A Statistical Analysis on the Wenchuan Aftershock Activity Triggered

Earthquake Research in China
Volume 27，Number 1，2013
A Statistical Analysis on the
Wenchuan Aftershock Activity
Triggered by Earth Tide1
Li Jin 1 ) and Jiang Haikun 2 )
1 ) Earthguake Administration of Xinjiang Uygur Autonomous Region，Urumqi 830011 ，China
2 ) China Earthquake Networks Center，Beijing 100045 ，China
A statistical analysis on the Wenchuan aftershock activity triggered by tidal forces is
systematically studied based on Schusters test，including earthquakes triggered by tidal
force，tidal stress and tidal coulomb failure stress． The results show that a group of strong
aftershocks which occurred at the end of July to early August in 2008 at the north of
Wenchuan were obviously triggered by earth tide， the same conclusion is drawn by
Schusters smooth test of the tidal force，tidal stress and tidal coulomb failure stress． In
addition，the Wenchuan aftershock activity is obviously triggered by fortnight tide． In the
north，the aftershocks happened more frequently in the first and last quarters of the
moon，and in the south，the aftershocks happened more frequently in the first and last
quarters of the moon and during the full moon．
Key words: Wenchuan aftershocks; Tidal triggering; Schusters test
INTRODUCTION
Solid tidal stress is a stress which is caused by earth tide in the interior of the Earth and has
a feature of periodical change with a magnitude of about 10 3 Pa． Though much smaller than the
stress drop associated with earthquake，the cumulative rate of solid tidal stress change is two
orders of magnitude larger than that of tectonic stress ( Heaton，1975，1982 ) ． Simultaneously，
tidal stress has a feature of affecting the same location in the interior of the earth repeatedly，and
this characteristic of oscillation，rather than the amplitude，may play a more important role in
tidal triggering of earthquakes． Thus，tidal stress may have an impact on earthquakes，especially
on the faults that are in a critical stress state ( Aki，1956) ． Therefore，the relationship between
tidal stress and earthquakes has been the concern of scientists both at home and abroad． Heaton
(1975) studied the seismic activity triggered by the tidal stress and found that shallow，dip-slip
1
Received on September 2，2011． This project was sponsored by the National Key Technology R＆D Program，
China (2008BAC38B03) ．
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or oblique-slip earthquakes are obviously triggered by tidal stress． Tanaka  s research ( 2002 )
found that there was a strong correlation between tidal stress of reverse faulting and the shear
stress，he considered that when the fault stress is at or near the limit value，a small amplitude
tidal stress may trigger earthquake． According to the study of Zhang Guomin et al． (2001) ，71%
of the earthquakes of M L ≥ 7. 0 in the 20th century in China were modulated by tidal force．
Further study on the number of modulated earthquakes in active periods shows that the rate is as
high as 82. 4% ． Zhang Jing et al． ( 2007 ) used the seismic sequence data with M L ≥ 7. 0 in
China since 1970 to analyze the relationship between the origin time of strong earthquakes and
variation of the horizontal tidal force component，and found that there is a predominant direction
for tidal force in a certain range of space and time at the time when the foreshock，main shock and
aftershock sequence happens，so they believe there is a certain correlation between the tidal force
and triggering of earthquakes． According to the characteristic that the direction of the horizontal
tidal force was relatively concentrated at the origin time of several small earthquakes in Sichuan
Yajiang before February 2001，Chen Ronghua (2003) forecast，to a certain extent，the February
23，2001 M S 6. 0 Sichuan Yajiang earthquake．
At 14: 28 p． m． of May 12，2008， the M S 8. 0 Wenchuan earthquake occurred at the
Longmenshan fault zone in Sichuan，with an affected area of more than 10 5 km 2 ，more than
80，
000 dead or missing． Aftershock activity is very frequent． According to the data from China
earthquake networks，by the end of 2008，the number of aftershocks totaled about 41 000，among
which were eight with magnitudes from 6. 0 to 6. 9，34 with magnitudes from 5. 0 to 5. 9，245 with
magnitudes from 4. 0 to 4. 9，and 3 345 with magnitudes from 3. 0 to 3. 9． Previous studies show
that the Wenchuan earthquake activity was obviously modulated by earth tide． Jiang Haikun et al．
(2008) found that the main shock and most of the aftershocks with M S ≥5. 4 occurred in the first
quarter，last quarter，and full moon or new moon． Zhao Xiaomao et al． (2010) made a statistical
analysis on the relationship between the tidal force and the strong earthquakes with M ＞ 5. 0
happening from May 12，2008 to September 30，2009，and found that there is a good correlation
between the occurrence time of the wave crest / trough of tidal force that causes linear strain
paralleled fault and the origin time of the Wenchuan earthquake and strong aftershocks． According
to the latest research from Li et al． (2011) ，the earthquakes that had happened on the SongpanGarzê tectonic belt before the Wenchuan earthquake may be related to tides．
On the basis of previous studies，using the Wenchuan aftershock data from May 12，2008 to
