waveforms? The period of the most intense aftershock
activity between 07:00 and 13:00 UTC on March 11, 2011, was selected. The
number of REB events in the aftershock zone of the Tohoku earthquake was a
total of 232 with 173 of them having SEL3 seed events as the start points for
the interactive review. There were no REB events within the studied Kamchatka region
during these 6 hours of March 11, 2011.
The numbers of
XSEL events in the twelve LA version-tolerance case configurations (indices 1
through 12) for the actual waveforms (StN=0.0) are shown in Table 4.
These are the XSEL events found by the 20MEs within the Kamchatka region and StN=0.0 in the column “0.0” in Table 1. These
are all new XSEL events as there were no REB events to match. The numbers
decrease from 245 for index 1 to 2 for index 12. These are all false
events wrongly created and located within the Kamchatka region from the WCC
detections. The WCC detections were made by the 20 MEs and thus the WCC
detection has relatively high side-sensitivity to the Kamchatka templates. For
MKAR, KURK, and TXAR, this can be explained by the close station-event azimuths
between the Kamchatka Peninsula and Japan; the southern border of the Kamchatka
region is approximately 4° far away from the northern edge of the Tohoku zone
as shown in Figure 1. Station PETK has arrivals from various azimuths from the
2025 Kamchatka aftershocks ranging from orthogonal to parallel to the direction
of the Tohoku epicentre. Therefore, the side-sensitivity of the Kamchatka MEs
to the Tohoku earthquakes is a natural result of their relative position with
respect to the IMS stations.
The MEs near the
southern edge along the 45° parallel should be the most sensitive to the
creation of false events from valid detections. As an alternative, a sensitive
ME can be deep and have short templates with lower specificity. Table 5
presents the numbers of XSEL events generated for two indices 1 and 7. These
indices correspond to the weak and strict LA versions with a 5.0 s origin time
tolerance which is the most prone to the creation of false events from valid
detections. The most effective masters are indicated in bold. They are all
close to the southern border of the studied region. The only exclusion is a
deep event indicated in bold italic.
Table 4. Dependence of the number of
XSEL events on StN for Tohoku earthquake found by the 20 MEs used for
Kamchatka region.
|
index |
0.00 |
0.005 |
0.01 |
0.05 |
0.10 |
0.25 |
0.50 |
1.00 |
2.50 |
5.00 |
|
1 |
235 |
238 |
264 |
312 |
298 |
243 |
161 |
90 |
27 |
0 |
|
2 |
234 |
220 |
246 |
314 |
287 |
228 |
150 |
81 |
23 |
0 |
|
3 |
197 |
197 |
224 |
300 |
263 |
205 |
141 |
71 |
21 |
0 |
|
4 |
137 |
140 |
174 |
265 |
235 |
166 |
107 |
47 |
13 |
0 |
|
5 |
102 |
90 |
121 |
187 |
179 |
124 |
82 |
28 |
7 |
0 |
|
6 |
63 |
54 |
68 |
132 |
118 |
76 |
58 |
21 |
5 |
0 |
|
7 |
43 |
50 |
77 |
148 |
149 |
103 |
68 |
31 |
5 |
0 |
|
8 |
33 |
35 |
59 |
129 |
113 |
84 |
55 |
25 |
5 |
0 |
|
9 |
24 |
24 |
40 |
105 |
104 |
67 |
44 |
18 |
4 |
0 |
|
10 |
9 |
15 |
29 |
77 |
72 |
39 |
23 |
13 |
2 |
0 |
|
11 |
4 |
5 |
12 |
38 |
37 |
22 |
12 |
4 |
1 |
0 |
|
12 |
2 |
3 |
5 |
18 |
17 |
10 |
4 |
1 |
0 |
0 |
Table 5. The number of XSEL events per one
ME for index 1 and index 7 for the six-hour period on March 11, 2011.
