A large earthquake could occur in southeastern Sumatra or Jawa Indonesia within the next several years

A large earthquake could occur in southeastern
Sumatra or Jawa฀ Indonesia within the next several
years
Xuezhong Chen (  cxz8675@163.com )
 Institute of Geophysics, CEA, Beijing 100081
Yane Li
 Institute of Geophysics, CEA, Beijing 100081
Lijuan Chen
 Chongqing Earthquake Administration, Chongqing 401147

Research Article

Keywords: Large earthquake, b-value, apparent stress, Earth's rotation-correlated, Seismicity, Indonesia

Posted Date: January 4th, 2023

DOI: https://doi.org/10.21203/rs.3.rs-2427597/v1

License:   This work is licensed under a Creative Commons Attribution 4.0 International License.
Read Full License

Additional Declarations:
Table 1 is available in the Supplementary Files section.

A large earthquake could occur in southeastern Sumatra or Jawa，
Indonesia within the next several years

Xuezhong Chen1, Yane Li1 and Lijuan Chen2
a
 Institute of Geophysics, China Earthquake Administration, Beijing, China; bChongqing Earthquake

Administration, Chongqing, China

 Abstract—In this article, we focused on the region including southeastern Sumatra and Jawa,Indonisia,

conducted a joint analysis of the b-value and apparent stress to investigate the stress in the crustal rock. We

also examine the correlation between the variations in the rate of Earth’s rotation and the occurrence of

earthquakes there by means of P-value. The results are outlined below.

In the area 100km south of Jakarta, the b value decreased ~48% within ten years from 2009 to 2018 in and around

the area. An obvious upward trend in the apparent stress started at the beginning of 2002 and ended in July 2019.

From August 2019 until July 2022, the apparent stress decreased, reflecting that a stage of sub-instability or critical

state could have occurred. It‘s shown that lower P-values concentrate mainly around Bengkulu, about 370km west of

Jakarta, indicating a significant correlation between the occurrence of earthquakes and the Earth’s rotation there.

Based on the above results, we can conclude that there could occur a strong earthquake of Mw ≥8.0 in Jawa or

southeastern Sumatra, Indonesia within the future several years. This is maybe important to reduce the seismic

damage there.

 Key Words: Large earthquake; b-value. apparent stress. Earth's rotation-correlated. Seismicity. Indonesia

 1. Introduction
 The region in southeastern Sumatra and Jawa, Indonesia is located at the boundary between
the Indian ocean plate and the Eurasian plate. As a part of the Eurasian seismic belt, strong
earthquakes have frequently occurred there since 1900 (Fig. 1). Accordng to the earthquake
catalog obtained from the China Earthquake Networks Center, China Earthquake Administration,
four enormous earthquakes have occurred there since 1900, i.e., the February 27, 1903 MS8.1,

1 Institute of Geophysics, CEA, Beijing 100081, China.E-mail: cxz8675@163.com.
2 Chongqing Earthquake Administration, Chongqing 401147, China.

