Chi-chi 199 Earthquake

download Chi-chi 199 Earthquake

of 9

Transcript of Chi-chi 199 Earthquake

  • 8/3/2019 Chi-chi 199 Earthquake

    1/9

    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

    mailto:[email protected]://dx.doi.org/10.1016/j.jog.2008.01.002http://dx.doi.org/10.1016/j.jog.2008.01.002mailto:[email protected]
  • 8/3/2019 Chi-chi 199 Earthquake

    2/9

    C.-F. Shieh, S.-Y. Sheu / Journal of Geodynamics 45 (2008) 208216 209

    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

  • 8/3/2019 Chi-chi 199 Earthquake

    3/9

    210 C.-F. Shieh, S.-Y. Sheu / Journal of Geodynamics 45 (2008) 208216

    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.

  • 8/3/2019 Chi-chi 199 Earthquake

    4/9

    C.-F. Shieh, S.-Y. Sheu / Journal of Geodynamics 45 (2008) 208216 211

    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

    (

  • 8/3/2019 Chi-chi 199 Earthquake

    5/9

    212 C.-F. Shieh, S.-Y. Sheu / Journal of Geodynamics 45 (2008) 208216

    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

  • 8/3/2019 Chi-chi 199 Earthquake

    6/9

    C.-F. Shieh, S.-Y. Sheu / Journal of Geodynamics 45 (2008) 208216 213

    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.

  • 8/3/2019 Chi-chi 199 Earthquake

    7/9

    214 C.-F. Shieh, S.-Y. Sheu / Journal of Geodynamics 45 (2008) 208216

    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

  • 8/3/2019 Chi-chi 199 Earthquake

    8/9

    C.-F. Shieh, S.-Y. Sheu / Journal of Geodynamics 45 (2008) 208216 215

    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

    (

  • 8/3/2019 Chi-chi 199 Earthquake

    9/9

    216 C.-F. Shieh, S.-Y. Sheu / Journal of Geodynamics 45 (2008) 208216

    the occurrence of aftershocks in the deep crust, but that they

    affect the shallow aftershocks to a much lesser degree (