December 31，2008， a systematical analysis was made on the Earth tide triggering of the
Wenchuan aftershock activity at different periods of time and regions based on Schuster  s test，
including the possible triggering effect of tidal force，tidal stress and tidal Coulomb failure stress
on earthquakes．
1
DATA SELECTION
This paper chooses the period from May 12，2008 to December 31，2008 as the statistical
study period． The temporal distribution of the Wenchuan earthquake sequence is shown in Fig． 1．
We can see from the figure that there are two obvious strong active periods． The first is the initial
stage following the Wenchuan earthquake，in which strong aftershocks with magnitudes from 5. 0
to 6. 0 were frequent; the second is from the end of July to early August，during which three
events with M ＞ 6. 0 occurred． Accordingly，taking roughly the Qingchuan M6. 4 earthquake of
May 25 and a cluster of strong earthquakes happening from end of July to early August as the time
dividing point，we divide the Wenchuan series into three time periods，namely，period 1: May
12，2008 ～ May 25，2008，period 2: May 26，2008 ～ August 15，2008，and period 3: August
16 ～ December 1，2008．
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Fig． 1
The magnitude-time plot of the Wenchuan earthquake sequence ( May 12，
2008 ～ December 31，2008)
( a) The Wenchuan earthquake sequence with M S ≥4. 5;
( b) The north segment of Wenchuan earthquake sequence with M S ≥4. 0;
( c) The south segment of Wenchuan earthquake sequence with M S ≥4. 0
On the basis of time division，taking Beichuan-Anxian as the boundary，we divide the
Wenchuan aftershock area into the southern and northern segments． The main basis for the spatial
segmentation is: ( 1 ) the rupture mechanism difference between the south and north segments．
According to the study on the Wenchuan earthquake rupture process ( Wang Weimin et al． ，
2008; Huang Yuan et al． ，2008; Cheng et al． ，2009; Hua Wei et al． ，2009; Zhang Yong et
al，2009; Cheng Wanzheng et al． ，2009a; Guo Xiangyun et al． ，2010; Wang Qincai et al． ，
2009) ，the aftershock activity along the strike of the Longmenshan fault presents obvious
segmentation characteristics with Beichuan as the boundary，along the direction of main rupture
from SW to NE，where the type of focal mechanism turns from thrust to strike-slip． In the
northeast segment，the direction of regional principal compressive stress is NE，being consistent
with the fault strike，and in the southwest segment，the direction of regional principal compressive
stress is NW，oblique or vertical to the fault，and consistent with the background principal
compressive stress in the Longmenshan area ( Shi Yutao et al． ，2009 ) ; ( 2 ) the difference of
aftershock activity between the southern and northern segments; the southern part presents the
mainshock-aftershock type sequence attenuation characteristics，but the northern part presents the
multiple earthquake type sequence characteristics ( Fig． 1( b) ，( c) ) ( Jiang Haikun et al． ，2008，
Li Zhixiong et al． ，2009 ) ; and ( 3 ) the structural difference and the gaps of aftershocks in
spatial distribution ( Ren et al． ，2010; Zhu Ailan et al． ，2008; Jiang Haikun et al． ，2008;
Cheng Wanzheng，2009b; Li Zhixiong et al． ，2009; Li Chuanyou et al． ，2008 ) ． In addition，
there are obvious differences in focal depth，structural lithology，geographical landscape and so on
between the southern and northern segments． For example，the relocation results of the Wenchuan
Earthquake Research in China
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earthquake sequence show that the focal depth of the aftershock sequence is mainly within the
range of 24km，but the depth of aftershocks in Beichuan is shallower，distributed in the 10km ～
20km ( Zhao Bo et al． ，2011 ) ． The width and spatial geometry of the aftershock zone exhibit
obvious segmentation ( with Anxian as the boundary ) and inhomogeneity． The rigid Pengguan
Massif controls the distribution of the earthquake sequence and the complex rupture process
( Chen Jiuhui et al． ，2009) ． Zhang Zhuqi (2010) inversed the 2-D models of the Longmenshan
fault，and the result shows that there is an obvious north-south division characteristic in the
seismogenic fault system of the Longmenshan central fault． Lying south to the Beichuan-Nanba
transition zone，the sub-fault breaking through south Beichuan to Qingping is featured by a duplex
faulting system，which includes two parts，one being a shallow steeply-dipping reverse fault with
dip angle over 70° and bottom depth of 10km ～ 15km， and the co-seismic displacement is
distributed mainly above 10km depth，with an average displacement over 6m． In contrast，the
deeper and gentle-dipping reverse fault，with dip-angle of 25° and the bottom reaching a depth of
30 km，was ruptured only at its top and bottom，with an average co-seismic displacement of 4m．
Therefore，we take Beichuan-Anxian as the boundary and divide the Wenchuan sequence into
southern and northern segments for the discussion．
According to the G-R relation，the magnitude completeness thresholds of the sequence for
each period ( Fig． 2 ) are M S 3. 2，M S 2. 2 and M S 1. 9． The gradual increase of magnitude of
completeness of the sequence is related to the increase of the mobile seismic network and
