13th World Conference on Earthquake Engineering
Vancouver, B.C., Canada
August 1-6, 2004
Paper No. 3286

CHARACTERIZATION OF DYNAMIC ASPERITY SOURCE MODELSFOR SIMULATING STRONG GROUND MOTION
Luis A. DALGUER1, Hiroe MIYAKE2, and Kojiro IRIKURA3SUMMARY

Asperity source models are important since recent studies have clarified that the main
contribution to strong ground motion comes from the asperity area. These models are defined bythe fault parameters: fault area, average slip, maximum slip, peak slip velocity, and stress drop
both of the overall fault and asperity area. The ratios of these parameters between the asperity
and the total rupture area, together with the scaling relations of fault models, make feasible thedefinition of the asperity source model. Since dynamic rupture models take into account thephysical conditions of the friction and stress distribution across the fault, we estimated the ratios
between the above parameters from dynamic models capturing more realistic seismic source
properties. We started assuming that the combined asperity area is 0.22 times the total rupturearea as following the slip characterization for kinematic models of Somerville et al. [1]. Subsurface earthquakes, represented as circular faults, and surface earthquakes, represented asrectangular faults that break the free-surface, are simulated for single and multiple asperities. We
assumed different conditions of stress drop surrounding the asperity (background area) that varyfrom –0.2 to 0.2 times the stress drop of the asperity area. A fixed rupture velocity (0.8 of Swave velocity) and the simple slip-weakening friction model on the fault were used for thedynamic rupture propagation. The dynamic rupture simulation suggests that the characterized
source model of Somerville et al. [1] is valid when the ratios of stress drop between thebackground and asperity is between –0.05 to 0.1 for sub-surface earthquakes and between –0.15
to 0.05 for surface earthquakes. We also found that the average peak slip velocity in thebackground area with zero stress drop is around 0.3 times the one in the asperity area. These
characterized parameters verified by dynamic faulting are playing an important role for practicalapplication of strong ground motion prediction.

1DPRI, Kyoto University, Japan. E-mail: dalguer@egmdpri01.dpri.kyoto-u.ac.jp
ERI, University of Tokyo, Japan. E-mail: hiroe@eri.u-tokyo.ac.jp
3
DPRI, Kyoto University, Japan. E-mail: irikura@egmdpri01.dpri.kyoto-u.ac.jp2

INTRODUCTION

The source model for strong ground motion prediction and earthquake scenario is usuallydeveloped from scaling relations of characterized source models developed by kinematic
approach (e.g. Somerville et al. [1]). Since the origin of these scaling relations comes fromkinematic approach, they do not take into account the physical causes of the earthquakes, that is,
the stress that causes or participates in the source process is neglected. The target of this paper is
to fill this gap and complement these models using dynamic approach. We attempt to investigate
the physical causes and under which conditions the kinematic source characterized source
models are valid.
The recent studies developed by Miyake et al. [2] have clarified that the main contribution tohigh and low frequency strong ground motion comes from the asperity area. The asperity
models, as well as the barrier models, are widely used for representation of the fault-zone
heterogeneity, in which both terms are related to the stress and strength distribution along thefault plane. The classical definition of these models (e.g., Kanamori and Stewart [3], Aki [4]) isa simple as well as robust description of such heterogeneity. From the definition that the seismic
radiation and the slip on the fault are produced by the stress drop and, that the asperity areas is
the main responsible for generating the strong ground motion during earthquakes, asperity area
can be defined as the zone with the high stress drop. Therefore, the identification andcharacterization of asperity models play an important role for practical application of strong
ground motion prediction and ground motion simulation for engineering purpose. From classicalcircular single-asperity source model studied by Madariaga [5], Das and Kostrov [6] andBoatwright [7] it is possible to approximately derive the relationship between the stress drop on
the asperity (∆σa), the total seismic moment (Mo), the combined asperity area and total rupturearea as follow:∆σ a =

