COMBINING A KINEMATIC FRACTAL SOURCE MODEL WITH HYBRID GREEN’S
FUNCTIONS TO MODELING BROADBAND STRONG GROUND MOTION
Ruiz J.1, D. Baumont 2, P. Bernard 1 and C. Berge-Thierry 2
1
2
IPGP, Institut de Physique du Globe de Paris, France.
IRSN, Institut de Radioprotection et de Sûreté Nucléaire, France
E-mail: jruiz@ipgp.jussieu.fr
SUMMARY
A hybrid empirical method is proposed to simulate broadband strong ground motion that combines a
kinematic complex source model with both Numerical and Empirical Green’s Functions (EGF). The
kinematic approach is based on a composite source model description where subevents are generated using a
fractal distribution of sizes. Each subevent is set up with a size-dependent rise-time. Each elementary source
is described as a crack-type slip model that starts radiating when the rupture front reaches the nucleation
point located randomly inside a size-dependent nucleation region. The synthetic acceleration spectra follow
the 2 model and the spectral amplitudes are scaled by a frequency-dependent directivity coefficient. In this
study, the hypothesis of constant stress drop of subevent is released and a stochastic fluctuation of stress drop
is introduced to better modeling the high-frequency level radiated by the source. Taking advantage of small
magnitude events, synthetic seismograms are computed using hybrid Green’s functions (HGF) to model the
impulsive response of the medium. The procedure consists to model HGF for each sub-fault combining the
numerical low-frequency and the empirical high-frequency Green’s functions with appropriate amplitude and
phase correction (geometrical spreading and delay times due to the S-wave travel time propagation). This
methodology is applied to modeling strong ground motion of 1997 Mw 5.9 Yamaguchi-ken Hokubo, Japan
earthquake. Some of the finite-source rupture parameters proposed in literature are fixed and only random
generation of k-2 composite slip distribution are allowed. The comparison of synthetized and observed
strong-motion caracteristics shows that the predictions are largely improved, when both HGF and variable
stress drop of subevent are used.
Key words: fractal source model, empirical Green’s functions, strong ground motion prediction, 1997
Yamaguchi earthquake
1
Introduction
Predicting strong ground motion in the vicinity of the faults is crucial in the earthquake engineering domain
and seismic hazard assessment studies, that can be achieved either empirically or numerically. Most of the
numerical predictions need to compute broadband ground-acceleration time series up to a few tens of Hz.
Several numerical approaches have been proposed in particular to model the high-frequency content of the
accelerograms. Assuming that the high-frequency content is related to complex rupture processes, several
kinematic source models with a heterogeneous slip distribution were developed (e.g. Andrews 1980;
Boatwright, 1982; Bernard et al., 1996). Some of these models based on the idea that an earthquake can be
seen as the superposition of numerous small events (or subevents) have also been proposed such as (1) the
composite source model with fractal distribution of sizes (Boatwright, 1988; Frankel, 1991; Zeng et al.,
1994) or (2) the specific barrier model (Papageorgieu and Aki, 1983) that assumes a uniform distribution of
sizes of subevents.
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The complexity observed on records is not only due to source effects, but also it is related to the interaction
of the radiated wave field with the geological medium (including source-station path and site effects). When
modeling broadband accelerograms, a problem arises because of the difficulties of calculating theoretical
realistic Green’s functions for the medium for a large frequency band. In some cases, the impulsive earth
response can be estimated “accurately” and deterministically through 3-D numerical simulations, but this
strategy is often limited to low-frequencies modeling (< 2 Hz) due to computational limitations and a lack of
knowledge of subsurface geometry structures and small-scale elastic properties of the medium.
An alternative empirical approach proposed by Hartzell (1978) consists to use the records of a small
earthquake having a focal mechanism and hypocentral location similar to the target event as empirical
Green’s functions (EGF).
The basic idea consist to model a large earthquake adding up recording of small earthquakes shifted in time
to take into account delay times due to rupture propagation and distance from the receiver to points onto the
fault plane. The -2 spectral scaling law (Aki, 1967) is normally assumed for small and large size
earthquakes. Both events must to be having the same focal mechanism. The more important advantage of
this method is that path and site effect are take into account.