|
orid |
5050040 |
5376373 |
7220668 |
11231455 |
12618922 |
12688414 |
14686581 |
16007199 |
16313833 |
16438469 |
17328560 |
18425349 |
18517208 |
18683607 |
20280472 |
21227220 |
22605238 |
23316512 |
23329683 |
|
index 1 |
1 |
5 |
1 |
8 |
21 |
45 |
20 |
3 |
9 |
34 |
6 |
4 |
30 |
4 |
12 |
7 |
1 |
12 |
5 |
|
index 7 |
0 |
0 |
0 |
2 |
6 |
10 |
2 |
0 |
0 |
4 |
0 |
0 |
12 |
0 |
1 |
3 |
0 |
0 |
0 |
The
other nine columns in Table 4 illustrate the change in the numbers of XSEL
events for the twelve indices as a function of StN. There is a range of StN
values where these numbers increase relative to the actual waveforms case in
line with the findings reported in [Adushkin et al., 2025; Kitov et al.,
2026; Kitov, 2026c]. The StN value
maximizing the XSEL numbers for all indices likely resides between 0.05 and
0.1. This is an important observation for the WCC processing of the 2025
Kamchatka earthquake. The results presented in [Kitov, 2026d] can be improved
by the addition of stochastic noise with scaled amplitude of approximately
0.075.
The
largest StN value of 5.0 completely
suppresses the generation of false events for all twelve indices. Unfortunately,
this value also prohibits the creation of valid XSEL events in the WCC
processing of the July 2025 data. The addition of stochastic noise is not
helpful in the solution of the problem with the side-sensitivity of the WCC
applied to IMS arrays. There is an indication of how to solve that problem,
however, illustrated in Table 5. The events on the border of the studied
Kamchatka region generate most of the false events. This effect does not significantly
influence the estimates of the parameters important for the earthquake
prediction as the MEs at the rim of the region should be excluded from the XSEL
dataset related to these precursory variables.
Therefore,
the use of the MEs within the Tohoku region would resolve the issue of false
XSEL event hypotheses. These MEs should create valid XSEL events around their
geographical positions from the valid detections at the same stations. Figure 1
shows the relative position of the twelve MEs, which cover the whole Tohoku
region. This is a low number for the WCC processing to achieve high resolution
for the Tohoku aftershocks, especially in the period of the most intense
activity. These events are much more appropriate for the study of the Tohoku
seismicity than any of the MEs used for the Kamchatka region.
The
set of 32 MEs was used to process the same six-hour-long time interval with the
region 35°N-65°N, 140°E-165°E, as shown in Figure 1. Table 6 presents the
result of this processing. For StN=0.0,
the total number of XSEL events for the set of 32 MEs decreases with index as
for the other configurations in this study and as in [Kitov, 2025bd]. The
number of matched REB events slightly grows from 113 for index 1 to 119 for
index 3. The number of new XSEL events follows the decreasing trend of the total
number of events. The partial result for the set of 20 Kamchatka MEs out of the
full set of 32 MEs demonstrate non-zero values, i.e. the Kamchatka MEs found
the Tohoku REB events. This possibility cannot be ruled out for the northernmost
Tohoku aftershocks and high-quality Kamchatka MEs. For StN=0.05, which is the best value for XSEL event generation using
the added stochastic noise in Table 4, the number of XSEL events is lower, but
the number of matched REB events is larger than for StN=0.0. The number of false
REB matches drops to the range between 0 and 2, and the number of new XSEL
events falls within a range of 0 to 5. These new XSEL events were found in the
high-amplitude Tohoku noise and are likely valid earthquakes within the
Kamchatka region.
Table 6. Result of the WCC processing
with 32 MEs of the 6h interval on March 11, 2011.