improvements in cataloging． In the early stages of the earthquakes，lots of small earthquakes were
omitted because of overlapping of seismic phases， even including some earthquakes with
magnitudes M S ＞ 3. 2．
2
RESEARCH METHODS
Using the Schusters test， this paper studies the relationship between the Wenchuan
aftershocks and earth tide． First，we calculate the tidal stress components ( including tidal force，
tidal normal stress，shear stress and tidal Coulomb failure stress on the fault plane) in the seismic
source，then assign the value of the tidal phase angle at the occurrence time of the earthquake
according to the time series of tidal stress ( Fig． 3 ) ，and pick up the stress peak nearest to the
earthquake occurrence，assigning its phase angle to be 0° and that of the following and preceding
troughs to be ± 180° respectively． Then，we perform linear division to the angular distance
between a tidal peak and adjacent troughs． The time interval between a tidal peak and adjacent
troughs is not constant，but dependent on the angular distance between the peak and the trough．
Such phase-based analysis allows uniform comparison of data，regardless of the asymmetry of tidal
stress history．
After determining the tidal phase angle for all earthquakes，we can investigate whether they
are concentrated near a specific angle by Schuster  s test，that is，to judge whether or not the
earthquake is triggered by the tide． In Schusters test，each earthquake is represented by a unit
length vector in the direction defined by its tidal phase angle，the length of the vectorial sum is
described by L． The tidal phase angle of L is the preponderant phase angle for the data set． The
value of L is calculated by equation (1) ，and the geometric meaning is shown in Fig． 4．
{
L = 槡A 2 + B 2
N
A =
∑ cosθ ，B
i
i=1
(1)
N
=
∑ sinθ
i
i=1
Where θ i is the phase angle of the ith earthquake and N is the total number of earthquakes．
If earthquakes take place randomly，θ i is distributed randomly，and the probability that the length
of a vectorial sum is equal to or larger than L is ( Tsuruoka et al，1995)
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Fig． 2
The magnitude-frequency distribution of the Wenchuan aftershock sequence
( a) May 12，2008 ～ May 25，2008; ( b) May 16，2008 ～ August 15，2008;
( c) August 16，2008 ～ December 31，2008
Fig． 3
Definition of tidal phase angle ( Tanaka et al． ，2004)
27
Earthquake Research in China
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Fig． 4
Geometric meaning of L ( L is the vectorial sum of N unit-length vectors)
(
)
L2
(2)
N
If we definean earthquake as randomly occurring，independent of the tidal phase angle as the
zero hypothesis，then p is the significance level for rejecting the null hypothesis，and the p-value
ranges between 0 and 1，and the smaller the p-value，the higher the confidence in rejecting the
null hypothesis． In this study，we usually adopt a threshold of p ＜ 5% to judge whether or not the
earthquake is triggered by tides． However，this threshold can in fact be adjusted appropriately or
determined subjectively by the actual situation and the confidence we need．
p = exp －
3 RESULTS
3. 1 The Statistical Test for Tidal Force M odulating in Day Scale
This paper conducts the day-scale modulating test for the tidal force by using the earthquakes
above selected within the scope of space and time，with results shown in Table 1． We can see that
except for the earthquakes in the south segment with magnitude larger than 4. 5，the p-values in
almost all periods are greater than the trigger threshold of 0. 05． This result is basically consistent
with relevant research abroad ( Tanaka，2010; Tanaka et al． ，2004; Cadicheanu et al． ，2007) ．
The reason for this may be that the trigger relationship which might exist originally is concealed by
the averaging effect to a certain extent ( Wu Xiaoping et al． ，2009 ) ． In order to reveal the
phenomenon that may be concealed，the common treatment is to seek the p-value by adding
windows to the data ( Tanaka，2010; Tanaka et al． ，2004 ) ． Commonly used are the smoothing
by time window and spatial window． Due to the small spatial distribution of the Wenchuan
earthquake sequence，we only perform time window smoothing to the above north-south divided
data． The smoothing over the earthquake data of the north and south segments is done with a
60-day window ( the value of the curve takes the data 30 days before and after the earthquake)
and one day step length． The result is shown in Fig． 5．
We can see from Fig． 5，the p-value on the curve for the north segment was relatively high
before August 1，2008 and after October 1，2008，the aftershocks presented the characteristic of
random distribution and there was no tidal modulation or clear tidal modulation observed．
However，from early August to the end of September，the p-value was relatively low，lower than
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the threshold 0. 05 which is used for judging the tidal triggering of the earthquake． This shows that
the earthquake is to some extent affected strongly by the tides． It is noteworthy that in this period
especially from the end of July to early August， there was an obvious undulation of strong
earthquake activities ( Fig． 1( a) ) ． During this period，three earthquakes with magnitude larger
