chi-chi 199 earthquake
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Available online at www.sciencedirect.com
Journal of Geodynamics 45 (2008) 208216
The Chi-Chi 1999 earthquake: Correlation between the spatio-temporaldistribution of aftershocks and viscoelastic stress changes
Chiou-Fen Shieh , Shyh-Yang Sheu
Institute of Seismology and Applied Geophysics, National Chung Cheng University, Chia-Yi, Taiwan
Received 7 June 2007; received in revised form 31 December 2007; accepted 1 January 2008
Abstract
The Chi-Chi 1999 (ML = 7.3) earthquake generated a large number of aftershocks in the vicinity of the rupture plane. The spatial-temporaldistribution of these aftershocks was recorded with high precision and thus provided a unique possibility to study whether the correlation between
aftershocks and stress changes are primary due to coseismically induced stress changes (static), or whether stress relaxation processes (viscoelastic)
in the lower crust contribute significantly to this correlation. From our analysis of a 3D finite element model simulating the viscoelastic stress
changes due to the coseismic displacement and tectonic loading we found that the aftershocks are highly correlated with the stress variations
(static and viscoelastic) caused by the main shock. Although we found that the correlation between seismicity rate changes and viscoelastic stress
fluctuation is slightly better than that of the static stress changes, these differences can only be identified well in the lower crust. As a result, it
is reasonable to conclude that static stress changes are the key mechanism for triggering early and shallow aftershocks in the upper crust. It is
reasonable to infer that the viscoelastic relaxation in the lower crust does affect the occurrence of early aftershocks in the deep crust, but it does
not significantly affect the shallow aftershocks. However, the stress changes induced from the lower crust gradually transfer to the upper crust and
may influence the occurrence of aftershocks after a longer time period (>four Maxwell times).
2008 Elsevier Ltd. All rights reserved.
Keywords: Earthquakes triggering; Aftershocks; Static stress changes; Viscoelastic stress changes
1. Introduction
The existence of aftershock sequences following a main-
shock shows that one fault can be triggered by an earthquake
on another fault. A growing body of studies on the triggering
of aftershocks by the sudden change of a stress field around the
source supports those observations (Nostro et al., 1997; Harris,
1998; Hardebeck et al., 1998; Marcello et al., 2003; Robinson,
2004). Aftershocks triggering relationships have typically been
quantified by changes in the Coulomb Failure Stresses occur-
ring coseismically. Numerous papers over the past 20 yearshave shown that aftershocks are more likely to occur in loca-
tions where, due to the main shock, static stress has increased.
Unfortunately, any correlation between static stress and seismic-
ity rate changes are not perfect, because other possible processes
and factors undoubtedly influence the seismicity rate change as
well. For instance, time-dependent local stresses in the seismo-
Corresponding author. Tel.: +886 5 2720411; fax: +886 5 2720807.
E-mail address: [email protected] (C.-F. Shieh).
genic zone are redistributed after a mainshock. The fact that
coseismically induced stresses can be relieved by viscoelastic
stress relaxation in the lower crust was a prominent discovery
(Hergert and Heidbach, 2006). The redistributed stress may also
affect the occurrence of aftershocks and perhaps, the next large
earthquake. Studies (e.g. Deng and Sykes, 1997; Deng et al.,
1998, 1999; Freed and Lin, 1998, 2001; Zeng, 2001; Hergert and
Heidbach, 2006) on the evolution of stress redistribution seem
to provide other information for understanding the important
factors of the triggering mechanism. The question can be asked:
can aftershocks be generated by viscoelastic stress changes? Inaddition, different triggering mechanisms may be important at
different depths, something that has not yet been fully explored.
For example, recent analyses have shown that the viscous flow in
the lower crust or upper mantle after a large earthquake can lead
to a significant increase in stress and strain in the seismogenic
upper crust (Deng et al., 1999; Freed and Lin, 2001; Hergert and
Heidbach, 2006).
