13th World Conference on Earthquake Engineering
Vancouver, B.C., Canada
August 1-6, 2004
Paper No. 1371

RECIPE FOR PREDICTING STRONG GROUND MOTIONSFROM FUTURE LARGE EARTHQUAKES
Kojiro IRIKURA1, Hiroe MIYAKE2, Tomotaka IWATA3,
Katsuhiro KAMAE4, Hidenori KAWABE5, and Luis Angel DALGUER6SUMMARY
From recent development of the waveform inversion analyses for estimating rupture process using strong
motion data during large earthquakes, we have understood that strong ground motion is relevant to slip
heterogeneity inside the source rather than average slip in the entire rupture area. Asperities arecharacterized as regions that have large slip relative to the average slip on the rupture area, based on slip
distributions estimated from the source inversion (Somerville et al. [1]). Then, the asperity areas as well as
total rupture areas scale with seismic moment. We examined that strong motion generation areas
approximately coincide with the asperity areas where stresses are largely released (Miyake et al. [2]).
Based on the scaling relationships, the source model for the prediction of strong ground motions ischaracterized by three kinds of parameters, outer, inner, and extra fault parameters. The outer fault
parameters are defined as entire rupture area and total seismic moment. The inner fault parameters aredefined as slip heterogeneity inside the source, area of asperities, and stress drop on each asperity. We
developed a recipe for predicting strong ground motions, which is to characterize the source model for the
future large earthquakes. For the outer fault parameters, at first the total fault length is given as a sum ofactive fault segments. The fault width is related to thickness of seismogenic zones. The entire source area
is defined as a product of the length and width, then the total seismic moment following the empiricalscaling relationship. For the inner parameters, the area of asperities is estimated from the scaling with thetotal seismic moment. Stress drop on each asperity is derived based on a multiple-asperity model, which is
given as an extension of a single-asperity model by Das and Kostrov [3]. The pattern of rupture nucleationand termination as the extra fault parameters are related to geomorphology of active faults and plates. We
have examined the validity of the earthquake sources constructed by the recipe, comparing simulated andobserved ground motions for recent large earthquakes, such as the 1995 Kobe and the 2003 Tokachi-oki
earthquakes.

1

Disas. Prev. Res. Inst., Kyoto University, Japan.
Earthq. Res. Inst., University of Tokyo, Japan.
3
Disas. Prev. Res. Inst., Kyoto University, Japan.
4
Res. Reac. Inst., Kyoto University, Japan.
5
Res. Reac. Inst., Kyoto University, Japan.
6
Disas. Prev. Res. Inst., Kyoto University, Japan.
2

Email: irikura@egmdpri01.dpri.kyoto-u.ac.jp
Email: hiroe@eri.u-tokyo.ac.jp
Email: iwata@egmdpri01.dpri.kyoto-u.ac.jp
Email: kamae@kuca.rri.kyoto-u.ac.jp
Email: kawabe@rri.kyoto-u.ac.jp
Email: dalguer@egmdpri01.dpri.kyoto-u.ac.jp

INTRODUCTION
High-quality ground motions have been recorded from recent large earthquakes, such as the 1994
Northridge, the 1995 Kobe (Japan), the 1999 Kocaeli (Turkey), the 1999 Chi-Chi (Taiwan), and the 2003
Tokachi-oki (Japan) earthquakes. Accumulated data of strong ground motions have been providing usvery important knowledge about rupture processes of earthquakes, propagation-path, and siteamplification effects on ground motion, the relation between ground motion and damage, and so on. Then,
we have learned that earthquake damage resulted from destructive ground motion generated by rupture
propagation effects inside the source as well as geological conditions. It shows that strong ground motion
prediction is one of key factors for mitigating disasters for future earthquakes.
We made a framework of strong motion prediction as shown in Fig. 1. The strong motion from thescenario earthquake is evaluated from source modeling and Green's function estimation based on
geological and geomorphological surveys of active faults, analyses of strong motion recordings,
geophysical profiling of underground structures, and so on. The results will lead to improvement of thebuilding code and bridge earthquake-resistant design.

Fig. 1. Framework of predicting strong ground motion from scenario earthquake.