|
StN=0.0 |
StN=0.05 |
|||||||||
|
index |
32 MEs |
20 MEs |
32 MEs |
20 MEs |
||||||
|
Total |
REB |
New |
REB |
NEW |
Total |
REB |
New |
REB |
NEW |
|
|
1 |
152 |
113 |
39 |
2 |
33 |
144 |
133 |
11 |
0 |
5 |
|
2 |
148 |
115 |
33 |
1 |
25 |
147 |
137 |
10 |
0 |
3 |
|
3 |
147 |
119 |
28 |
2 |
21 |
152 |
140 |
12 |
1 |
4 |
|
4 |
137 |
110 |
27 |
2 |
19 |
155 |
143 |
11 |
1 |
2 |
|
5 |
126 |
104 |
22 |
4 |
15 |
151 |
139 |
12 |
0 |
3 |
|
6 |
113 |
95 |
18 |
1 |
12 |
161 |
154 |
7 |
0 |
1 |
|
7 |
69 |
62 |
7 |
1 |
4 |
103 |
100 |
3 |
1 |
3 |
|
8 |
69 |
63 |
6 |
3 |
3 |
108 |
102 |
6 |
1 |
4 |
|
9 |
66 |
63 |
3 |
2 |
1 |
105 |
104 |
1 |
1 |
0 |
|
10 |
56 |
53 |
3 |
2 |
1 |
111 |
105 |
6 |
0 |
4 |
|
11 |
47 |
46 |
1 |
1 |
0 |
108 |
101 |
7 |
2 |
3 |
|
12 |
44 |
43 |
1 |
0 |
0 |
103 |
98 |
5 |
0 |
1 |
It is worth
noting that the total number of XSEL events within the Tohoku region created by
12 MEs is lower than the total number of the false events created by the 20
MES. The CR process worked effectively to suppress the association of valid
detections with false events. Additionally, station PETK, which is the most
efficient for the Kamchatka region, has mediocre statistics for the Tohoku
aftershocks. The station weights in the LA and CR process must be different for
the 12 MEs. Nevertheless, even in a suboptimal setting of the WCC processing,
the 12 MEs resolve the problem of IMS station side-sensitivity. In the
prototype WCC pipeline, which worked several years in a test mode at the IDC,
there were approximately 42,000 MEs optimally tuned to the localized station
weights. There was no problem with the side-sensitivity as such with the dense
covering of the whole zones of seismic activity. This problem was practically
solved in [Kitov, 2026d] by the extension of the zone of the earthquake
preparation to a broader region covering all seismic areas around the Kamchatka
Peninsula.
Discussion
The progress in seismological observations in the 20th
century allowed scientists to obtain a large dataset of various seismic signals
together with the estimates of their kinematic and dynamic parameters. The
travel time curves were improved by the introduction of 3-D velocity models [Dziewonski, 1984; Tromp et al.,
2005; Shapiro et al., 2010]. The
amplitude-distance curves for primary and secondary seismic phases are
converted into various magnitude scales [Gutenberg, 1945; Gutenberg and
Richter, 1956; Veith and Clawson, 1972; Vanĕk et al., 1982; Granville et al.,
2005]. Attenuation coefficients and Q-factors are used to describe nonlinear
mechanical processes in the Earth. Dispersion curves serve to understand the Earth’s
fine elastic and inelastic properties. There is one common feature of all these
parameters – extended statistics and well-defined uncertainty bounds. For
example, the IDC does not use actual travel time residuals in the location
algorithm [Coyne et al., 2012]. Instead, the theoretical travel time
uncertainties are used, which are also dependent on the signal SNR value. These
theoretical uncertainties are based on those in the travel time model ak135
[Kennett et al., 1995].
The WCC processing lacks such extensive datasets and
accurate estimates of the principal parameters for the detected signals. In part,
this is due to the extremely low SNR values, often below 1.0, of these WCC
signals. The main reason, however, is the sporadic character of seismic studies
based on the WCC processing. There is no global dataset to estimate the
uncertainty of the travel time residuals and signal amplitudes to create a
reference model allowing for the statistical assessments. One can make such
estimates for the WCC signals that are also detected by standard methods and
extrapolate the results to weaker signals. This is a promising start but there
is no guarantee that the statistics for the weaker signals will follow the
estimates for the visible seismic signals.
The value added by the addition of at least the same
number of (low-magnitude) events to the global dataset as they contain now is
worth the effort to reprocess the available raw waveform data. Small-scale
experiments were conducted at the IDC with interactive review of the
(automatic) XSEL bulletins in a few areas: China [Bobrov et al., 2014],
Sumatra [Bobrov et al., 2016ab], Northern Atlantic [Bobrov et al.,
2017]. From the XSEL seed events, IDC analysts added from 60% to 100% of newly
created REB events. These are the events with visible signals and there were
many more events not matching the analysts’ “visibility” experience. These
exercises were important for the WCC results for the May 24, 2013, Sea of
Okhotsk deep megaearthquake. There were no REB events detected prior to this
event by standard methods, but hundreds of low-magnitude seismic events were
detected by the WCC-based pipeline. The statistical significance of these XSEL
events is supported by the results of the current study.