June 25, 1914 MS8.1, July 23, 1943 MS8.1, August 19, 1977 MS 8.1 (showed by the red stars in
Fig. 1). The longest event-to-event time interval thirty-four years. Forty-five years have elapsed
since the last event. We can legitimately raise the question of whether an enormous earthquake
could occur there in the future. Evidently, it is impossible for us to obtain a definite answer
according to the time interval.
 It has been known from the results of rock mechanics experiments that the preparatory
process of strong earthquakes could be divided into two stages. The first stage is related to the
tectonic stress accumulation, and followed by the second stage, i.e., a critical state when the
stress reaches a critical value. For the former stage the stress state at the focal source is needed to
obtain. Despite it is difficult to directly detect the stress at the focal source within the focal depth
range of a few kilometers to tens of kilometers, the stress state can be inferred using the
Gutenberg–Richter b value or the apparent stress. A reverse relation between b-value and stress
has been found in laboratory experiments (Scholz, 1968a; Wyss, 1973). Fluctuations of b are also
related to the degree of material heterogeneity(Mogi, 1962), even geothermal gradients(Warren
& Latham, 1970). The apparent stress is a product of the shear modulus and the ratio of seismic
energy to seismic moment, equals a product of seismic efficiency and the average stress on the
focal fault(Wyss, 1970; Wyss & Molnar, 1972). When the tectonic stress increases, the b-value
decreases, meanwhile the apparent stress increases and vice versa, i.e., there also exists an
inverse correlation between b-value and apparent stress. As a consequence, by conducting a joint
analysis of the b-value and apparent stress the stress at the focal source can be indirectly detected
with other influencing factors excluded. Observations of earthquake cases have recently shown
that the b-value decreased while the apparent stress increased before the occurrence of strong
earthquakes(Chen et al., 2021a; Li & Chen, 2021; Li et al., 2021a).
 When a focal region is stressed to a critical state, it may become extremely unstable and
small to moderate earthquakes around it could be susceptible to tiny stress changes.When a
strong earthquake is approaching, its focal region may become extremely unstable.and small to
moderate earthquakes around it could be susceptible to tiny stress changes. It is known that weak
stress changes on the focal fault plane can be caused by variations in the Earth's rotation
rate(Chen et al., 2018). Therefore, if a focal region is at critical state, variations in the Earth's
rotation could trigger earthquakes resulting in a significant correlation between the triggered

earthquakes and the variation in the Earth's rotation rate. We can investigate the Earth's
rotation-correlated seismicity to evaluate whether the focal region reaches a critical state.
Observations have shown that the triggered earthquakes are significantly correlated with Earth's
rotation when strong earthquakes are approaching (Wei et al., 2018; Chen & Li, 2019; Chen et al.,
2019; Chen et al., 2020; Li et al., 2021b; Chen et al., 2022c). Thus, we investigate the Earth's
rotation-correlated seismicity to evaluate whether the focal medium reach a critical state.
 In this study, we jointly use the b-value and the apparent stress to investigate the
fluctuations of stress and investigate the Earth's rotation-correlated seismicity to evaluate
whether the focal medium reach a critical state. Eventually, we present a result about the seismic
hazard in southeastern Sumatra and Jawa, Indonesia.

 Figure 1

 Epicenters of MS≥7.0 earthquakes since 1900. These earthquake data were obtained from the China Earthquake

 Network Center (CENC). The red stars alongside the numbers 1,2,3 and 4 indicate the epicenters of MS≥8.0

 earthquakes.The blue thick line marks the plate boundary.

 2. b-value
 The catalogue used here was obtained from USGS (https://earthquake.usgs.gov/
earthquakes/search/). Based on the earthquakes that occurred in the region including southeastern
Sumatra and Jawa of Indonesia during the period of 1 January 1990- 31 August 2022, the
temporal and spacial fluctuations of the b-value were calculated. The magnitude of completeness
MC as a function of time [MC(t)] was computed using the maximum curvature technique (Wiemer
& Wyss, 2000), applying sample sizes of 200 events and a step size of 10 events. MC ≤4.7 can be

suggested (Fig. 2). Due to underestimation of MC by the maximum curvature technique, an
increment of 0.2 should be added to MC (Huang et al., 2016). Therefore, in analysis, we picked
earthquakes of M4.9. In total, there are 2565 M4.9 shocks, their epicenters are plotted in Fig.
3.

 Figure 2
Magnitude of completeness MC as a function of time computed according to the maximum curvature technique,
using sample sizes of 200 events and a step size of 10 events.

 Figure 3
 Epicenters of earthquakes with magnitudes of M≥4.9 occurring from 1 January 1990 to 31 August 2022, as
published by USGS. The red thick lines indicate the plate boundary.

 Herein, the maximum likelihood method was applied to estimate the b-value(Aki, 1965).