We attempted to make a recipe to popularize the prediction of ground motions for engineering
purpose based on seismological fruits. There are two important factors for predicting strong groundmotion, one is source characterization based on geological features for active faults and statistical analysis
of source processes from the waveform inversion of strong motion records, the other is the estimation of
the Green's functions from source to site.
For the former, we know that most of the uncertainties in predicting strong ground motion is tospecify the proper methods of characterizing the source models of future earthquakes. We studied thescaling of the fault parameters based on the waveform inversion results of source process using the strong
motion data. We found that the source model for estimating strong ground motion is characterized by threekinds of parameters, which we will call: outer fault parameter, inner fault parameters, and extra
parameters, as discussed later.
For the latter, numerical Green's functions are calculated for ground motions longer than 1 sec
based on methods such as Discrete Wave Number Method, Finite Deference Method, and Finite Element
Method. The short period motions are estimated by the empirical Green's functions and stochastic
simulation method for small events. To combine both methods, we introduce the idea of a hybrid scheme
estimating broad-band Green's functions, deterministic and stochastic approaches in low (< 1 Hz) andhigh (> 1 Hz) frequency ranges, respectively, to obtain broad-band ground motions (Irikura and Kamae,[4]). Influence of variances of estimated source parameters on ground motions are discussed fromsynthetic waveforms based on our recipe.

BASIC IDEA FOR PREDICTING STRONG GROUND MOTION

Fig. 2. Concept of source characterization based on the slip distributions by the waveforms inversions.
From recent development of the waveform inversion analyses for estimating rupture processes
during large earthquakes, we have understood that strong ground motion is relevant to slip heterogeneity
inside the source rather than the entire rupture area. The waveform inversion has shown that fault motions

consist of some asperities with large slip and background region with less slip (Fig 2). We have examinedthat strong motion generation areas approximately coincide with the asperity areas where stresses are
released (Miyake et al. [2]). Such slip heterogeneity on the fault plane plays an important role on shortperiod motions. Somerville et al. [1] found that slip heterogeneity inside the fault plane as well as entire
rupture area follow the self-similar scaling laws with respect to total seismic moment. It suggests thatsource parameters for predicting ground motion are predictable when the total seismic moment or thesource area for a future earthquake is given.
We introduce the idea of source characterization for predicting strong ground motion based on themultiple-asperity source model, which is given as an extension of a single-asperity source model by Das
and Kostrov [3]. Relationship between the asperity-source model and source characterization issummarized in Fig. 3. Once distribution of the stress filed is characterized, dynamic simulation provides
slip distribution. The procedure of the source characterization is derived high stress region from the slip
distribution obtained by the waveform inversions.

Fig. 3. Asperity source model for simulating strong ground motions. Distribution of stress change (left)
and final slip (right) for a single-asperity source model (after Boatwright [7]).
For a single-asperity source model, where an asperity locates in arbitrary position inside the stressfree field, seismic moment, stress drop on the asperity, and acceleration source-spectral level are derived
as follows.

16∆σ a r 2 R
7
7 M0∆σ a =
16 Rr 2M0 =

A0a = 4πβv r ∆σ a r(1)from Boatwright [7] based on Das and Kostrov [3](2)from Boatwright [7] based on Das and Kostrov [3](3)from Madariaga [8]where β is S-wave velocity and vr is rupture velocity. These equations are extendable for the multipleasperity source models, taking into account that low frequency motions from plural asperities arecoherently summed while high frequency motions are randomly summed. The low and high frequency
motions are related to the seismic moment and the acceleration level, respectively. Regardless of thenumber of asperities, the stress drop on each asperity is the same as long as the sum of the asperity areas isconstant. Stress drop on the asperities ∆σ a is derived as a multiple of the average stress drop over thefault ∆σ c and the ratio of asperity area Sa to total rupture area S (e.g., Madariaga, [9]).

∆σ a = ∆σ c ⋅

S
Sa

(4)

FUNDAMENTAL RELATIONSHIPS CONTROLLING FAULT PARAMETERS
Scaling Relations of Outer Fault Parameters
The outer fault parameters are parameters characterizing the entire source area such as total
rupture area and seismic moment. Conventional scaling relations of the fault parameters such as fault
length and average slip on fault with seismic magnitude are mostly determined geologically from surface
offsets and geophysically from forward source modeling using teleseismic data and geodetic data. Those
data are only available for very long period motions but not enough for near-source strong motions
dominating short period motions less than 1 sec of engineering interest.
We examined the scaling relations of seismic moment versus total rupture area based on thestatistical analysis of source processes from the waveform inversion of strong motion records from crustal
earthquakes (Somerville et al. [1]; Miyakoshi [10]). Analyzed data range from Mw 5.7 to Mw 7.6. For
moderate-size earthquakes, the total fault area S follows the self-similar scaling relation with seismic
moment M0 expressed as equation (5) by Somerville et al. [1]. For larger earthquakes, we proposed thescaling departing from self-similar model (Irikura and Miyake [11]) adding the reliable data from Wells
and Coppersmith [12] to support the saturation of the fault width. This scaling shown in equations (5) and(6) has been also found in Hanks and Bakun [13]. For extra large earthquakes, we quoted the idea by
Scholz [14] changing from L-model into W-model. Relationship between seismic moment and rupturearea for inland crustal earthquakes are summarized. Saturation of the fault width is assumed as 20 km.