7 M0
16 Rr 2(1)where R and r are the radii of the circular fault and circular asperity respectively. And It isassumed for an arbitrary position of the asperity area.
But this relation is limited to only one asperity with zero stress drop out of the asperity area.
Furthermore, this expression may be accepted only for self-similar sub-surface earthquakes.
Since earthquakes are the results of dynamic rupture process in which the friction and stress
distribution across the fault are taking in to account, and they can be surface or sub-surface
earthquakes, the dynamic analysis of the asperity-source model certainly provides more realistic
seismic source properties. Therefore, we developed dynamic rupture simulations for single andmultiple asperity-source models for surface and sub-surface earthquakes, and from the results we
propose the ratios of the fault parameters (fault area, average slip, maximum slip, peak slipvelocity, and stress drop) between the asperity and the total rupture area. The sub-surface
earthquakes are simulated by means of circulars faults, and the surface earthquakes byrectangular faults in which the faulting breaks the free-surface. The ratios obtained with these
dynamic rupture simulations together with the scaling relations of fault models (e.g. Somervilleet al. [1]) make feasible the definition of the asperity source model for ground motion
simulation.

CIRCULAR ASPERITY MODELS (SUB-SURFACE EARTHQUAKES)

We performed 3D simulations of dynamic faulting for a series of single and multiple circularasperity-source models (Figure 1) using the staggered-grid finite-difference code of Pitarka [8].
The problem is tackled assuming that the fault is embedded in an unbounded medium with nofree surface. Then the simulated earthquakes would be considered as self-similar in which theratios obtained from the slip, slip velocity, and stress drop remain invariant with the size of thefault. The ratio between the combined asperity area and total rupture area is equal to 0.22 for all
the models. This ratio, proposed by Somerville et al. [1] fits the characteristic slip models ofrecent large earthquakes. The size of total rupture area is S= 400km2, size of combined-asperity
area Sa=88km2, stress drop for asperities ∆σa=10.5MPa, stress drop for background area ∆σb=0.20, 0.0, 0.10, 0.15 and 0.20∆σa, rigidity µ=3.0GPa, S-wave velocity Vs =3.2km/s, density
ρ=2.8gr/cm3. The dynamic rupture propagation is developed assuming a fixed rupture velocity(0.8 of S-wave velocity) and the simple slip-weakening friction model in the form given byAndrews [9] with a critical slip-weakening distance Dc=0.4m is used. This friction law that was
first proposed by Ida [10] is extensively used for dynamic simulation of fault rupture process(e.g., Andrews, [9]; Day, [11]; Olsen et al., [12]; Fukuyama and Madariaga, [13]; Harris andDay, [14], Dalguer et al., [15] and supported by laboratory experiments (e.g. Ohnaka et al., [16];Ohnaka and Shen [17] these authors conclude that their experiments could be explained with asimple slip weakening friction law model.

1 Asp

2 Asp

3 Asp

RRr

r

r

Rr

r
r

Figure 1. Circular asperity models for dynamic rupture simulation of sub-surface earthquakes. Rand r are the radii of the circular fault and circular asperity respectively. The star represents thehypocenter.
Figure 2 shows the ratios of average slip and maximum slip for the circular asperity
models of Figure 1. The gray arrow represents the band in which the characterized kinematic
slip model proposed by Somerville et al. [1] is equivalent to the dynamic model. From thisfigure we can conclude that the kinematic scaling models fit the dynamic models when the ratiosof stress drop is in the band of -0.05 < ∆σb/∆σa < 0.10. Corresponding ∆σb/∆σa ≈ -0.05 for triple,∆σb/∆σa ≈ 0.0 for double and ∆σb/∆σa ≈ 0.1 for single asperity models. These figures alsosuggest that the number of asperities decreases the ratios. A more detail analysis and moregeneral cases of circular asperity models are studied in our paper in preparation (Miyake et al[18]).

Figure 2. Average slip ratio (Dasp/D) and maximum slip ratio (Dmax/D) plotted with the stressdrop ratio (∆σb /∆σa) for the dynamic solution of the asperity models shown in Figure 1. The
arrow specifies the band of the stress drop ratios in which fit the characterized slip model
proposed by Somerville et al. [1].
The peak slip-velocity ratio between the back ground area and the asperity area is also
estimated from the dynamic rupture models. For this calculation we used a single asperity modelwith the asperity located at the center of the fault. Figure 3 shows these results as a function of
the stress drop ratio. The average peak slip-velocity in the background area with zero stress dropis around 0.3 times the one in the asperity area. As the stress drop ratios increase, the ratios ofpeak slip-velocity increase.