After the EGF method proposed by Hartzell (1978), several techniques and applications have been proposed
in literature, among which, Irikura (1986), Spudich and Miller (1990), Irikura and Kamae (1994), Frankel
(1995), Hutchings and Wu (1990), Hutchings (1994), Bour and Cara (1997), Kamae and Irikura (1998),
Miyake et al. (2003), Sansorny-Kohrs et al. (2005), Hutchings et al. (2006). More of these techniques are
based on summation methods to perform a 2 spectral shape by summing (e.g. Irikura and Kamae, 1994), or
summing and filtering (e.g. Frankel, 1995) EGFs.
A common limitation of these techniques is that the low-frequency content (usually < 1 Hz) of records of
small earthquakes is dominated by seismic noise, and the signal-to-noise ratio is worst when record
associated to small magnitudes earthquakes are used. To counterbalance this problem, it is possible to use
numerical Green’s functions to simulate the low-frequency content of the radiated wave field. It is the case
for hybrid techniques proposed in literature that combine numerical and stochastic modeling of the Green’s
function at low- and high-frequency respectively. By modeling 3D wave propagation at low-frequency, these
techniques have been applied to the Mw 7.3 Kobe, Japan earthquake (Kamae et al., 1998; Pitarka et al.,
1998, 2000), in California (Hartzell et al., 1999; Graves and Pitarka, 2006).
An alternative approach to summation techniques of EGF was proposed by Hutchings and Wu (1990) that
uses records of earthquakes having small magnitudes to obtain the Green’s function of the medium. The
hypothesis of impulsive response of the medium is only valid up to the corner frequency of the small
earthquake. For higher frequencies, radiation is controlled by the finiteness of the fault and source effects
associated to the small earthquake. For instance, for a M w 3.0 event, the corner frequency estimated using
Brune’s (1970) relations is roughly equal to 10 Hz. The EGF is used as a Green’s function in the
representation theorem relationship to synthesize ground motion (Hutchings and Wu, 1990; Hutching 1994;
Hutching et al., 2006). The most important advantage of this method is that the EGF can be combined with
any kinematic rupture source model. These authors combine a kinematic rupture process by using a Kostrovtype slip-velocity function. However, in the vicinity of the faults ground motion are also strongly and
directly influenced by complexity of the rupture process. The spatial and temporal variability of slip-velocity
function, the rupture velocity or the directivity effects can control largely the ground motion. When a
numerical approach is used to predict strong ground motion, the kinematic rupture history on the fault must
to be described in a physical way.
Inspired of method proposed by Hutchings and Wu (1990), this study presents a hybrid empirical method
able to simulate broadband ground motion that combines a kinematic stochastic fractal composite source
model (Ruiz et al., 2007) with Hybrid Green’s Functions (HGF). The kinematic fractal source model uses a
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set of subevent following a fractal distribution of sizes and scale dependent rise-time. The rupture process at
small-scale is controlled by a size-dependent nucleation region that controls and reduce the directivity
effects. The acceleration spectral amplitudes follows a 2 spectral shape scaled by a frequency-dependent
directivity effects (Ruiz et al., 2007). The hybrid empirical methodology is applied to the 1997 M w 5.9
Yamaguchi-Ken Hokubo, Japan, earthquake. The aim of this paper is (1) to compare strong ground motion
predicted when numerical and hybrid Green’s function are used, and (2) test the validity of use HGF to
predict the reported ground motion.
2
Methodology
The ground motion is computed by a kinematic rupture source model based in a discrete version of the
representation theorem of seismic source (Aki and Richard, 1980). The kinematic description needs a
complete description of the spatial and temporal evolution of the rupture process on the fault (Figure 1). The
rupture history is described assuming the hypocenter location, the rupture times, tijr , are obtained simply
assuming a circular rupture front propagated at constant rupture velocity, V r, and the slip-velocity functions
( sij ) are set up according to the kinematic source model description. The impulsive response of the medium
is the Green’s function (gnij) that is set up with a HGF (hnij). The synthetic seismogram is computed
convolving the slip-velocity functions with the respective HGF for each sub-fault.