After the devastating 1999 Chi-Chi Taiwan earthquake
(ML = 7.3, focal depth = 8 km), which occurred predominately
0264-3707/$ see front matter 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jog.2008.01.002
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Table 1
Elastic parameters of the central Taiwan region
Layera Th (km) Vp (km/s) (g/cm3) E(1011 Pa) v
1 0.7 3.50 2.25 0.23 0.25
2 3.8 3.78 2.40 0.29 0.25
3 5.7 5.04 2.50 0.53 0.25
4 3.8 5.71 2.60 0.71 0.25
5 4.0 6.05 2.75 0.84 0.256 4.0 6.44 2.90 1.00 0.25
7 8.3 6.83 3.20 1.24 0.25
8 7.28 3.20 1.41 0.25
Value Th is the thickness of the layer; Vp is P-wave velocity; is density; E is
Youngs modulus; v is Poissons ratio.a Layer numbers correspond to numbers shown in the bottom left corner of
Fig. 1.
along the Chelungpu fault (strike = 357,dip=30E), more than
20,000 aftershocks occurred within 1 year. The correlations
between seismicity rate changes and static stress changes were
investigated by Wang et al. (2003) using the wavenumber inte-gration method (Herrmann, 1996) with a layered elastic model.
In the present paper we use the finite element technique to study
the correlations between Chi-Chi aftershocks and the changes in
static Coulomb Failure Stresses due to the mainshock, and also
the effect of viscoelastic relaxation.
2. Computational viscoelastic earth model
We used the source-slip model of the Chi-Chi earthquake (Ji
etal.,2001) anda regional model driven by relativeplatemotions
of 8.15 cm/yr (Yu et al., 1997), to constrain the evolution of the
regional stress, in order to understand the stress transfer process.A 3D rheological model was adopted for the calculation of stress
changes. We inferred this rheological model from 3D velocity
inversion (Ma et al., 1996), measured the long-term strain rates
(Hung et al., 1999), 97-days geodetic measurements of post-
seismic deformation (Yu et al., 2001), and the viscosities of the
lower crust and upper mantle of 5.0 1017 and 1.0 1023 Pa s
(Sheu and Shieh, 2004), respectively. Fig. 1 illustrates the 3D
models (Fig. 1a) of central Taiwan (dashed rectangle in Fig. 1b)
and the vertical cross-section (Fig. 1c), using the elastic param-
eters listed in Table 1, with the thickness and viscosity of the
lower crust differing from west to east. In Fig. 1b, the three bold
lines represent the surface rupture of the Chelungpu fault, the
star denotes the epicenter of the Chi-Chi event, and the blackarrow shows the direction of the plate motion (N61W). The
applied tectonic loading is set on the east boundary of the 3D
model (Fig. 1a) with a velocity of 8.15 cm/yr, and the top bound-
ary is a free surface, where displacements are calculated. On the
other four boundaries, thedisplacements are assumed to be zeros
(fixed boundary) in both horizontal and vertical directions.
A 3D finite element method (Deng et al., 1998) is used to
compute the static and time-dependent changes in the Coulomb
Failure Stress for five different time spans in units of Maxwell
relaxation time after the Chi-Chi earthquake. The gravity effect
is not included in this study because it can be neglected in a short
time evolution.
The Maxwell relaxation time is
=M
M(1)
whereM andM are the effective viscosity and rigidity, respec-
tively. Sheu and Shieh (2004) inferred the viscosity of a lower
crust beneath Taiwan from the grid-search procedure. On the
basis of this relation, they estimated the Maxwell relaxation timeof the lower crust to be 116 days.
3. Seismological data
Theaftershocksin the700-day period after the Chi-Chi main-
shock in the region of central Taiwan (Fig. 1b), recorded by the
Central Weather Bureau Seismic Network (CWBSN) from a
dense 75-station seismic network were used. The CWBSN net-
work was operated at high gain in order to capture the frequently
occurring small events (Shin and Teng, 2001). The location
errors in horizontal and vertical distances are generally less
than 2 and 5 km, respectively. In the following, the events withML 2.0 (magnitude completeness Mc = 2) and good quality
data (classified as A and B) were used.
4. Static stress and distribution of aftershocks
The Coulomb Failure Stress (CFS) is defined as (Deng and
Sykes, 1997):
CFS = + (2)
where and are shear stress and normal stress changes
caused by the main shock, respectively, and is the effective
friction coefficient, = 0.6 is chosen for the area of Taiwan
(Wang et al., 2003).