Comparison with the random noise waveforms is an
attempt to estimate the reliability of the event hypotheses obtained in the WCC
processing relative to the most basic case. This effort is important for the understanding
of the WCC processing as such since it is a version of the matched filter
method relying on stochastic noise conditions. For the purpose of the prediction
of the May 24, 2013, Sea of Okhotsk and the July 29, 2025, Kamchatka
earthquakes, which are based on the evolution of low-magnitude, and, thus, invisible
to standard processing events, the estimates of statistical significance of the
WCC-based hypotheses, are a mandatory step in the overall methodology. Any
source of disturbance in the WCC processing has to be formally addressed and
investigated in detail. The same applies to the side-sensitivity of the WCC at
array stations. The Global Grid of master events [Kitov et al., 2016]
practically dismisses this source of false events, but extended observations
are needed to make this assumption measurable.
The operational
constraints and stability metrics established in our numerical experiment
provide the necessary methodological foundation for a targeted precursory
wavefield analysis. It was demonstrated that the automated WCC pipeline is
statistically protected against the random generation of XSEL event hypotheses
under the optimized set of the origin-time tolerances. This allows the isolation
of genuine tectonic activation patterns from baseline seismic field
fluctuations related to a large number of seismic events with various
magnitudes occurring at different distances from the studied area. The
statistical significance of the XSEL events used to calculate the parameters
for the precursory variables in [Kitov, 2026bd] is confirmed at a high level of
confidence, as well as the statistical power of the XSEL events matching the
REB during the periods of extremely high post-seismic activity.
The results for
the first six hours of July 30 confirmed a saturation limit in the automated
processing revealed in [Kitov, 2026d]. During this period of the highest
seismic activity, the total number of XSEL events is almost independent of the
origin time tolerance window. This behaviour is related to the rules governing
the minimum allowable spacing between subsequent arrivals in the WCC detection
process. When the aftershock activity is extremely intense, the smaller events
are almost fully suppressed by the pipeline requirements. In this case, the
total number of events remains constant between different tolerance cases for a
given version.
The stochastic
time series was generated by the ran3
Fortran program. The random noise waveforms were added to the actual data after
they were scaled to the maximum amplitude of the waveform in a given interval.
The scaling factor StN was varied in
a wide range from 0.001 to 100. For the largest StN value the random noise time series completely suppressed the
actual waveform and the results of the WCC processing demonstrate the random
generation of the XSEL event hypotheses. For the lower StN values, the efficiency of the WCC detector increased in line
with the results of the previous studies [Adushkin et al., 2025; Kitov, 2026c; Kitov et al., 2026].
A grid search in
the StN range from 0.0 to 1.0 allowed
the estimation of the optimal value of StN=0.075
that maximizes the number of valid detections, XSEL events, and the match rate
of the REB events. This is the closest point to the perfect matched filter
conditions – the sought signal does not lose similarity with the template and
the noise is as random as possible considering further degradation in the shape
of the sought signal. This effect is similar to noise "whitening",
which makes the matched-filter detector more sensitive to low-magnitude events.
These events have an SNRcc deep below the routine IDC thresholds and are
usually not visible to analysts. Therefore, the StN=0.075 configuration may help to improve the estimates of the
precursory variables from the same actual data.
The
determination of the optimal stochastic noise scaling factor—parametrically
fixed at StN=0.075 — enables a
high-resolution reprocessing of the continuous waveforms immediately preceding
the megathrust failure. In the subsequent study, this calibrated StN=0.075 configuration will be directly
deployed to investigate the evolution of low-magnitude seismicity prior to the
July 29, 2025, Kamchatka megaearthquake. Specifically, we reevaluate the
predictive power of the weak-to-strict XSEL event ratios as a linear function
of magnitude scaling, establishing a robust empirical framework for
intermediate-term earthquake forecasting within subduction zones.