Figure 3. Relationship between the ratio of maximum slip-velocity (Vmaxb /Vmaxa) withstress-drop ratio (∆σb /∆σa) for the dynamic solution of a circular single asperity model with theasperity located at the center of the fault. The Vmaxa and Vmaxb are the average of maximum
slip-velocity in the asperity area and in the back ground area, respectively.

RECTANGULAR ASPERITY MODELS (SURFACE EARTHQUAKES)

Larger earthquakes are expected not to be self-similar anymore, then, the ratios for circularasperity models estimated above my fail for this kind of earthquakes. In order to verify it, wedeveloped a series of rectangular asperity models assuming that the faulting breaks the freesurface. This kind of earthquake we can categorize as surface fault. Our simulations consist ofearthquakes with L>=Wmax, where L and W are the length and width of the fault, respectively.
Wmax is assuming to be 20km that represents the brittle crust of the earth. The fault models arecalculated up to L<=20Wmax. The ratio between the combined asperity area and total rupturearea is equal to 0.22 as also used for the circular asperity models. The number of asperities
increases with L, as shown in Figure 4, assuming single asperity for L=W=20km, double for
L=40km, triple for L=100km, and quadruple for L>=200km. The material properties andfriction law are the same as for the circular asperity models.
01 Asp2 Asp

0W -10(km)-10-10-20
020-20

3 Asp

0020

40-20

020

40

60

80

1001201401601802004 Asp

0-10-20020

406080100L (km)Figure 4. Rectangular asperity models for dynamic rupture simulation of surface earthquakes.
Single asperity model is for L=W=20km, double for L=40km, triple for L=100km, andquadruple for L>=200km. L and W are the length and width of the fault, respectively. The star
represents the hypocenter. The zero level is the free-surface.

Figure 5 shows the ratios of average slip and maximum slip for the rectangular asperity modelsof surface earthquakes. The gray arrow represents the band in which the characterized kinematic
slip model proposed by Somerville et al. [1] is equivalent to the dynamic model. For this kind ofearthquakes the ratios decrease when compared with the ratios of circular asperity models. Theband of stress drop ratio that fits the kinematic scaling model is now -0.15 < ∆σb/∆σa < 0.05.
This decrease of ratio is expected because the average slip (D) increases due to the free-surface
effect. It is interesting to observe that the ratios for models with 3 and 4 asperities are almost thesame. It is because the tendency of saturation of not only the average displacement when L
increases, but the average displacement of the asperity tends to saturate as well. Therefore theratio of average slip between the asperity and total rupture area also saturates. The results
suggest that fault with more than two asperities remain the same ratio for surface earthquakes
with L>4Wmax

Figure 5. Average slip ratio (Dasp/D) and maximum slip ratio (Dmax/D) plotted with the stress dropratio (∆σb /∆σa) for the dynamic solution of the rectangular asperity models of surface
earthquakes in which the number of asperities increases with L, assuming single asperity for
L=W=20km, double for L=40km, triple for L=100km, and quadruple for L>=200km. The arrowspecifies the band of the stress drop ratios in which fit the characterized slip model proposed bySomerville et al. [1].

CONCLUSIONSWe proposed scaling ratios calculated by dynamic models for single and multiple asperity
models for sub-surface earthquakes (circular faults) and surface earthquakes (rectangular faults
that reach the free surface) with different conditions of stress drop distribution along the fault.
The size of the combined asperity was fixed as 22% of the total rupture area, following the studyof Somerville et al. [1]. From the viewpoint of dynamic faulting, our finding indicates that thecharacterized source model of Somerville et al. [1] is valid when the ratios of stress drop
between the background and asperity is between –0.05 to 0.1 for sub-surface earthquakes andbetween –0.15 to 0.05 for surface earthquakes. The characterized ratios for slip and stress drop
make feasible the definition of asperity-source models for practical application of strong groundmotion prediction, accompanying with the source scaling relation of sub-surface to surface earthquakes.

Acknowledgments. This paper was supported by the Research Grant awarded by the Japan
Society for the Promotion of Science (JSPS) under the “FY2002 JSPS Postdoctoral Fellowshipfor Foreign Researchers” from the Ministry of Education, Science, Sports and Culture of Japan.

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