 
 = ̅− 
 
 （1）
 
 ( ) = 1.96
 √ −1}

 Where is the corresponding 95% confidence standard deviation of b. and M

represent the minimum magnitude and the average magnitude of events in the given sample
respectively, and N is the sample size.
 We believe that there should be a increasing trend in stress, corresponding the decreasing
trend in the b-value, in the focal source region before strong earthquakes. Observations of
earthquake cases have recently shown that the area with larger relative declines in the b value is
located very near to the epicentre (Chen et al., 2021b; Chen et al., 2022b; Li et al., 2021a).
Evidently, it is vitally important for an earthquake prediction to identify where the larger relative
declines in the b value distribute.
 For calculation of the b value as a function of time, we applied a moving time window
containing a constant number of events to ensure that the analysis was not influenced by a
change in sample size. First, we mapped the spatial distribution of relative declines in the b value.
The region limited by latitudes 1°S~13°S and longitudes 95° E~120° E was divided into 7686
grids of 0.2° × 0.2°. A circular space window of a radius of 200km (with seventy or more events)
centred at each node on each grid were considered. We calculated the b(t) curve for earthquakes
that occurred in each space window during the period from January 1990 to August 2022, using a
time window comprising 60 events and moving by one event. From each b(t) curve, we
calculated the relative decline in the b value during the period from January 2008 to August 2022,
taking the result as the value at the corresponding grid node. After calculating the relative
declines at all grid nodes, the spatial distribution of relative declines in the b value was created.
For a b(t) curve, m b-values between time t1 and time t2 (t2>t1) are used for calculation of the
relative decline in b. We first calculate differences Δbi between two adjacent b-values.
 ∆ = +1 − , = 1, . . . , − 1 (2)
 If the b-value drops continuously, the differences are negative. In our study when over 50%
differences are negative, the relative declince in b is calculated by
 ∆ 2 − 1
 = × 100 (3)
 1

where b1 is the value of b at time t1, and b2 at time t2.

 Figure 4

a Map of the relative decreases in the b value from January 2008 to August 2022(Δb/b≤-20%). Circular areas of a

radius of 200km (with 70 or more events) centred at each node on each grid of 0.2°× 0.2° was used. The relative

declines distributing in the area enclosed by the bold green line are greater than 45%. b b values (heavy line) as a

function of time for the area enclosed by the red line in Figure 4a, which was obtained by applying a sliding time

window of 100 events moved by three events. The gray area indicates the 95% confidence limit.

 The spatial distribution of the relative decreases in b of over 20% is exhibited in Fig. 4a.
Larger relative declines in the b-value distributes about 100km south of Jakarta. The spacial
extent of the area enclosed by the bold green line is limited by latitudes 7°S~10°S and longitudes

107° E~110° E, where the relative declines greater than 45% distributed.
 We calculated the b value versus time using 335 earthquakes of M≥4.9 in the area enclosed
by the red line in Fig. 4a, applying a time window comprising 100 events and moving by three
events. Fig. 4b shows the result (heavy line), where the gray area indicates the 95% confidence
limit. There is a decreasing trend in the b value from 2009 on. The b value decreased ~48% from
2.6 of 2009 to 1.35 of 2018.

 3. Apparent stress
 The apparent stress is defined as follows [Wyss, 1970]:
 
 = (4)
 0

 Here,  is the shear modulus (for the crustal media, can be considered as 3104MPa), Es
and M0 are the radiated seismic energy and seismic moment, respectively. The data used in this
study were obtained from the source parameter catalogue published online by Harvard University
(www.globalcmt.org/CMTsearch.html). The study area for the apparent stress is showed by the
red quadrilateral in Fig. 5a, larger than the region with the relative declines in b-value greater
than 20% in Fig. 4a. Certain source parameters for earthquakes that occurred between January
1990 and July 2022 (MW ≥4.9, the maximum MW=7.7) in the study area are listed in Table 1, for
a total of 390 earthquakes. Using the seismic moment and magnitude MS given in Table 1, ES is
obtained from formula (5). Then, by applying formula (4), the apparent stresses for the
earthquakes in Table 1 are obtained (Gutenberg & Richter, 1956).
 = 1.5 + 11.8 （5）

Figure 5

a Epicenters of earthquakes with magnitudes of MW≥4.9 occurring from January 1990 to July 2022, as published by

the USGS [https://earthquake.usgs.gov/earthquakes/search/]. The cyan thick lines indicate the plate boundary. The

blue line encloses the relative declines in b-value greater than 20% in Figure 4a. The red quadrilateral shows the

study area for the apparent stress. b Average apparent stress as a function of time obtained by using a sliding window

of 60 events moved by 10 events. c Average apparent stress as a function of time obtained by

applying a five-year time window moved by six months each time.