Assuming that the sub-fault (i0, j0) correspond to the location of the EGF ( eni0 j0 , Figure 1), the representation
theorem can be written by
g

ri j
M nij

u n   sij *  g nij Flp  eni0 j0 eni0 j  (t  t sij  t sobs ) 0 0 Fhp  ,
rij


M0 0 0
ij
(1)
where the bracketed term corresponds to the HGF (hnij). Flp and Fhp are low- and high-pass filters defined by
a corner frequency corresponding to the cut-off low-frequency that is obtained by signal-to-noise ratio
analysis of records of the small earthquake.
The EGF is shifted in time to synchronize the observed (tsobs) to the theoretical (tsij) S-wave arrival time. The
EGF is corrected in amplitude to take into account the geometrical spreading and it is re-normalized to obtain
the appropriate seismic moment. The EGF obtained at each sub-faults (i, j) is
g
enij  eni0 j 0
M 0 nij
M
e ni0 j 0
0
 (t  t sij  t sobs )
ri0 j 0
rij
(2)
where ri0 j0 et rij are the distance from the receiver to the hypocenter and the sub-fault (i, j) respectively. The
e
g
two terms M 0ni0 j0 and M 0 nij are the seismic moment of the small earthquake and the numerical Green’s
function respectively. In this procedure, the seismic moment of the small earthquake is determined by
measuring the spectral amplitudes of ground-displacement at low- frequencies. In the far-field
approximation, the seismic moment, M0, can be estimated using the following formula (Aki and Richards,
1980)
M0 
4c 3 R
Fc Rc
0
(3)
where 0 is the plateau level of the ground-displacement spectrum measured at low-frequencies,  is the
density, c represent the body wave velocity chosen (P or S), R is the hypocentral distance, R c is radiation
pattern amplitude, and Fc is free-surface amplitude.
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An inconvenient of this approach is that the usable frequency band of EGFs is limited up to the corner
frequency of the small earthquake. To enlarge it, under few hypothesis, it is possible to remove the source
effects of the small event (Hutchings et al., 2006). On the other hand an advantage of using HGF is that the
low-frequency can be improved by 3-D simulation of wave propagation in heterogeneous media. In addition,
the HGF can be combined with any kinematic complex source model describing a heterogeneous rupture
process. We prefer the kinematic fractal composite source model proposed by Ruiz et al. (2007) that allows
to control directivity effects and to model numerical standard deviation of strong-motion parameters which
are in better agreement with the ones predicted empirically. This approach uses a set of subevent following a
fractal distribution of sizes where each subevent is described by a crack-type slip and a scale-dependent risetime. By adjusting the total seismic moment of the subevents to the target moment of the main event, the
final slip distribution is characterized by a k-2 spectral decay at high wave numbers. The rupture process
introduced at small-scale is controlled by the extension of the size-dependent nucleation region defined
inside the crack. This stochastic rupture process diminish directivity rupture effects, generating accelerations
spectral amplitudes following a 2 spectral shape controlled by a frequency-dependent directivity effects
(Ruiz et al., 2007).
However, in composite source models the stress drop of subevents is assumed to be constant. Classically the
stress drop is a macroscopic measure of source properties, Kanamori and Anderson (1975) suggest mean
values of stress drop of about 60 bars. However, the fluctuations on the fault plane due to heterogeneous slip
can vary strongly as was shown by Bouchon (1997) by analyzing the imaged slip of past earthquakes. He
obtained values of about 100 MPa for the 1994 Morgan Hill earthquake. In addition, Nadeau and Johnson
(1998) analyzed repeating earthquakes in the San Andreas Fault for magnitude events included in the
interval, -0.7 to 1.4, and 3.5 to 4.9. In their study, stress drop values reported for magnitude 4 is about 30
bars, and extreme values can be reach 1000 MPa for magnitude 1 events. Nadeau et Johnson (1998) propose
a relation between magnitude and stress drop. Later, Ide and Beroza (2001) reinterpreting previous studies
show that not dependence of the apparent stress drop (ratio between seismic energy and seismic moment) on
magnitude for a large interval of magnitude. No doubt that all these elements give a large uncertainty of
stress drop variations with size of earthquakes.