Fig. 4. Empirical relationship between seismic moment and rupture area for inland crustal earthquakes.
Thick broken lines are 3-stage scaling relationships proposed by our studies (e.g., Irikura et al. [15])S (km2) = 2.23 x 10-15 x Mo2/3 for Mo < 7.5 x 1025 dyne-cm
S (km2) = 4.59 x 10-11 x Mo1/2 for Mo >= 7.5 x 1025 dyne-cm
S (km2) = 5.30 x 10-25 x Mo
for Mo >= 7.5 x 1027 dyne-cm

(5)
(6)
(7)

after Somerville et al. [1]after Irikura and Miyake [11]To support our proposed scalings, we developed a series of dynamic rupture simulations
rectangular sources with homogeneous stress drop with boundary condition of surface and sub-surface

earthquakes (Fig. 5). The relationship between the seismic moment and the total rupture area is shown in
Fig. 6, and that between the fault length and average slip in Fig. 7.

Fig. 5. Several examples of final slip distribution for rectangular crack models by dynamic simulations.

Fig. 6. Relationship between seismic moment and total rupture area for inland crustal earthquakes fromdynamic simulations. Wmax is assumed as 20 km.
We propose a 3-stage scaling relationship between seismic moment and rupture area for bothinland crustal and subduction-zone earthquakes. The first stage is a scaling with constant static stress drop
before fault width saturating the seismogenic zone, the second stage is a scaling increasing static stressdrop after the saturation of fault width, then the third stage is a scaling with constant static stress drop
again where the fault length becomes long enough. Source-scaling implied from dynamic rupture
simulation explains the circular-crack model, L-model, and W-model together cooperating with the idea by
Scholz [14].

Fig. 7. Relationship between fault length andmaximum slip from dynamic simulations.
Scaling Relations of Inner Fault Parameters
Strong ground motions are controlled by inner fault parameters for slip heterogeneity as well asouter fault parameters defining the entire rupture area and total seismic moment. Fig. 8 displays therelationship between rupture area S as the outer fault parameter and combined area of asperities Sa as theinner fault parameter, according to the waveform inversion results compiled by Somerville et al. [1] andMiyakoshi [10]. Sa / S seems to be constant regardless of the rupture area.
Sa / S = 0.215(8)after Irikura and Miyake [11]Fig. 8. Empirical relationship between combined
area of asperities and total rupture area (thickbroken line) for inland crustal earthquakes.
Shadow ranges ± σ (standard deviation). Thinsolid lines show a factor of 2 and 1/2 for the
average (after Irikura and Miyake [11]).
Database obtained by the waveform inversions
for the inland crustal earthquakes is Somervilleet al. (1999) and Miyakoshi (2002).

When the relationship between combined area of asperities and total rupture area is not given or
unclear, there is a choice to practice the relationship between seismic moment and acceleration source
spectral level. By using the relationships A0 ∝ M 0 obtained empirically (Fig. 9) and A0 ∝ M 0
theoretically from equation (3) together, the combined of asperities are derived as follows.
1/ 3

a

2

 7π 2
(M 0 ) 2
S a = βv R  ⋅a 2
 4
 S ⋅ ( A0 )

(9)

1/ 3

Fig. 9. Empirical relationship between seismic moment and acceleration source spectral level for the
subduction-zone earthquakes.
Constraints on Average Slip of Asperities from Dynamic Simulations
Slip distribution for the multiple-asperity source models is dynamically solved by numericalsimulation. The simulations suggest that even identical seismic moment decreases Da /D with increasingof the number of asperities, where Da and D are average slip of the asperities and the entire fault,
respectively (Fig. 10).
(c)

(a)

(b)

Masp/Mo
Dasp/D
Dmax/D∆σb/∆σa = 0.0
MEC1
M2DA3
0.530
0.458
2.363
2.052
2.921
2.638

M2EA3
0.450
2.027
2.476

Fig. 10. Dynamic solution of three selected circular asperity models with fixed rupture velocity (0.8Vs)
and critical slip Dc = 0.4 m. (a) Asperity location for each circular fault model. Star represents the
rupture starting point, R and r are the radii of the fault and asperity. The ratio between the combined
asperity area (Sa=90km2) and total rupture area (S=408km2) is 0.22. This ratio is partitioned for the
double asperities, 11% for each asperity of model M2EA3 and 6%-16% for M2DA3. The stress drop in
the asperity is ∆σa =10.5 MPa. (b) The table specifies the ratios of seismic moment (Masp / M0), averageslip (Dasp /D), and maximum slip (Dmax /D) between the asperity area and total rupture area in case of∆σb /∆σa = 0. (c) Final slip distribution along the diameter of the fault (in-plane direction) in the case of∆σb /∆σa = 0.