 The events occurring within the period of January 1990 to July 2022 were listed in a
chronological order. We calculated the average apparent stress using sliding windows of equal
time length and equal number of earthquakes. For the 387 earthquakes of 4.9 ≤MW ≤ 6.9, the
average apparent stress for 60 earthquakes was calculated with a sliding window moved by ten
events each time. The average apparent stress was also calculated with a five-year time window
moved by six months each time. The occurrence time of the last event in the window was taken
as the time of the calculated average apparent stress, yielding the temporal variation of the
average apparent stress, as shown in Figure 5b and 5c. Figure 5b shows the average apparent
stress calculated with the 60-event sliding window. Figure 5c shows the results calculated with
the five-year time window. The two sets of results are in good agreement. From early 2002 to
July 2019 the apparent stress exhibited an increasing trend over seventeen years and more, and
its value rose from ~0.8 MPa to ~2.0MPa, with an increase of 150%. A detailed analysis reveals
that the average rate was approximately 0.0445 MPa/a during the first eleven years and
~0.11 MPa/a during the last six years and more, an increase of approximately 147%. From
August 2019 until July 2022, the apparent stress decreased from a high level to a little below
1.6MPa.

 4. Earth's rotation-correlated seismicity
 The seasonal change in the rate of the Earth’s rotation is mainly caused by atmospheric
effects(Richard & David, 1985; Zharov, 1995; Hӧpfner, 1998 ). Usually, the induced stress did
not trigger earthquakes due to being too weak; but when a stressed focal medium reaches a
critical state for releasing a large/great earthquake, it could trigger small to medium-sized
earthquakes. We statistically investigated the correlation between the phase of the seasonal
variations in the rate of the Earth’s rotation and earthquake occurrence via Schuster’s test to
determine whether the study area reaches a critical state.
 From a temporal change series of the Earth’s rotation rate, the phase angle of the Earth's

rotation at the occurring time of each earthquake can be calculated. The phase angle at each
maximum of the Earth's rotation rate is defined as 0°, at the first minimum on the left of the
maximum as -180°, and at the first minimum on the right one as 180°. With the phase angles of
all earthquakes, we can statistically judge whether there is a significant correlation between those
earthquakes and the Earth's rotation by use of the Schuster’s test(Schuster, 1897; Heaton, 1975).
The results were valued by P-value between 0 and 1. In general, if P 5%, the earthquakes could
be non-random. The P-value of N earthquakes can be obtained on the base of the following
equation.

 −
 r2
 
 P=e N
 
  (6)
 r = ( i =1 sin i ) + ( i =1 cosi ) 
 N 2 N 2

 Where,i is the phase angle of the i-th earthquake. N >10. The Earth's rotation accelerates
when  is between -180 and 0 and decelerates between 0 and 180.
 We first created the spatial distribution of the P-values for earthquakes (M≥4.9) occurring
from April 2016 to March 2022, which is shown in Figure 6a. A spatial window of a circular area
with a radius of 200km is moved by 0.2° in both the along-latitude and along-longitude
directions was considered. When the number of earthquakes in a window is over 15, the P-value
can be worked out. It can be found from Figure 6a that lower P-values concentrate mainly around
Bengkulu, about 370km west of Jakarta.
 We considered the region enclosed by the the quadrilateral in Fig. 6a as the study area for
the P-value as a function of time, it is larger than the lower-P-value area. For earthquakes
(M≥4.9) that occurred in this area from January 2010 to August 2022, the P-value as a function
of time was also computed using a time window of 5 years moved by 4 months. The minimum
number of earthquakes in those time windows is 116, the mean and the maximum are 140 and
179 respectively. Therefore the requirement of earthquake number greater than 10 for the
Schuster’s test can be better met. The chart is shown in Fig. 6b. The P-value has begun to drop
from a higher value since the beginning of 2019, reached the lowest value of ~0.004% in April

2021, revealing a significant correlation between the occurrence of earthquakes and the Earth’s

rotation with confidence level of ~99.996%.