Since the fault planes of aftershocks are not known, we cal-
culate CFS on optimal oriented faults. To do so, the regional
stress needs to be taken into account in our calculation (King et
al., 1994; Nostro et al., 2001). TheCFS is assumed to be in the
direction in which the combination of regional stress and stress
changes is at maximum for the aftershocks to occur (Stein and
Ekstron, 1992; King et al., 1994; Nostro et al., 2001). The total
stress change is determined by
tij = rij +
cij (3)
where rij is the regional stress in the direction of N61W (Kao
and Angelier, 2001) and is determined from the stress drop ofthe Chi-Chi event with a value of 100 bars (Hwang et al., 2001);
cij is the deviatoric stress change caused by the main shock.
A search for the orientation of the maximum CFS for
each finite element node is then carried out. The calculated
Coulomb Failure Stress change is used to locate the aftershocks
and to detect triggering, i.e., to determine if these aftershocks
are caused by the positive stress change prior to its occurrence.
Fig. 2 shows the calculated static Coulomb Failure Stress for
the depths of 5, 10, 15, 20 and 25 km along with the aftershocks
that occurred within 580 days (five Maxwell times) of the main-
shock. The sketches in the top right corner of each drawing in
Fig. 2 show a fraction of the aftershocks occurring in regions of
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positive stress change (termed fa) and a fraction of the volumes
that have positive stress change (termed fv), respectively. The
main feature here is that the decrease in stress is mainly con-
centrated in two lobes of the western and eastern parts of the
fault trace, and that these two lobes gradually move away from
the source region with increasing depth. On the other hand, the
stress generally increases in the northern and southern ends of
the Chelungpu thrust fault and spreads over wider and wider
areas as the depth increases. In addition, we performed a simple
correlation test of the null hypothesis thatfa and fv in each com-
parison are independent. The estimated correlation coefficient
exceeded the value ofr= 0.878 which rejected the null hypoth-
Fig. 1. The 3D modelof central Taiwan with thecoordinate axes.TheX, YandZcoordinate axesare oriented E3S,N3E and depth, respectively. (a) The rheological
structure of the model. A viscoelastic lower crust (gray volume) is embedded between a purely elastic upper crust and the upper mantle. The model geometry covers
140, 180, 75 km in X, Y, and Z direction. (b) Map view of the 3D model with dashed rectangle showing the boundary. The three bold lines represent the surface
rupture of the 1999 Chi-Chi earthquake. The black arrow indicates the relative motion between the Philippine Sea plate and the Eurasian plate. (c) Schematic side
view of the 3D model. The black zone on top indicates the simplified topographic features. The 1999 thrust event is indicated by a bold line with arrows showing the
direction of the fault plane motions. The thickness, velocity, density, Youngs modulus and Poissons ratio for each layer indices are given in Table 1.
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Fig. 2. The static Coulomb Failure Stress (CFS) changes imposed by the Chi-
Chi earthquake for five different depths. The circles represent the aftershocks
that occurred within 580 days after the main event at each depth. The fv and
fa are the fraction of the volumes for positive CFS and the percentages of
earthquakes that were located in these areas, respectively. The results show that
static stress changes could be a triggering mechanism.
esis for the 95% confidence level, indicating that static stress
change could be a trigger mechanism. It is no surprise that in
general the percentages increased with the depth, because the
areas of stress-enhancement increase with the depth.
5. Viscoelastic stress and distribution of aftershocks
The low viscosity of the lower crust, 5.0 1017 Pa s, indi-
cates that the stress changes caused by viscoelastic relaxation
happen fast. These stress changes may add up to static stress
over time and significantly change the stress pattern (Hergert
and Heidbach, 2006). This effect is discussed next. The calcu-
lated time-dependent state of stress redistributions at each depth
are shown in Fig. 3, for time intervals from 1 to 5, where
= 116 days. The static stress changes after the Chi-Chi earth-
quake as shown in Fig. 2 were replotted in the first column.