In this study, we released the hypothesis of constant stress drop (d) of subevent for the fractal source
model developed by Ruiz et al. (2007). We proposed here to introduce at all scales a random fluctuation of
the stress drop value of subevents, bounded by a constant minimum value and a maximal value that increases
up to a saturation level for small sizes. The effects of increasing the stress drop at small-scale is to generate a
more heterogeneous slip distribution at short wavelength, while preserving a k-2 spectral decay and the final
seismic moment (see later for a numerical example).
3
Modeling the 1997 Mw 5.9 Yamaguchi Japan earthquake
This section presents the results of strong ground motion prediction applied to the main shock of the 1997
Mw 5.9 Yamaguchi earthquake. We aim to test the validity of strong ground motion prediction with HGF and
to compare simulations against the results when numerical Green’s functions are used. The analysis of the
results is carried out by comparing observed and predicted strong-motion parameters as peak groundacceleration (PGA) and velocity (PGV) and also waveform of ground motion.
3.1
Data
The Yamaguchi earthquake occurred on June 25th, 1997 in the western Japan. It was a strike-slip crustal
earthquake and several seismological agencies reported the hypocenter and source parameters of the main
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shock (Table 1). Three aftershocks were recorded by the Japanese strong motion network, K-NET
(Kinoshita, 1998). Figure 2 shows the epicenter location of the main shock and their aftershocks along with
the K-NET stations. Focal mechanism and fault geometry proposed by Ide (1999) are used in simulations
(Table 2). For comparisons purposes between ground motion simulations using numerical and hybrid
Green’s function, the layered crustal model (Table 3) was used to compute the numerical Green’s functions
up to 12 Hz using the Discrete Wave Number Method (Bouchon and Aki, 1977) and the AXITRA code
(Coutant, 1989). The fault plane (L × W = 16 × 12 km2) is buried at 0.5 km of depth and in this study it was
subdivided onto a 256 × 256 regular grid mesh of about 61 × 46 m2.
To compute the HGF, only the first aftershock (AFT1) was used as EGF for this application. An important
consideration when using EGF is to determine accurately seismic moment and the usable frequency-band of
records. This minimal frequency is determined by signal-to-noise ratio analysis and it value depends on
several factor such as the magnitude, source-station distance and site conditions. The maximal frequency is
related to the corner frequency of small events. Beyond this frequency, source duration and rise-time
associated to the seismic source of aftershocks dominate the frequency content and the hypothesis of an
impulsive point source is not valid anymore.
Neglecting site effects, the S-wave displacement is used to determine the seismic moment by using Eq. (3)
and, c = 3.43 km s-1,  = 2.7 gr cm-3, Rc = 4/15 chosen as the mean square radiation pattern over the focal
sphere and Fc = 2. Table 4 resumes the values for R, 0, M0 and Mw obtained using records at few stations.
The mean value is 2  1014 N.m with a magnitude of about Mw = 3.45 ± 0.11. Figure 3 shows examples of
spectral ratios (Figure 3a) and displacement spectrum of recording of the AFT1 (Figure 3b). Spectral ratios
values obtained at low-frequency confirm that the seismic moment of the AFT2 and AFT3 is the half of the
seismic moment of the AFT1.
The corner frequency of the aftershock can be estimated, for example, with the source spectral fitting method
proposed by Miyake et al. (1999) that yields additional parameters to perform simulations by summation
techniques of EGF. Here, the fc value is simply obtained by adjusting manually the theoretical2 spectrum to
the observed ones. Figure 4 shows the fitting of the theoretical 2 shape with the ground-acceleration
spectrum computed for the transversal component of records of the AFT1. The corner frequency obtained is
about 5 Hz, and comparing the spectral amplitudes of noise and signal, it is possible to determine the
minimum usable frequency in simulations. In this case the value varies around ~ 0.7 – 1 Hz, by simplicity it
was fixed to 1 Hz for all records.