Figure 6

 a Spatial distribution of P

(2) An obvious upward trend in the apparent stress started at the beginning of 2002 and
ended in July 2019, with a lasting time of seventeen and more years and an increase of 150%.
From August 2019 until July 2022, the apparent stress decreased. It reflects that a stage of
sub-instability or critical state could have occurred (Ma & Guo, 2014; Ma, 2016).
 The correlation between the Earth’s rotation and earthquake occurrence was statistically

investigated via Schuster’s test. It‘s shown that lower P-values concentrate mainly around

Bengkulu, about 370km west of Jakarta, indicating a significant correlation between the

occurrence of earthquakes and the Earth’s rotation there, the confidence level reached

~99.996% within the period from in April 2021.
 The b-value changes reversely with the tectonic stress. Observations of earthquake cases
have recently shown that larger relative declines in b value is located near to the epicentre of
strong earthquakes (Chen et al., 2021b; Li et al., 2021a; Chen et al., 2022b; Chen et al., 2022a).
Therefore ,we suggest that the epicentre of a strong earthquake could relate to the area with
larger stress increment, instead of high stress level. Lower P-values reflect that a stage of
critical state could have occurred, the stressed medium could be unstable to release a strong
earthquake. Observations of earthquake cases have also shown that a strong earthquake is
considerably possible to occur near the lower-P area(Wei et al., 2018; Chen & Li, 2019; Chen et
al., 2019, 2020 ). We mapped the spatial distribution of the P-value preceding the 2004 Mw9.0
Sumatra earthquake and the 2010 Mw8.8 Bio-Bío, Chile earthquake, the similar results were
obtained(see Fig. 7). Thus,we have reason to believe that strong earthquakes usually occur near
the lower-P area, also near the region with larger relative declines in the b-value. Based on this a
strong earthquake could occur in Jawa or southeastern Sumatra, Indonesia.

Figure 7

Spatial distribution of P. The irregular polygons show the rupture zones. The red stars indicate the epicenters of the

2004 Sumatra Mw 9.0 and the 2010 Mw 8.8 Bio-Bío mainshocks. The red dashed thick lines indicate the plate

boundary: a The 2004 Sumatra Mw 9.0earthquake. The dataset from USGS catalog (M≥5.0) over the period of

December 1999 to November 2004 was used. A spatial window of a circular area with a radius of 200km is moved

by 0.2° in both the along-latitude and along-longitude directions. b The 2010 Mw 8.8 Bio-Bío earthquake. The

dataset from USGS catalog (M≥4.7) over the period of February 2005 to January 2010 was used. A spatial window

of a circular area with a radius of 250km is moved by 0.2° in both the along-latitude and along-longitude directions.

 Because the strain energy will build up as the stress increases, the longer the stress increases,
the more energy the stressed medium accumulates. In this study, ~10 years long stress increasing
trend was identified by joint analysis of b-value and apparent stress. The apparent stress
exhibited an increasing trend over ~10 years preceding the 2004 MW9.0 Sumatra event, 3.5 years
for the 2008 Mw7.9 Wenchuan,China event, 6.16 years for the 2010 Mw 8.8 Bio-Bío, Chile
earthquake, 8.75 years for the 2011 MW9.0 Tohoku-Oki event, 5 years for the 2019 Mw7.1
Ridgecrest event and 9 years for the 2021 MW8.2 Alaska,USA earthquake(Chen et al., 2022b,
2022a,2022d ). For Mw ≥8.0 earthquakes the stress increasing lasted more than six years.
Considering that the critical state has occurred, we can conclude that there could occur a strong
earthquake of Mw ≥8.0 in Jawa or southeastern Sumatra, Indonesia within the future several
years.

On November 21, 2022, an M5.6 earthquake struck Jawa, Indonesia. The epicenter reported by
the United States Geological Survey (USGS) was located at 6.853° S and 107.095°E, which is
WSW of Ciranjang-hilir, Indonesia. Media reports said 56,320 houses were damaged to varying
degrees in the earthquake, while damage to 31 schools, three hospitals and 13 office buildings
were caused. If the larger earthquake occur in the future, more serious damage could be caused.
In view of this situation, the study in this article is probably important to reduce the seismic
damage there.