However, only those aftershocks that occurred within the time
period from 0 to 1were compared. By the first Maxwell time
(1), stresschanges hadchanged at many locations, especially in
thelower crust where the coseismic stress decreasesare reduced.The stress changes are continuously redistributed into the deeper
crust (20 and25 km). There were significant differences between
the first (t= 0) and the sixth (t= 5) time periods. The stress
variations over time were relatively small in the shallow crust
(
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Fig. 3. The Coulomb Failure Stress changes distributed at five different depths and time periods. The aftershocks (circles) that occurred at different depths and time
periods are plotted for comparison. The Maxwell time = 116 days is determined from the previous study (Sheu and Shieh, 2004). The results also show that later
aftershocks (after one Maxwell time) are located mostly in a stress-enhanced area.
effects of stress evolution on triggering an aftershock might be
secondary.
6. Seismicity rate changes
Since the Chi-Chi event, more than 20,000 aftershocks were
recorded over a large area of central Taiwan. Most of the
aftershocks were distributed in the low background seismic-
ity zones (Lin, 2001). To investigate whether the seismicity
is really affected by stress changes, a -statistic (Reasenberg
and Simpson, 1992) was used to quantify the changes of theseismicity rate, which is defined as
(Na, Nb, ta, tb) =Na E(Na)
(Var(Na))0.5
(4)
where ta and tb are time periods after and before the main shock;
Na andNb arethe numberof earthquakes in ta and tb, respectively,
and E(Na) = taNa/Nb; Var(Na) =Nbta.
A positive represents seismicity after a main shock that is
higher than the background seismicity and vice versa. Following
Reasenberg and Simpson (1992), the is calculated for events
within overlapping cells of a size 10 km 10 km located on a
grid with 1 km spacing.
In order to quantify the relationship between the seismic-
ity rate changes and the Coulomb stress changes, two data
sets from the earthquake catalog were studied. The mini-
mum magnitude of the catalog completeness was estimated
to be ML 2.0 in Taiwan during 19731998 with successive
1-year periods. Eliminating events for magnitudes less than
2.0 still involved 8000 aftershocks of quality A during the
first 2 years postseismic epoch after the Chi-Chi earthquake
to construct one set, and 2000 events defining the background
activity, starting 2 years before the main shock to the second
set.Taking tb = 2 years (20September 199719 September1999),
and ta = 1(116 days) to 5, the seismicity rates were compared
with the stress variations, and the set of all possible outcomes
of the comparisons, called the sample space, is denoted by S.
An element in S is called a sample point. The classification as
described below is used to identify the consistencies between
samplepoints. Theoutcome is called a consistency if it is located
in the sample space {CFS > 0 and > 0, CFS < 0 and < 0}with number of sample points{Ma,Mb}. On the other hand, it iscalled an inconsistency if the outcome is involved in the sample
space {CFS > 0 and < 0, CFS < 0 and > 0} with number
of sample points {Mc, Md}. When and CFS have the same
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Fig. 4. Statistical analysis for the aftershocks located in stress-enhanced areas. Percentages are shown on top of each plot, based on the total number of earthquakesat different depths and time periods. The peak at each plot indicates at what level of stress change most of the earthquakes occurred. A well-identified single peak is
obviously at the upper crust, while multiple peaks at the lower crust are a bit more difficult to distinguish.
sign, it indicates a causative relationship between the seismicity
rate and the stress changes. On the contrary, when the signs of
and CFS differ, the seismicity rate changes are not caused
by stress changes.
The consistency-percentage can therefore be defined as
P= 100
Ma +Mb
Ma +Mb +Mc +Md
(5)
Fig. 5 shows the results of the percentage of consistencies bycomparing the seismicity rate and the stress changes at differ-
ent depths and time periods. For ease of analysis the results are
plotted in commonly used 2D Cartisian coordinates with four
quadrants separated by two lines, where the origin ( =0 and
CFS = 0) is the intersection of these two lines. In each sub-plot
ofFig. 5, we defined the first quadrant (upper right) by >0a nd
CFS > 0, the second (upper left) by >0 and CFS < 0, the
third (lower left) by < 0 and CFS < 0 and the fourth (lower
right) by < 0 and CFS > 0. In each figure, the aftershocks
located in the first and the third quadrants (inside panel) indi-
cate that the seismicity rate ()andCFS both increase (the first
quadrant) and both decrease (the third quadrant), respectively,
and are therefore classified as a consistency, while in the second
and the fourth quadrants (different signs between and CFS)
theyare an inconsistency. The consistency-percentage as defined
in Eq. (5) is marked on the top of each drawing. They are found
to be between 61.2 and 99.5%, which indicates a high correla-
tion between seismicity rate and viscoelastic CFS changes. In
addition, the stress level at which aftershocks were triggered is
noted in each figure. Please note that the consistency-percentage
is generally higher at the deep crust (20 and 25 km) than at the
shallow crust for different time periods. This raises the question:does this result imply that viscoelastic stress changes affect the
occurrence of aftershocks in the lower crust in a more signifi-
cant waythan the static stresschanges?By fixing the static stress
variation for each time period (using the static stress changes in
Fig. 2 for all time periods), an analysis, similar to that in Fig. 5
for static stress and seismicity rate changes was conducted (see
Fig. 6). The consistency-percentage for the static case ranged
between 58.4 and 98.5%, which is very close to the results for
the viscoelastic case shown in Fig. 5. It is too difficult to distin-
guish them simply by comparing their consistency-percentages.