The HGF are estimated between the receiver and all points of the fault grid mesh. Each of them is computed
in the frequency domain by using high- and low-pass complementary null phase filters defined with a cut-off
frequency equal to 1 Hz. Following the method detailed previously, the filters are applied to the empirical
and the numerical Green’s function respectively, by correcting EGF by geometrical spreading and
renormalizing it by the seismic moment. The EGF is shifted in time to synchronize the theoretical and
observed S-wave arrival of the numerical and the empirical Green’s function respectively. Finally the
synthetic seismograms are computed convolving the HGF with the respective slip-velocity function modeled
at each grid mesh.
3.2
Modeling strong ground motion with HGF
A few finite-source rupture models for the Mw 5.9 Yamaguchi earthquake have been published (Ide, 1999;
Miyakoshi et al., 2000). In this study, the fault geometry, the main dimension of the asperity, and the mean
rupture velocity proposed by Ide (1999) are used. He provided a set of source rupture models inverting
strong motion data for various frequency bands, using numerical Green’s functions (0.1 – 0.5 Hz) and EGF
(0.5 - 2 Hz). Figure 6 displays one solution for the slip distribution and the rupture times obtained by this
author which are available on-line (Mai et al., 2006). The slip distribution is characterized by a main patch
-5-
distributed over a surface of roughly equal to l  w = 9  10 km2, reaching a maximum slip of about 0.5 m.
The mean rupture velocity is, Vr = 3 km s-1.
The strong ground motion simulations performed for this application were computed using the main
characteristics of the finite-source rupture model solution, that is to say fault geometry, hypocenter location,
mean rupture velocity and dimension of the asperity. The kinematic fractal source model (Ruiz et al., 2007)
was used to model the kinematic rupture process and numerical and hybrid Green’s function were used to
modeling the medium response. The slip distribution was generated using N = 35000 crack-type sources, the
maximum radius allowed to cover the fault plane Rmax = 0.23 W. The parameter defining the extension of the
nucleation region is h = 0 (see Ruiz et al., 2007), which corresponds to a persistency of directivity at all
scales. The maximum rise-time, max = 1 s. The rupture front propagates circularly from the hypocenter at
constant rupture velocity, Vr = 2.95 km s-1. By fixing all these parameters, the ground motion variability is
only due the few random slip distributions that were generated. To better model the main asperity, the
surface cover by subevents was reduced to 12 × 9 km2.
We introduce a stochastic fluctuation at all scales of the stress drop of subevents, d. In average the stress
drop is slightly increased up to a constant level when the size of subevents decreases. First, d is assumed
to be constant, d = 3 MPa, and in a second step it was varied randomly between two limits, with minimum
value equal to 2.5 MPa, and a maximal fluctuation equal to 15 MPa for the smallest sources. Figure 7a shows
the comparison of the stress drop of subevents as a function of their radius when a constant and variable
stress drop is considered. The fluctuation on stress drop varies from 2.5 to 20 MPa, where larger fluctuations
affect mainly the small sources, whereas the biggest sources are dominated by low values. Figure 7b display
the comparison of the cumulated seismic moment of the set of subevents. Notice the redistribution of the
seismic moment among the subevents.
The slip computed with constant stress drop of subevents is shown in Figure 8a that exhibits a heterogeneous
spatial distribution. On the other hand, one can notice that the slip generated with variable stress drop is
highly spatially heterogeneous (Figure 8b). When comparing the slip spectral amplitudes for both cases, the
k-2 spectral decay is preserved, but at high radial wave numbers amplitudes are larger for a variable stress
drop.