Data Availability Statement

 Earthquakes catalog used in this paper are available from the USGS
(https://earthquake.usgs.gov/earthquakes/map/?extent=35.17605,-121.51428&extent=36.42349,-
118.98743&range=search&sort=oldest&timeZone=utc&search=%7B"name":"Search%20Results
","params":%7B"starttime":"1970-01-01%2000:00:00","endtime":"2021-11-30%2023:59:59","m
axlatitude":36.3,"minlatitude":35.3,"maxlongitude":-119.5,"minlongitude":-121,"minmagnitude":
1,"eventtype":"earthquake","orderby":"time-asc"%7D%7D). Source parameters relating to
apparent stress and the data of length of day relating to the Earth's rotation were acquired from
the source parameter catalogue published online by Harvard University
(www.globalcmt.org/CMTsearch.html) and the Earth Orientation Center (EOC)
(http://hpiers.obspm.fr/eop-pc/) respectively.

References
Aki, K. (1965). Maximum likelihood estimate of b in the formula log N = a-bM and its
 confidence limits. Bulletin of the Earthquake Research Institute, the University of Tokyo, 43,

 237–239.

Chen, L. J., Chen, X. Z., Li, Y. E., & Gong, L. W. (2022a). Relationship between decreasing
 amplitude of b-value and seismogenic zone of the Wenchuan Ms 8.0 earthquake. Seismology
 and Geology, 44(4), 1046-1058.
Chen, X. Z., Wang, H. X., Wang, S. W., Wei, Y. G., Guo, X. Y., Chen, L. J., & Li, Y. E. (2018).

Effect of the Earth's rotation deceleration on the occurrence of the 2008 Wenchuan Ms 8.0
 earthquake. Earthquake(in Chinese with English abstract), 38(2), 127-136.
Chen, X. Z., & Li, Y. E. (2019). Relationship Between the deceleration of Earth’s rotation and
 earthquakes that occurred before the Ms 8.0 Wenchuan earthquake. Pure and Applied
 Geophysics, 176, 5253-5260.
Chen, X. Z., Li, Y. E., & Wei, Y. G. (2019). Earth's rotation-triggered earthquakes before the
 2018 MS5.7 Xingwen earthquake. Earthquake Science, 32, 35-39. https//:doi:
 10.29382/eqs-2019-0035-4.
Chen, X. Z., Li, Y. E., Wei, Y. G., Guo, X. Y., & Chen, L. J. (2020). Relationship between the
 Earth's rotation rate and earthquakes occurring prior to the 2011 Mw9.1 Tohoku-Oki Japan
 earthquake. Chinese Journal of Geophysics(in Chinese with English abstract), 63, 440-444.
Chen, X. Z., Li, Y. E., Gong Y, & Chen L. J. (2021a). Variations in apparent stress and b
 value in the rupture area before the 2019 Ms 6.0 Changning earthquake. Progress in
 Earthquake Sciences(in Chinese with English abstract), 51(2), 49-58.

Chen, X. Z., Li, Y. E., & Chen, L. J. （2021b）. Anomalies of the b value prior to the Ms7.8

 Tangshan earthquake of 1976. Chinese Journal of Geophysics(in Chinese with English
 abstract), 64(1), 3612-3618.
Chen, X. Z., Li, Y. E., & Chen, L. J. (2022b). The characteristics of the b-value anomalies
 preceding the 2004 Mw9.0 Sumatra earthquake. Geomatics, Natural and Hazards Risk, 13(1),
 390-339. https//:doi:10.1080/19475705.2022.2029582.
Chen, X. Z., Li, Y. E., & Chen, L. J. (2022c). Why the Mw 6 parkfield earthquake expected in the
 1985–1993 interval was postponed till 2004? Geomatics, Natural and Hazards Risk., 13(1),
 2151-2165. https//:doi: 10.1080/19475705.2022.2109998.
Chen, X. Z., Li, Y. E., & Chen, L. J. (2022d). Investigation on variations of apparent stress in the
 region in and around the rupture volume preceding the occurrence of the 2021 Alaska
 earthquake. Earthquake Science, 35(3), 147-160. https//:doi: 10.1016/j.eqs.2022.06.002.
Gutenberg, B., & Richter, C. F. (1956). Magnitude and energy of earthquakes. Annales
 Geophysicae, 9(1), 1–15.
Heaton, T. H. (1975). Tidal triggering of earthquakes. Geophys. J. R. Astr. Soc. 43(2), 307-326.