than 6. 0 and several earthquakes with magnitude larger than 5. 0 occurred in the north segment
( Fig． 1( b) ) ． According to this，we preliminary believe that this strong aftershock activity and
the group of earthquakes with magnitude of about 6 may have some correlation with tidal
triggering． The p-value in the south segment was also relatively low in early August，but did not
reach the threshold of 0. 05 for tidal triggering．
Table 1 The p-value of the statistical test for tidal force by the Wenchuan earthquake sequence
with different lower limits of magnitude
Period
Whole period
Period I
Period II
Period III
Time range
( a-m-d)
2008-05-12
～ 12-31
2008-05-12
～ 25
2008-05-26
～ 08-15
2008-08-16
～ 12-31
Mc
North segment
South segment
p
Mc
p
Mc
p
Mc
p
3. 2
0. 2595
3. 2
0. 3830
2. 2
0. 1434
1. 9
0. 2733
3. 5
0. 8044
3. 5
0. 6758
2. 5
0. 4200
2. 0
0. 3936
4. 0
0. 2555
4. 0
0. 1151
3. 0
0. 4250
2. 5
0. 4497
4. 5
0. 1973
3. 5
0. 6530
3. 0
0. 7479
4. 0
0. 9238
3. 5
0. 3067
4. 0
0. 8191
3. 2
0. 5646
3. 2
0. 4784
2. 2
0. 8405
1. 9
0. 9392
3. 5
0. 4271
3. 5
0. 3733
2. 5
0. 7636
2. 0
0. 9555
4. 0
0. 3245
4. 0
0. 2385
4. 5
0. 0193
3. 0
0. 9977
2. 5
0. 5162
3. 5
0. 9244
3. 0
0. 8011
4. 0
0. 3629
3. 5
0. 8780
4. 0
0. 4079
Fig． 5
The result for the p-value of tidal force smoothed by the 60-day length time window
using the data of the Wenchuan sequence with magnitude M S ≥3. 2
( dotted line: south segment，solid line: north segment)
In order to further analyze the tidal triggering of the aftershock in this period，we choose the
data from August 1，2008 to October 1，2008 in the north aftershock area to perform Schuster s
test． Selecting the magnitude lower limits 2. 5，3. 0，3. 5 respectively， we get p-values of
0. 0471，0. 0690 and 0. 0870，all close to or reaching the threshold 0. 05 of tidal triggering of
earthquakes． This indicates that the Wenchuan aftershocks in this period were exactly triggered by
the Earth tide． Analysis of the tidal phase angle distribution of aftershocks with magnitude larger
Earthquake Research in China
30
than 3. 0 in this period ( Fig． 6 ) shows that the earthquakes are concentrated on tidal phase 0°
and ± 150°，close to the maximum( full moon) or minimum ( new moon) value of the tidal force．
Fig． 6
The tidal force phase angle distribution histogram of the Wenchuan sequence
with M S ≥3. 2 on the north segment from August 1，2008
to October 1，2008 with Schusters test ( the total number is normalized to 1)
3. 2
The Statistical Test for Fortnightly Tidal M odulation
Further study was done on the relationship between the origin time of aftershocks and the
fortnightly tide，in which the tidal stress value of 12 oclock each day is selected ( this paper uses
the value of the north-south component，because the phase of each component is consistent or
different by 180°) to successively determine the tidal phase angle for each earthquake according
to the fortnightly tide curve． The fortnight tide phase angle distributions for the north and south
segments are shown in Fig． 7．
Fig． 7
The statistical rose diagram of the fortnightly tidal phase angles of the
Wenchuan sequence with magnitude M S ≥3. 2
( Left: south segment，right: north segment． The total number is normalized to 1)
It is clear that the aftershocks are concentrated on － 120° in both the north and south
segments，and meanwhile，the p-values gotten by using Schuster  s test for different magnitude
lower limits are all very small ( close to 0 ) ，indicating that under the monthly-scale tidal
changes，the tidal modulation of earthquakes is very obvious． However，we must point out that in
the early stage after the Wenchuan earthquake ( before June ) ，the aftershock frequency was
relatively high，which may affect the statistical result． Furthermore，the main shock and several
strong earthquakes in this period all occurred near the first quarter moon and the last quarter
moon． In order to reduce the influence of aftershock clustering on the statistical results，we
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randomly select 30 earthquakes from the complete catalog of the north and south segments every
month to make the statistics，and repeat this 100 times to reduce the influence of random effects．
The results of Schusters test show that the p-values are also very small ( close to 0) ，less than the
threshold 0. 05 for the tidal triggering of earthquake． According to this we can draw a conclusion
that the Wenchuan aftershock activity was obviously triggered by the tidal forces in the monthly
scale． We can also see from the tidal phase histogram ( Fig． 8 ) that in the south segment
( Fig． 8( a) ) ，earthquakes mostly occurred near ± 90° and 0°，that is，at the first quarter，last
quarter and the full moon． However，in the north ( Fig． 8 ( b ) ) ，besides at ± 90°，many
earthquakes also occurred near 180°，which means that except for the first and last quarters，the
new moon is also a risk period．
Fig． 8
The statistical histogram for the fortnightly tidal phase angle of the Wenchuan
earthquake sequence at the south ( a) and north ( b) segments．
( Randomly select 30 earthquakes each month and repeat 100 times，
the total number is normalized to 1)
3. 3 Phase Angle Test for Tidal Stress on the Fault Plane