Figure 9 shows the results of the horizontal PGA and PGV predictions compared to the observed values
when constant and variable stress drop are used. Numerical predictions correspond to 5 realizations of
random slips. For a constant stress drop, the PGA predicted values are weaker that the observed ones, the
amplitudes as a function of distance decay faster than the observations (Figure 9a). The set of PGV
predictions are in agreement with the observations (Figure 9b). When a variable stress drop is used, the
predicted PGA (Figure 9c) increases in term of amplitudes in relation to a constant stress drop, but predicted
values cannot still well describe the observations, especially at large distances. PGV shown in Figure 9d,
minor changes in amplitudes are noticed in relation to a constant stress drop. Predicted PGV values can
describe in a better way the observations that PGA. These results show that the high-frequency content is
strongly affected by considering variable fluctuations of the stress drop amplitude for the set of subevent
generated by a fractal approach. Minor changes are notice at mid- and low-frequencies which dominate
mainly the PGV.
Figure 10 shows the horizontal PGA and PGV numerical values obtained with HGF and variable stress drop.
One can notice a good agreement between the predictions and the observations for the PGA (Figure 10a), the
amplitudes decay with distance is better described with HGF than numerical Green’s functions. Figure 10b
shows the results for the PGV. In the case of PGV predictions, in terms of amplitudes and the attenuation
with distance, are in good agreement with the observations. In general, the PGA and PGV tendency is well
modeled, except for two receiver located at a source distance, ~ 40 km corresponding to stations YMG010
and YMG013. Differences can be attributed to the validity frequency range of simulations (up to fc = 5 Hz).
-6-
Figure 11 displays the time series for the ground-displacement, ground-velocity and ground-acceleration and
their spectra modeled at a few stations and compared with the observations. The main characteristics of the
ground motion are well modeled in terms of amplitude and duration for displacement and velocity. The
accelerograms modeled are in good agreement with the record at the stations SMN014 and YMG003, where
as at the stations SMN013, SMN011, and YMG009 some deficiencies are observed at high-frequencies. It
can be associated, in part, to the source effects of the small earthquake.
Let us recall that synthetics computed with HGF are only valid up ~ 5 Hz (corner frequency of the small
earthquake), and 12 Hz was kept only for comparison purposes with the synthetics predictions computed
with numerical Green’s functions. To enlarge the frequency band it is possible to remove the source-time
function associated to the small earthquake. Hutching et al. (2006) proposed to apply a deconvolution to
EGF records by a Brune’s (1970) source-time function. It assumes that the rupture is circular. A nonazimuthal dependence is introduced and the frequency characterizing the Brunes’s function is simply the
corner frequency of the small earthquake. In order to test the effect of this first order correction, Figure 12
shows the results for the horizontal PGA and PGV predictions. The PGA predictions shows in Figure 12a are
in better agreement with the observations, numerical values are increased in relation to the previous case
(Figure 10). A minor impact is observed for the PGV, that is controlled mainly by the intermediated
frequency band radiated by the source.
4
Discussion and conclusions
The methodology proposed in this study demonstrates the necessity to introduce realistic Green’s functions
to predict broadband strong ground motion in the vicinity of the faults. We have proposed an empirical
hybrid technique that combines a kinematic complex fractal source model (Ruiz et al. 2007) with hybrid
(numerical at low frequencies and empirical at high frequencies) Green’s functions. To describe the
kinematic of the source model, we released the hypothesis of constant stress drop of subevents and stochastic
fluctuations of stress drop were introduced. The final composite slip becomes highly heterogeneous, while
preserving a k-2 spectral decay, and the effect is to increase the high-frequency content radiated by the
source. The kinematic rupture was defined with a quasi-determinist nucleation region at all scales i.e. a
similar directivity effect at all scales. The impulsive response of the medium is take into account by a HGF
that is computed in the frequency domain by adding the low- and high-frequency content of the numerical
and empirical Green’s function respectively. We have applied this methodology to model the strong ground
motion of the main shock of the Mw 5.9 Yamaguchi-ken Hokubo Japan earthquake. The finite-source rupture
model proposed by Ide (1999) was used to define fault geometry and location of the main asperity.
Independently of the Green’s function used, the strong-motion parameters analyzed in this study (PGA and
PGV) show that introducing a variable stress drop, mainly affects the high-frequency level radiated by the
source. As a consequence, minor impacts were observed in the predicted PGV, whereas the PGA is increased
in terms of amplitudes in relation to a constant stress drop.