However, the statistical analysis discussed next may help to
distinguish them.
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Fig.5. The results are plotted in commonlyused 2D Cartisiancoordinateswith fourquadrants. The consistency analysis between seismicityrate () andstresschanges(Fig. 3) at different depths and different time periods. The earthquakes located in the first and the third quadrants (inside panel) are classified as a consistency, while
those located in the second and the fourth quadrants are classified as an inconsistency. The consistency-percentage (see text for the discussion) marked on top of
each figure indicates that the seismicity rate changes are caused by the viscoelastic stress changes.
7. Differences between static and viscoelastic stresses
To identify the significance in the differences of consistency-
percentage (P) between static and viscoelastic stress changes
(Figs. 6 and 5), the 95% confidence interval (CI) ofP is defined
(Sachs, 1982) as
CI =
P 1
2M
P (1 P)
M
0.5= (PL, PU) (6)
where PL and PU are the lower and upper bounds of the interval,
and Mis the total sample (M=Ma +Mb +Mc +Md in Eq. (5)).
The intervals (PL and PU) for the static and viscoelastic cases
at each depth and time period are calculated. If the intervals for
thestatic andviscoelastic cases aresuperimposed, then thebetter
consistency-percentage corresponding to the most likely trigger-
ing mechanism cannot be distinguished, even though they are
identifiable when completely separate. Table 2 shows the calcu-
Table 2
The 95% confidence interval ofP
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Fig. 6. The consistency analysis between the seismicity rate and static stress changes at different depths and time periods. Simply substitute the stress changes inFig. 3 for the static stress changes in Fig. 2 for all time periods, and then conduct an analysis similar to the one in Fig. 5. The consistency-percentage for the static
case is very close to the results for the viscoelastic case shown in Fig. 5.
lated interval of (PL and PU) for the static(first) and [PL and PU]
for the viscoelastic (second) cases at each depth and time period
(note that there isonlyone interval at 0).In Table 2, thebetter of
the completely separated intervals are shown shaded when the
consistency-percentage for the viscoelastic case is better than
that of the static case. It is worth noting that the superiority of
the viscoelastic cases (shaded intervals) only exist in the lower
crust at 25 km, and only for a short period of time (12) and
then at 20 km at a later time (25). However, it is not distin-
guishable in the upper crust. In other words, the mechanism ofviscoelastic stress variations can explain the occurrence of deep
aftershocks in a statistical manner that is better than the static
stress variations, but this does not apply to the shallower after-
shocks. This result was not unexpected, because the viscoelastic
response occurs mainly in the lower crust, and the viscoelastic
stress changes play a role in triggering aftershocks. The sepa-
rated interval in the upper crust only appears for a time period of
5at 10 km. This result seems to show the trend that disturbing
the viscoelastic stress changes leads to the occurrence of after-
shocks. The stress change imposed by the viscoelastic response
in the lower crust affects the occurrence of aftershocks at the
deeper crust in the early stage, and with time the stress changes
transfer gradually to the shallower crust and have an effect on
triggering shallower aftershocks at a later time. It is therefore
inferred that the viscoelastic stress changes may influence the
occurrence of shallower aftershocks after a longer time period
(>4). However, the superimposed intervals in the upper crust
(
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the occurrence of aftershocks in the deep crust, but that they
affect the shallow aftershocks to a much lesser degree (