We collected the focal mechanism data of 1006 Wenchuan aftershocks． The data includes the
focal-mechanism solutions of 906 earthquakes with M L ≥3. 5 determined by Zhang Zhiwei et al．
(2010) using amplitude ratios and P wave onsets，the calculation results of strong aftershocks
from Zheng Yong et al． (2009) and the results from Hu Xingping et al． (2008) ，Guo Xiangyun
et al． (2010) ，as well as research from the Harvard University CMT and USGS website． For the
results of the same earthquake from different sources，we keep a more consistent result after
comparison ( first pick up the two closest results，then comprehensively compare all results and
choose one of them ) ． The two nodal planes of focal mechanism are basically NE- and NWoriented． Since it is difficult to distinguish the real fault planes of small earthquakes，for the
convenience of statistics，we define the focal mechanism with a NE direction as the nodal plane I
and NW direction as the nodal plane II． Based on the above data，we perform Schusters test on
the tidal normal stress and tidal shear stress on the fault plane．
The statistical results show the p-value for tidal normal stress is 0. 9448，p-value for tidal
shear stress is 0. 8371，much higher than the threshold 0. 05 for tidal triggering of earthquakes．
We perform time window smoothing on the normal stress and shear stress，selecting a 90 day
window length． The smooth curve is shown in Fig． 9． The result of tidal shear stress on the fault
plane from a 90-day window length smoothing is still high，failing to reach the threshold 0. 05，
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but the result of tidal normal stress in mid-September is smaller，reaching the threshold 0. 05，
and the period has a one month lag with the fluctuation of strong aftershock activities mentioned
above ( Fig． 1) ． However，considering that the window length is 90 days ( the value of the curve
is calculated from the earthquake data 45 days before and after the shocks ) ， the three
earthquakes with magnitude larger than 6. 0 and several earthquakes with magnitude larger than
5. 0 in the north segment are still in this time range． According to this，the strong aftershock
activity from the end of July to early August may be related to the tidal normal stress．
Fig． 9
The result for the p-value of tidal stress on the fault plane smoothed by 90 days
length of time window using the data of the Wenchuan aftershock sequence
( Solid line: normal stress，dotted line: shear stress)
Fig． 10
The statistical histogram for the tidal normal stress ( a) and tidal shear
stress ( b) phase angle of the whole Wenchuan aftershock area
( The total number is normalized to 1)
Statistic analysis was done on the tidal phase angles of the tidal normal stress and shear
stress， respectively ( Fig． 10 ) ． We can see from Fig． 10， in respect of normal stress
( Fig． 10( a) ) ，earthquakes happened mostly in the vicinity of － 120° and 0° ( 180°) ，namely，
near the maximum and minimum value of the tidal normal stress; but for the tidal shear stress
( Fig． 10( b) ) ，earthquakes also happened mostly at 0° ( 180°) and 90°，corresponding to the
maximum of the shear stress． In other words，although tidal shear stress does not pass the
statistical test for earthquake triggering，there are still more events happening at the interval of the
maximum values， and the earthquake-concentrating period is indeed near the extrema or
( maximum or minimum) of the tidal normal stress．
We further perform Schusters test on the tidal normal stress and tidal shear stress on the fault
planes ( Fig． 11 ) ，and the result shows that the p-values are very high and dont reach the
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threshold mentioned above． However，after smoothing，the p-value for the normal stress in the
north becomes very small after mid August，which is quite similar to the results of the tidal force
( Fig． 5 ) and the tidal normal stress of the whole aftershock area data． This means that the
fluctuation of strong aftershock activity in the north in this period was indeed related to tidal
triggering．
Fig． 11
The result for the p-value of tidal normal stress and shear stress on the
fault planes smoothed by 90-day length of time window using the data of the
Wenchuan aftershock sequence
( ( a) South segment; ( b) North segment，solid line: normal stress，dotted line: shear stress)
3. 4
The Test for Tidal Coulomb Failure Stress
Because the increase of the normal stress ( define the extension as positive) and shear stress
inthe sliding direction is all propitious to the fault rupture，the comprehensive effect of the two
stresses on the fault can be reflected by tidal Coulomb failure stress． The changes of Coulomb
failure stress caused by tide can be obtained by the formula of Coulomb failure stress ( Fisher et
al，2006，Wan et al． ，2004，Cochran et al． ，2004) ．
ΔCFS = Δτ + μ'Δσ
In the formula，ΔCFS represents the changes of Coulomb failure stress caused by tide，Δτ is
the changes of tidal shear stress in the sliding direction on the fault，μ' is the effective friction
coefficient，μ' = μ (1 － B) ，μ is the friction coefficient，B is the Skempton coefficient，the theory
range is 0 ～ 1． In this study we usually set μ' = 0. 4 ( Fisher et al． ，2006; Wan et al． ，2004;
Cochran et al． ，2004) ．