The simulation with the 2011 Tohoku earthquake
confirms that the side-sensitivity of the Kamchatka MEs is a natural result of
their relative position to the IMS stations. High-amplitude regular phases from
remote sources can travel along similar azimuths and generate valid WCC
detections at stations PETK, MKAR, and KURK, which are then associated with
false XSEL hypotheses. These false hypotheses are located within the Kamchatka
region with a significant bias in hypocenter. The processing with the full set
of 32 MEs demonstrates that the addition of 12 Tohoku MEs completely resolves
this issue because the Tohoku MEs win the conflict resolution process. This
confirms that the side-sensitivity problem can be solved by the extension of
the master events list to a broader region covering adjacent seismic zones.
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Appendix 1. IDC parameters for 32 MEs.
|
IDC
orid |
origin
time, s |
Lat,
deg |
Lon,
deg |
Nass* |
mb |
depth,
km |
|
23689063 |
1678291851.10 |
51.621 |
159.579 |
54 |
4.9 |
12 |
|
23329683 |
1671934664.20 |
56.12 |
160.994 |
90 |
4.5 |
115.7 |
|
23316512 |
1671816197.60 |
54.894 |
159.942 |
83 |
4.1 |
116.1 |
|
22605238 |
1659376874.20 |
50.535 |
150.466 |
65 |
3.8 |
478.2 |
|
21227220 |
1633993802.20 |
48.281 |
153.773 |
90 |
5.1 |
87.3 |
|
20280472 |
1615919903.20 |
54.786 |
162.806 |
91 |
5.9 |
21.8 |
|
18683607 |
1585166167.90 |
55.894 |
160.257 |
109 |
4.7 |
190.4 |
|
18517208 |
1581590025.80 |
45.758 |
148.842 |
96 |
6 |
155.6 |
|
18425349 |
1579691054.10 |
54.918 |
161.407 |
119 |
5 |
67.2 |
|
17328560 |
1557210493.60 |
49.518 |
155.738 |
78 |
4.7 |
55 |
|
16438469 |
1539380306.30 |
47.197 |
146.587 |
108 |
4.4 |
373.7 |
|
16313833 |
1536524928.20 |
52.296 |
157.106 |
77 |
4 |
146.8 |
|
16007199 |
1530841206.30 |
51.57 |
157.753 |
75 |
5.4 |
64.4 |
|
14686581 |
1501448448.90 |
46.179 |
150.959 |
101 |
5.5 |
89.4 |
|
12688414 |
1450387899.40 |
47.935 |
146.905 |
143 |
4.7 |
449.5 |
|
12618922 |
1448704593.10 |
52.677 |
152.704 |
95 |
4.2 |
527.2 |
|
11231455 |
1410892779.90 |
45.125 |
147.038 |
51 |
4.7 |
0 |
|
7220668 |
1299285065.70 |
52.798 |
160.797 |
63 |
4.7 |
0 |
|
5376373 |
1241817750.30 |
58.084 |
164.32 |
36 |
5 |
12.1 |
|
5050040 |
1227552258.00 |
53.029 |
159.581 |
64 |
4.4 |
43.8 |
|
21963352 |
1647441392.94 |
37.71 |
141.55 |
103 |
6 |
59.4 |
|
17806771 |
1567036001.90 |
40.99 |
143.00 |
94 |
5.4 |
42.1 |
|
17236058 |
1554970703.24 |
40.36 |
143.35 |
93 |
5.3 |
35.8 |
|
17078267 |
1551900361.07 |
38.7 |
141.60 |
74 |
4.5 |
67.9 |
|
13552398 |
1473421997.68 |
36.36 |
140.98 |
71 |
4.7 |
51.9 |
|
10997485 |
1404513724.83 |
39.67 |
142.00 |
69 |
5.4 |
47.5 |
|
9669379 |
1365192052.13 |
36.72 |
141.34 |
118 |
4.8 |
46.2 |
|
9001616 |
1346267113.19 |
38.39 |
141.84 |
116 |
5.2 |
68.1 |
|
7363085 |
1300221003.01 |
35.21 |
141.06 |
56 |
5.1 |
42.3 |
|
7360668 |
1300182590.91 |
37.32 |
142.42 |
80 |
5.5 |
0 |
|
7336822 |
1299838230.51 |
39.24 |
142.77 |
88 |
5.6 |
0 |
|
7297161 |
1299899521.09 |
35.94 |
141.44 |
77 |
5.2 |
41.3 |
*Nass – number of associated phases
“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.
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.”