On the other hand, this study show that the best predictions were obtained when both HGF and variable
stress drop of subevents are used. In term of PGV, no big differences were observed when using either
numerical or empirical Green’s functions. However, the predicted PGA are largely improved, when HGF are
used. The amplitudes and the attenuation with distance are better described with hybrid Green’s function
than with the numerical ones. Some deficiencies at high-frequencies are still observed in the band 5 to 12 Hz,
perhaps due to finite source effects associated to the small earthquake. For this latter case, using a
deconvolution technique seems to be necessary to better describe the high-frequency content.
Using recording of small magnitude events (EGF) combined with a kinematic complex source model seems
to be a useful tool to predict strong ground motion. Some of advantage of to use HGF is the possibility of to
-7-
incorporate 2D or 3D low-frequency wave field propagation in a more realist medium. However, further
work must to be done to remove the source effect associated with small earthquakes. Also, is important to
test the limits of use this technique by modeling large magnitude earthquakes, in this case it is advisable to
use records from several small earthquakes as EGF to better sampling the wave propagation to the station.
Acknowledgements
Figures were drawn by GMT v3.4 (Wessel and Smith, 1998).
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- 10 -
Figure 1. Scheme showing the principle of a kinematic source rupture description using empirical Green’s
functions to compute HGF (see text for details).
- 11 -
Figure 2. Fault-trace and epicenter location of the 1997 Mw 5.9 Yamaguchi earthquake and three aftershocks
(after Ide, 1999). Triangles indicate the stations of the K-NET Japanese strong motion network, and stations
used in the simulations are plotted with gray dark triangles.
- 12 -
Figure 3. Example of verification of the seismic moment of aftershocks for the station SMN014 and
YMG010. (a) Spectral ratios AFT1/AFT3, AFT1/AFT2, and AFT2/AFT3 computed for the using the radial
and transverse components. (b) Measure of the 0 plateau level at low-frequency using displacement
spectrum for the transverse component.
- 13 -
Figure 4. Example of signal-to-noise analysis for the transversal component of records of the AFT1 at three
stations. (a) Accelerograms times-series, and (b) comparison of signal (dark lines), noise (gray lines) and
theoretical spectrum (dashed lines). The theoretical 2 spectrum was plotted with a corner frequency
estimated at 5 Hz.
- 14 -
Figure 5. Hybrid Green’s function at YMG010 (north component). Right-hand graphs display the
accelerogram time series for the (top) numerical, (middle) empirical and (bottom) hybrid GFs. Left-hand
graphs show (top) a comparison between the theoretical and empirical GFs versus seismic noise acceleration
spectra, (middle) low- and high-pass filters with a cut-off frequency equal to 1.0 Hz and (bottom) hybrid GF
spectrum.
- 15 -
Figure 6. Slip distribution and rupture times contours for the 1997 Mw 5.9 Yamaguchi earthquake imaged by
Ide (1999) using kinematic inversion of strong ground motion records.
- 16 -
Figure 7. Example of (a) the stress drop parameter distribution, d, and (b) the cumulated seismic moment
as a function of radius of subevents when a hypothesis of constant (squares) and stochastic fluctuation
(circles) of d is assumed. The set of subevents generated for this example is one used to model the M w 5.9
Yamaguchi, Japan earthquake.
- 17 -
Figure 8. Example of a k-2 slip distributions when using a (a) constant and (b) stochastic fluctuation of the
stress drop of subevents. (Left to right) 2-D and 3-D representation of the slip and the slip spectral
amplitudes. Gray line superposed to spectrum represents a reference k-2 decay, u(k) ~ 1 /( 1 + (k/kc)2), kc =
2/Lc, Lc = 8 km.
- 18 -
Figure 9. Comparison of simulated (circles) and observed (squares) strong-motion parameters for the 1997
Mw 5.9 Yamaguchi Japan earthquake using numerical Green’s functions. The predicted (a) PGA and (b)
PGV numerical values were computed assuming constant stress drop, where as numerical values for (c) PGA
and (d) PGV were computed using stochastic fluctuation of stress drop. The empirical attenuation
relationships plotted corresponds to one derived by Kanno et al. (2006) where thick and thin gray lines
represents the mean ± the standard deviation.