Tidal Coulomb failure stresses on the fault plane are calculated according to the division of
the north and south segments of the aftershock area and the rupture types，and the results are
shown in Table 2． We can see that the p-value of Schusters test for the reverse fault in the north
segment is quite small，having reached the threshold for earthquake triggering． We did further
statistic analysis on the tidal phase angles for the reverse fault in the north segment，and found
that earthquakes are concentrated mostly near 45° ( Fig． 12) ，this may be related to the absence
Earthquake Research in China
34
of consideration of the ocean loading which affects the selection of real phase ( Tsuruoka et al． ，
1995) ．
Table 2 The p-value of the statistical test for tidal Coulomb failure stresses by regions and
rupture types in the aftershock area．
All faults
Normal fault
Reverse fault
Strike-slip fault
Oblique-slip fault
Whole area segment
0. 5956
0. 7971
0. 3457
0. 9664
0. 8526
North segment
0. 4941
0. 8005
0. 0268
0. 7314
0. 3706
South segment
0. 4667
0. 9139
0. 9331
0. 6791
0. 3511
Fig． 12
The tidal Coulomb failure stress phase angle distribution histogram
for the reverse fault in the north segment
( The total number is normalized to 1)
Forthe whole aftershock area，we perform Schusters test for the tidal Coulomb failure stress on the
fault plane，and from the result of smoothing of p-values with a 90-day window length ( Fig． 13) ，
we can see that the p-value of early August is very close to the threshold for the tidal triggering of
the earthquake，which again shows that the group of strong earthquakes happening from the end of
July to the early August are very much likely to have been triggered by the earth tide．
Fig． 13
The result for the p-values of tidal Coulomb failure stress
smoothed by 90 days length of time window using the data of
Wenchuan aftershock sequence
4
CONCLUSION AND THE DISCUSSION
A statistical analysis on the Wenchuan aftershock activity triggered by earth tide is
systematically conducted based on Schusters test as per periods and segments， including
earthquakes probably triggered by tidal force，tidal stress and tidal Coulomb failure stress． The
main results are summarized as follows:
(1) Because of the average effect，the simple Schuster  s test is often unable to pass the
statistical test， that is， the p-value is generally higher． After selecting the appropriate time
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window and smoothing，the statistical relationship between the aftershock activity and the Earth
tide could be found．
( 2 ) The statistical result of tidal force inthe day scale shows that the strong earthquake
activity happening from the end of July to early August is obviously modulated by earth tide． The
p-value of Schusters smoothing is very small in this period，having reached the threshold of 0. 05
for tidal triggering of earthquakes． Further study on the distribution of the tidal angles shows that
the earthquakes of this period are distributed mostly near 0° and ± 150°，and near the interval of
the maximum ( full moon ) and minimum ( new moon ) of the tidal force，but in the south
segment，this relationship is not obvious，and we assume that there is no triggering or that the
triggering is not obvious．
(3) The statistical test for the fortnightly tidal force shows that，for both north and south
segments of the aftershock zone，the p-values are very small，much less than the threshold for
tidal triggering of earthquake，so the tidal triggering of the Wenchuan aftershocks is very obvious
on a monthly scale． The statistics of the tidal phase angles show that the earthquakes in the north
are concentrated near ± 90° and 180° of the monthly tidal curve，that is，in the first quarter of
the moon，last quarter of the moon and the new moon; and in the south，the earthquakes are
concentrated near ± 90° and 0° on the monthly tidal curve，i． e． The first quarter，last quarter
and full moon．
(4) The test results of the tidal normal stress and shear stress on the fault planes in the
whole aftershock area show that the smoothing result for the tidal normal stress is less than the
threshold in the period of mid-September． This is quite similar to the result of the tidal force by
Schusters test in the north segment． According to calculations on the data divided into the north
and south segments，it is found that the time range where the smoothed p-value of the tidal normal
stress in the north reaches the threshold is broader，which verifies the correctness of the previous
calculations． The smoothed p-value for the tidal normal stress in the south is relatively low in the
middle of August，but it did not reach the threshold． With respect to the tidal normal stress，the
earthquakes are concentrated mostly near 0°，180° and － 120°，that is，near the maximum and
minimum of the tidal normal stress． However，with respect to the whole aftershock area，the
calculation results of the tidal shear stress all failed to reach the threshold for the tidal triggering of
the earthquake，regardless of calculating per segment or the whole area．
(5) According to the rupture types in the north and south segments of the aftershock area，
Schusters test wasperformed on the tidal Coulomb failure stress on the fault plane，and the result