RECIPE FOR CHARACTERIZING EARTHQUAKE SOURCE
We outline the procedure for characterizing the source model to estimate strong ground motion for
future large earthquake. For estimating strong ground motions using a deductive approach, we need tohave three kinds of source parameters, outer, inner, and extra fault parameters.
Outer Fault Parameters -Estimation of Seismic Moment for Possible EarthquakeStep 1: Total Rupture Area (S = LW)
Total fault length L of the possible earthquake is defined as sum of the lengths of the fault
segments grouping simultaneously activated. Fault width W is related to the total fault length
before reaching the thickness of the seismogenic zone Wmax.
W (km) = L (km)W (km) = Wmax (km)for L < Wmax
for L >= Wmax

(10)
(11)

Step 2: Average Stress Drop ( ∆σ c ) on the Fault
The average stress drop is assumed depending on the rupture size or depth dependency.
Step 3: Total Seismic Moment (M0)When crack-like fault model is adopted, Eshelby [22]’s equation is applied.
Otherwise, relationship between seismic moment and rupture area would be considered.

M0 =

16
∆σ c ⋅ S 1.5
1.5
7π

(12)

Inner Fault Parameters - Slip Heterogeneity or Roughness of Faulting Step 4. Combined Area of Asperities (Sa)From the empirical relation of Sa-S (Somerville et al. [1]; Irikura and Miyake [11]), where the
combined area of asperities is specified to be about 22%.
Step 5. Stress Drop on Asperities ( ∆σ a )As shown in equation (4), ∆σ a as the inner fault parameter is derived as a multiple of ∆σ c as
the outer fault parameter and Sa /S from Step 4.
Step 6. Number of Asperities (N)The asperities in the entire fault rupture are related to the segmentation of the active faults or to
information of past earthquakes. Locations of the asperities are from surface offsets measured
along fault or from back-slip rate studied by GPS observation.
Step 7: Average Slip on Asperities (Da)Based on Step 6 and empirical relationships from dynamic simulations of the slip distribution forthe multiple-asperity source model.
(Examples: Da /D = 2.3 for N = 1, Da /D = 2.0 for N = 2, Da /D = 1.8 for N =3)
Step 8: Effective Stress on Asperity (σa) and Background Slip Areas (σb)
We treat stress drop on asperity ( ∆σ a ) as effective stress (σa) on asperity for strong motion
generation. The effective stress on background slip area is constrained by the empirical
relationship between seismic moment and acceleration source spectral level.
Step 9: Parameterization of Slip-Velocity Time Functions
Modeling of peak slip-velocity and rise time for both asperity and background areas.
Extra Fault Parameters - Propagation Pattern of Rupture The extra fault parameters are related to the fault geometry rupture starting point, characterizing

rupture propagating pattern, and rupture velocity. For inland crustal earthquakes, rupture nucleation andtermination are related to geomorphology of active faults (e.g., Nakata et al. [23]; Kame and Yamashita[24]). For subduction-zone earthquakes, information from past earthquakes is applied as possible.

EXAMPLES FOR SIMULATING STRONG GROUND MOTION
Inland Crustal Earthquake: 1995 Kobe Earthquake
We have successfully made characterize earthquake rupture models for the prediction of groundmotions from statistical analysis of the source inversion results for inland crustal earthquakes. Cooperatingwith high-quality ground motion records from recent earthquakes in California, Japan, and Taiwan, we
verified the applicability of the methodology comparing simulated ground motions with observed ones forthe 1994 Northridge, 1995 Kobe, 1999 Kocaeli, and 1999 Chi-Chi earthquakes. Fig. 11 shows the groundmotion simulation following the recipe, for the 1995 Kobe earthquake, Japan, by Irikura et al. [25] using
the stochastic Green’s function method.
(a)
(b)

(c)

(d)

Fig. 11. Ground motion simulation for the 1995 Kobe earthquake using the stochastic Green’s function
method. (a) Characterized source model based on Kamae and Irikura [26]. (b) Source parameters. (c)Variability of simulated response spectra for 10 different element earthquakes. (d) Comparison
between observed and simulated velocities of NS component at KBU station.