Hӧpfner, J. (1998). Seasonal variations in length of day and atmospheric angular momentum.
 Geophysical Journal International, 135, 407–437.
Schuster, A. (1897). On lunar and solar periodicities of earthquakes. Proc. R. Soc. London, 61,
 455-465.
Huang, Y. L., Zhou, S. Y., & Zhuang, J. C. (2016). Numerical tests on catalog-based methods to
 estimate magnitude of completeness. Chinese Journal of Geophysics(in Chinese with English
 abstract), 59(4), 1350–1358.
Li, Y. E., & Chen, X. Z. (2021). Variations in apparent stress and b value preceding the 2010 Mw
 8.8 Bio-Bío, Chile earthquake. Pure and Applied Geophysics, 178, 4797–4813.
 https://doi.org/10.1007/s00024-020-02637-3.
Li, Y. E., Chen, X. Z., & Chen, L. J. (2021a). Joint analysis of b-value and apparent stress before
 the 2011 Mw 9.0 Tohoku-Oki, Japan earthquake. Earthquake Science, 34, 1-11.
Li, Y. E., Chen, X. Z., & Chen, L. J. (2021b). The Earth's rotation-triggered earthquakes
 preceding the occurrence of the 2019 Mw 7.1 Ridgecrest earthquake. Geomatics, Natural and
 Hazards Risk., 12(1), 3021-3034. https//:doi:10.1080/19475705. 2021.1993355.
Ma, J., Guo, Y. S. (2014). Accelerated synergism prior to fault instability: evidence from
 laboratory experiments and earthquake case. Seismology and Geology(in Chinese
 with English abstract), 36(3), 547-561.
Ma, J. (2016). On “whether earthquake precursors help for prediction do exist”. Chinese Sci. Bull.,
 61(4-5), 409-414.
Mogi, K. (1962). Magnitude-frequency relationship for elastic shocks accompanying fractures of
 various materials and some related problems in earthquakes. Bull. Earthquake Res. Inst. Univ.
 Tokyo, 40, 831–883.
Richard, D. R., & David, A. S. (1985). Contribution of stratospheric winds to annual and
 semiannual fluctuations in atmospheric angular momentum and the length of day. Journal of
 Geophysical Research, 90, 8033–8041.
Scholz, C. H. (1968a). The frequency-magnitude relation of microfracturing in rock and its
 relation to earthquakes. Bull. Seismol. Soc. Am., 58, 399-415.
Warren, N. W., & Latham, G. V. (1970). An experiment study of thermal induced microfracturing
 and its relation to volcanic seismicity. Journal of Geophysical Research, 75, 4455-4464.

Wei, Y. G., Chen, X. Z., & Li, Y. E. (2018). Relation between Earth’s rotation and small
 earthquakes occurring before the Ms7.8 Tangshan mainshock. Chinese Sci. Bull.(in Chinese
 with English abstract), 63, 1822-1828.
Wiemer, S., & Wyss, M. (2000). Minimum magnitude of completeness in earthquake catalogs:
 examples from Alaska, the western United States, and Japan. Bull. Seismol. Soc. Am., 90(4),
 859–869.
Wyss, M. (1970). Stress estimates for South American shallow and deep earthquakes. Journal of
 Geophysical Research, 75(8), 1529–1544.
Wyss M, Molnar P. 1972. Efficiency, stress drop, apparent stress, effective stress, and frictional
 stress of Denver, Colorado, earthquakes. Journal of Geophsical Research, 77(8), 1433-1438.
Wyss, M. (1973). Towards a physical understanding of the earthquake frequency distribution.
 Geophys. J. R. Astron. Soc., 31(4), 341–359.
Zharov, V. E. (1995). Connection of the Earth’s rotation with the atmospheric angular momentum
 and the strongest earthquakes. Astronomical and Astrophysical Transactions, 9, 317–327.

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download.

 table1.docx