shows that the p-value of Schusters test for the reverse fault in the north is quite small，reaching
the threshold for triggering earthquakes． We further made statistical analysis on the tidal phase
angles for the reverse fault in the north segment，and found that the earthquakes are mostly
concentrated near 45°． This may be related to not taking into account the ocean loading，which
affects the choice of the real phase ( Tsuruoka et al． ，1995) ．
In summary，on the whole，tidal triggering of earthquake is more obvious in the north than
the south，the result on a monthly scale is clearer than that on a day scale，and the tidal force
triggering is more obvious than that from tidal stress and tidal Coulomb failure stress． This may be
related to the followingthree reasons: ① Though we tried to collect the focal mechanisms of strong
aftershocks，the focal mechanism solutions of some earthquakes were still missed，and for the
tidal force， we can only consider the completeness of the earthquake catalog． ② There is
uncertainty in the calculation of the focal mechanism solutions． There are great differences in the
focal mechanism solutions with magnitude larger than 5. 0 calculated between different
researchers，and the result of small earthquakes is more difficult to test． ③ There is also impact
from uncertainty of the real fault planes on the results． In order to simplify the study，according to
the spatial distribution of the Wenchuan aftershocks，we define the NE direction of the focal
36
Earthquake Research in China
mechanism as the real fault plane for the calculation，but the fact is likely not the case． In other
words，the completeness and the accuracy of the focal mechanism is the foundation of studying the
tidal triggering of earthquake when considering the direction of stresses applied． Due to the
uncertainty of the focal mechanism，the result from the seemingly more “accurate”method that
resolves the tidal stress on the fault plane is not more precise than the method that only concerns
the change of the tidal force．
In addition，in this paper we do not take ocean loading into account，and that may influence
the final result and lead to some un-explanatory phenomena，such as the case in Fig． 12，for when
dealing with the earthquakes in a sub-region，the neglect of ocean tide loading will not likely have
a great effect on the phase selection，since the time lag of the ocean tide behind the direct earth
tide is nearly constant，but the phase selected by such an analysis is not necessarily the true tidal
phase ( Tsuruoka et al． ，1995) ．
ACKNOWLEDGMENTS
The authors would like to express their heartfelt thanks to research professors Zhang Jing，Xi
Qinwen，Yan Chunheng，Li Zhirong and research professor Li Shengle for their help in writing the
program for this study，and Zhang Zhiwei for providing the focal mechanism data with magnitude
larger than 3. 5．
REFERENCES
Aki K． Some problems in statistical seismology ［J］． Zisin H，1956，8:205 ～ 208 ( in Japanese) ．
Cadicheanu N． ，Ruymbeke M． V． ，Zhu P． Tidal triggering evidence of intermediate depth earthquakes in the
Vrancea zone［J］． Nat Hazards Earth Syst Sci，2007，7:733 ～ 740 ( in Romania) ．
Chen Jiuhui，Liu Qiyuan，Li Shuncheng et al． Seismotectonic study by relocation of the Wenchuan M S 8. 0
earthquake sequence ［J］． Chinese J． Geophys． ，2009，52 ( 2 ) : 390 ～ 397 ( in Chinese with English
abstract) ．
Chen Ronghua． Relation between tidal force triggering of significant shocks and the large earthquake and its
application in the prediction of Yajiang earthquake ［J］． Earthquake，2003，23 ( 1 ) :53 ～ 56 ( in Chinese
with English abstract) ．
Cheng Wanzheng，Zhang Zhiwei，Ruan Xiang． Spatio-temporal variation and focal mechanism of Wenchuan M S 8. 0
earthquake sequence ［J］． Earthquake Science，2009a，22(2) :107 ～ 117．
Cheng Wanzheng． Phased estimating for the temporal and spatial development of the seismic sequence of the 2008
M8. 0 Wenchuan earthquake and its strong aftershocks ［J］． Earthquake Research in Sichuan，2009b，133
(4) :1 ～ 11 ( in Chinese with English abstract) ．
Cheng Wanzheng． The Wenchuan M S 8. 0 earthquake sequence and shock type determination ［J］． Earthquake，
2009a，29(1) :15 ～ 25( in Chinese with English abstract) ．
Cochran E． S． ，Vidale J． E． ，Tanaka S． Earth tides can trigger shallow thrust fault earthquakes［J］． Science，
2004，306:1164 ～ 1166．
Fischer T，Kalenda P，Skalsky L． Weak tidal correlation of NW-Bohemia / Vogtland earthquake swarms ［J］．
Tectonophysics，2006，424:259 ～ 269．
Guo Xiangyun，Chen Xuezhong，Li Yane． Focal mechanism solutions for the 2008 M S 8. 0 Wenchuan earthquake
and part of its aftershocks ［J］． Earthquake，2010，30(1) :50 ～ 60( in Chinese) ．
Heaton T． H． Tidal triggering of earthquakes［J］． Bull Seism Soc Am，1982，72 (6) :2181 ～ 2200．
Heaton T． H． Tidal triggering of earthquakes［J］． Geophys J，1975，43(2) :307 ～ 326．
Hu Xingping，Yu Chunquan，Tao Kai et al． Focal mechanism solutions of Wenchuan earthquake and its strong
aftershocks obtained from initial P wave polarity analysis［J］． Chinese J． Geophys． ，2008，51 ( 6 ) :1711 ～
1718( in Chinese with English) ．
Hua Wei，Chen Zhangli，Zheng Sihua． A study on segmentation characteristics of aftershock source parameters of
Wenchuan M S 8. 0 earthquake in 2008 ［J］． Chinese J． Geophys． ，2009，52(2) : 365 ～ 371( in Chinese) ．