Subduction-Zone Earthquake: 2003 Tokachi-oki Earthquake
For subduction-zone earthquakes, accurate source inversion results have not been obtained
enough to make scaling relations of source heterogeneities. Some inversion results using near-field
displacements with low-amplification seismographs and teleseismic data from the 1944 Tonankai and1946 Nankai earthquakes as well as those using the strong motion records from the 1985 Michoacan
earthquake have showed slip-heterogeneity scaling similar to the inland earthquakes. We apply theprocedure similar to the inland earthquakes to estimating strong ground motions from the subduction-zone
earthquakes. Fig. 12 shows the source modeling for strong ground motion from the 2003 Tokachi-oki
earthquake, Japan, by Kamae and Kawabe [27] using the empirical Green’s function method.

Fig.
12.
Groundmotionsimulation for the 2003
Tokachi-oki earthquake (after
Kamae and Kawabe [27])using the empirical Green’s
function
method.
Upper:
characterized source modelingconsists of three asperities.
Black contours show the slip
distribution in every 1mobtained by Yamanaka andKikuchi[28].
Lower:
comparison between observed
and simulated waveforms for
TKCH07 station.

DISCUSSIONAre Asperities Repetitious?
Estimation of the asperity location from future earthquakes is challenging issue as well as central
importance for the source characterization. As some proofs of the characteristic source models, Kikuchi
and Yamanaka [29] has been proposed the repetition of asperities for subduction-zone earthquakes,
comparing the source inversion results for both present and past large earthquakes by retrieving thehistorical waveforms. Fig. 13 displays that the location of asperities seems to be overlapped for the event
pairs of the 1952 and the 2003 Tokachi-oki earthquakes by Yamanaka and Kikuchi [28], and for the 1968
Tokachi-oki and the 1994 Sanriku-Oki earthquakes by Nagai et al. [30].

How to Find the Asperities?
Geological, geomorphological, seismological, geodetic surveys imply the information to locate theasperities.
- Coincidence of surface offsets measured along active fault and locations of asperities on fault
segments: Wald and Heaton [31] for the 1994 Landers earthquake and by Lee et al. [32] and Iwata etal. [33] for the 1999 Chi-Chi earthquake.
- Seismic activity: Less active inside asperities and relatively more active surrounding the asperities
before the earthquake. Measuring b values, a values, and local recurrence time as indication whereasperities may be located (Wyss et al. [34]).
- Reflected (scattered) waves: strong/less reflection (scattering) coefficients inside asperities andrelatively high outside asperities. Locked segments with weaker scattering and low microseismicity,and segment boundaries with stronger scattering and stationary microseismicity. The locked segments
are ruptured as asperities for future earthquakes (Nishigami [35]).
- Back-slip estimation from by GPS analyses indicating coupling-rate of the plate boundary.

Fig. 13. Some proofs of the repetition of asperities.
Left: Slip distributions for the 1952 and 2003
Tokachi-oki earthquakes (after Yamanaka andKikuchi [28]). Right: Spatial distribution of the
moment release and aftershocks for the 1968
Tokachi-oki and 1994 Sanriku-Haruka-oki
earthquakes. (after Nagai et al. [30]).

CONCLUSIONSWe propose a recipe for predicting strong ground motions from future large earthquakes for inland
crustal earthquakes caused by specific active faults and subduction-zone earthquakes. The recipe is madeby the source characterization based on the multiple-asperity source model, and the hybrid method for
simulating ground motions. The source model is characterized by three kinds of parameters, which we
call: outer, inner, and extra fault parameters. The outer fault parameters define the entire source area forpossible earthquake. The inner fault parameters are parameters characterizing fault heterogeneity inside
the fault area. The extra fault parameters are related to the propagation pattern of the rupture.
The validity and applicability of the procedures for characterizing the earthquake sources forstrong ground prediction are examined in comparison with the observed records and broad-band simulated
motions for the 1995 Kobe and the 2003 Tokachi-oki earthquakes. In future directions, strong groundmotions taking into account the source dynamics are encouraged to constrain fault parameters.

ACKNOWLEDGEMENTS
We are grateful to Takao Kagawa and Ken Miyakoshi for their contributions at the early stage ofthis study. We used near-source ground motion data of KiK-net and CEORKA. GMT by Wessel andSmith [36] was used for making several figures. This work was supported in part by the Special
Coordination Funds titled 'Study on the master model for strong ground motion prediction toward
earthquake disaster mitigation' from the Ministry of Education, Science, Sports and Culture of Japan.

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