- 19 -
Figure 10. Comparison of simulated (circles) and observed (squares) for horizontal peak ground (a)
acceleration, PGA and (b) velocity, PGV for the 1997 Mw 5.9 Yamaguchi Japan earthquake. The predicted
numerical values were computed using HGF and five random slip distributions generated with a fractal
approach assuming variable stress drop for subevents. The empirical attenuation relationships plotted
correspond to one derived by Kanno et al. (2006) where thick and thin gray lines represents the mean ± the
standard deviation.
- 20 -
Figure 11. Comparison of synthesized (gray lines) and observed (black lines) waveforms of displacement,
velocity, acceleration, and acceleration spectrum for the 1997 Mw 5.9 Yamaguchi earthquake. Synthetic were
computed using HGF and a random composite slip assuming a variable stress drop of subevents.
- 21 -
Figure 12. Comparison of predicted (circles) and observed (squares) for the horizontal (a) PGA and (b) PGV
for the 1997 Mw 5.9 Yamaguchi Japan earthquake. Synthetics were computed using deconvolved HGF and
five random slip generated with a fractal approach assuming variable stress drop for subevents. The
empirical attenuation relationships were derived by Kanno et al. (2006) where thick and thin gray lines
represent the mean ± the standard deviation.
- 22 -
Table 1. Hypocenter location and source parameters for the 1997 Mw 5.9 Yamaguchi earthquake
proposed by different seismological agencies.
Agency
Date Time
Latitude
Longitude
Depth
M0
°
°
(km)
(N.m)
Mw
JMA(1)
9:50:00
34.438
131.669
8.29
-
6.1
CMT
9:50:10.70
34.43
131.35
15
6.711017
5.8
NEIC
9:50:12.49
34.395
131.603
12
9.11017
5.9
Ide (1999)(2)
18:50:13.10
34.4412
131.6761
7.5
-
5.9
JMA, Japan Meteorological Agency.
CMT, Centroid Moment Tensor (Dziewonski et al., 1999).
NEIC, National Earthquake Information Center.
(1)
JMA magnitude.
(2)
Local Japanese time.
- 23 -
Table 2. Source parameter of the main shock and aftershock proposed by Ide (1999).
Date
Latitude
Longitude Depth Mw Strike Dip Rake
JST
°
°
(km)
Main shock
25/6 18:50:13.1
34.4412
131.6761
7.5
AFT1
25/6 18:58:23.0
34.4544
131.6965
AFT2
25/6 19:30:02.4
34.4412
AFT3
25/6 19:49:43.9
34.4483
°
°
°
5.9
-125
86
-178
9.7
3.6
55
84
175
131.6800
11.3
3.4
55
82
174
131.6927
5.2
3.4
-122
86
178
- 24 -
Table 3. Crustal structure model used in the simulations. These values correspond to
ones proposed by Ide (1999).
Depth
Vp
Vs

(km)
(km/s)
(km/s)
(gr/cm3)
0
5.60
3.23
3
6.00
16
Qp
Qs
2.50
400
200
3.47
2.70
600
300
6.60
3.82
3.00
800
400
30
7.80
4.50
3.20
1000
500
70
8.00
4.62
3.25
1000
500
- 25 -
Table 4. Seismic moment (M0) and magnitude (Mw) determined for the aftershock 1
(AFT1) using displacement spectrum of S-wave.
R
0
M0
(m)
(cm.s)
(N.m)
SMN011
33598
8.0010-4
3.021014
3.59
SMN012
26939
5.0010-4
1.521014
3.39
SMN013
29072
4.0010-3
1.311014
3.34
SMN014
12370
1.0010-3
1.391014
3.36
YMG002
29221
9.0010-4
2.961014
3.58
YMG003
15280
1.5010-3
2.581014
3.54
YMG009
29141
6.0010-4
1.971014
3.46
YMG010
37904
3.0010-4
1.281014
3.34
Mean values
2.001014
3.45 ± 0.11
Station
- 26 -
Mw