Huang Yuan，Wu Jianping，Zhang Zhongtian et al． Relocation of the M S 8. 0 Wenchuan earthquake and its
aftershock sequence ［J］． Science in China ( Earth Sciences) ，2008，30(10) :1242 ～ 1249( in Chinese) ．
Volume 27，Number 1
37
Jiang Haikun，Li Mingxiao，Wu Qiong et al． Features of the May 12 Wenchuan M S 8. 0 earthquake sequence and
discussion on relevant problems ［J］． Seismology and Geology，2008，30(3) :34 ～ 47( in Chinese) ．
Li Chuanyou，Ye Jianqing，Xie Furen et al． Characteristics of the surface rupture zone of the M S 8. 0 Wenchuan
earthquake，China along the segment north to Beichuan ［J］． Seismology and Geology，2008，30(3) :483 ～
496( in Chinese with English) ．
Li Q． ，Xu G． M． Tidal triggering of earthquakes in Longmenshan region: the relation to the fold belt and basin
structures［J］． Earth Planets Space，2011，doi:10. 5047 / eps． 2011. 06. 037
Li Zhixiong，Shao Zhigang，Zhao Cuiping et al． Study on the sectional features of the aftershock sequence of the
Wenchuan M S 8. 0 earthquake ［J］． Earthquake，2009，29(1) :26 ～ 32( in Chinese with English abstract) ．
Lockner D． A． ，Beeler N． M． Premonitory slip and tidal triggering of earthquakes［J］． J Geophys Res，1999，
B104(9) :20133 ～ 20151．
Ren J． J． ，Chen G． H． ，Xu X． W． ，et al． Surface rupture of the 2008 Wenchuan，China，earthquake in the
Qingping stepover determined from geomorphologic surveying and excavation，and its tectonic implications
［J］． Bulletin of the Seismological Society of America，2010，100:2651 ～ 2659．
Shi Yutao，Gao Yuan，Zhao Cuiping et al． A study of seismic anisotropy of Wenchuan earthquake sequence［J］．
Chinese J． Geophys． ，2009，52(2) :398 ～ 407( in Chinese with English abstract) ．
Tanaka S． Tidal triggering of earthquakes precursory to the recent Sumatra megathrust earthquakes of 26 December
2004 ( M W 9. 0) ，28 March 2005 ( M W 8. 6 ) ，and 12 September 2007 ( M W 8. 5) ［J］． Geophys Res Lett，
2010，
37，L02301，doi:10. 1029 /2009GL041581．
Tanaka S． ，Ohtake M． ，Sato H． Evidence for tidal triggering of earthquakes as revealed from statistical analysis of
global data［J］． J． Geophys Res，2002，107:2211，doi:2210. 1029 /2001JB001577．
Tanaka S． ，Ohtake M． ，Sato H． Tidal triggering of earthquakes in Japan related to the regional tectonic stress
［J］． Earth Planets Space，2004，56:511 ～ 515．
Tsuruoka H． ，Ohtake M． ，Sato H． Statistical test of the tidal triggering of earthquakes: contribution of the ocean
tide loading effect［J］． Geophys J Int，1995，122:183 ～ 194．
Wan Y． G． ，Wu Z． L． ，Zhou G． W． Focal mechanism dependence of static stress triggering of earthquakes［J］．
Tectonophysics，2004，390:235 ～ 243．
Wang Qincai，Chen Zhangli，Zheng Sihua． Spatial segmentation characteristic of focal mechanism of aftershock
sequence of Wenchuan Earthquake［J］． Chinese Sci Bull，2009，54(16) :2348 ～ 2354．
Wang Weimin，Zhao Lianfeng，Li Juan et al． Rupture process of the M S 8. 0 Wenchuan earthquake of Sichuan
［J］． Chinese J． Geophys． ，2008，51(5) :1403 ～ 1410 ( in Chinese with English abstract) ．
Wu Xiaoping，Mao Wei，Huang Yong et al． Tidal stress triggering effects of earthquakes based on various tectonic
regions in China and related astronomical characteristics ［J］． Science in China ( Physics，Mechanics ＆
Astronomy) ，2009，52(8) :1271 ～ 1283．
Zhang Guomin，Li Li，Li Kaiwu et al． Group strong earthquakes and triggering by tidal stress［J］． Earthquake
Research in China，2001，17(2) :110 ～ 120( in Chinese with English abstract) ．
Zhang Jing，Xi Qinwen，Yang Linzhang et al． A study on tidal force / stress triggering of strong earthquake［J］．
Chinese J． Geophys，2007，50(2) :448 ～ 454( in Chinese) ．
Zhang Yong，Xu Lisheng，Chen Yuntai． Spatio-temporal variation of the source mechanism of the 2008 great
Wenchuan earthquake ［J］． Chinese J． Geophys． ，2009，52(2) :379 ～ 389( in Chinese) ．
Zhang Zhiwei，Zhang Yongjiu，Cheng Wanzheng et al． Focal mechanisms and stress field of small earthquakes of
the M S 8. 0 Wenchuan earthquake sequence ［J］． Journal of Seismological Research，2010，33 ( 1 ) :43 ～ 49
( in Chinese) ．
Zhang Zhuqi，Zhang Peizhen，Wang Qingliang． The structure and seismogenic mechanism of Longmenshan high
dip-angle reverse fault ［J］． Chinese J． Geophys． ，2010，53 ( 9 ) : 2068 ～ 2082 ( in Chinese with English
abstract) ．
Zhao Bo，Shi Yutao，Gao Yuan． Relocation of the Wenchuan M S 8. 0 earthquake sequence ［J］． Earthquake，
2011，31(2) :1 ～ 10( in Chinese with English abstract) ．
Zhao Xiaomao，Wang Xin，Ke Chang  an et al． Preliminary research on relation between strong aftershocks of
Wenchuan earthquake and tidal force［J］． Seismological and Geomagnetic Observation and Research，2010，
31(3) :46 ～ 51( in Chinese with English abstract) ．
Zheng Yong，Ma Hongsheng，Lv Jian et al． Source mechanism of strong aftershocks ( M S ≥5. 6) of the 2008 /05 /
12 Wenchuan earthquake and the implication for seismotectonics ［J］． Science in China ( Earth Sciences) ，
2009，39(4) :413 ～ 426．
38
Earthquake Research in China
Zhu Ailan，Xu Xiwei，Diao Guiling et al． Relocation of the M S 8. 0 Wenchuan earthquake sequence in part，
preliminary seismo-tectonic analysis ［J］． Seismology and Geology，2008，30 ( 3 ) :759 ～ 767 ( in Chinese
with English abstract) ．
About the Author
Li Jin，born in 1986，obtained his Masters degree at the Institute of Earthquake Science，CEA
in 2012． His research interest is in earthquake prediction methods． E-mail:lijin6305@ 163． com