Dynamic Rupture of Earthquake

Two results of simulations will be shown as examples of dynamic rupture simulation: The 2000 western Tottori, Japan (Mw 6.6) and the 1992 Landers, California (Mw 7.3) earthquakes. The western Tottori earthquake is a recent earthquake occurring inside a densely distributed seismographic network [Fukuyama et al. (2003a)]. There are several fault models for this earthquakes [Iwata and Sekiguchi (2001); Mikumo et al. (2003); Semmane et al. (2005)]. The Landers is a famous earthquake which occurred near the

San Andreas fault system in southern California for which many earthquake source analyses have been conducted [Cohee and Beroza (1994); Wald and Heaton (1994); Cotton and Campillo (1995); Olsen et al. (1997); Aochi and Fukuyama (2002)].

For the western Tottori earthquake, we have a very precise image of the aftershock distribution [Fukuyama et al. (2003a)] using the double difference method [Waldhauser and Ellsworth (2000)]. Based on this distribution, a fault model for the simulation was constructed, which consists of 4 fault planes [Fukuyama et al. (2003a)] (Fig. 2). Although, unfortunately, no in-situ stress measurements were conducted near the source region because of an unclear fault location on the surface, a stress tensor inversion of aftershock moment tensors was conducted [Fukuyama et al. (2003a); Kubo and Fukuyama (2004)] to obtain a relative stress field. By combining the relative stress information with the assumed absolute stress values, taking into account the lithostatic stress at seismogenic depth, a stress model for the simulation was constructed. The slip weakening distance for this earthquake has been estimated from the source time functions estimated by waveform inversions [Mikumo et al. (2003)].

Numerical simulations were conducted based on the above information of fault geometry, stress field and constitutive relation. The computational results are shown in Fig. 7. In this plot, three simulation results with flfiC

Slip [mj

Slip [mj

tfifi cfia ijvjva

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Fig. 7 Result of dynamic rupture simulation of the 2000 western Tottori earthquake. Snapshots of stress (left column), slip velocity (center column) and slip (right column) are shown at a constant time step of 0.75 s. Scale of each column is shown as a color bar. Maximum principal stress directions of initial stress are (a) N90°E, (b) N105°E and (c) N120°E, respectively [Modified from Fukuyama (2003b)].

different maximum principal stress directions are shown. Other conditions such as slip weakening distances and magnitudes of principal stresses were kept the same. One can see that the rupture propagation is controlled by the stress field around the fault. This is convincing because the stress field applied to the fault controls the initial shear and normal stress on the fault. Shear stress corresponds to the coseismic slip (Dmax in Fig. 5) allowed and normal stress applied to the fault controls the breakdown stress drop (Arb in Fig. 5), which is also dependent on the fault geometry. Thus the fault geometry plays a very important role for the propagation of dynamic rupture on the fault.

In the simulation, although we did not assume any spatial heterogeneities on the fault, one can observe a non-uniform rupture along the fault, especially, whether the rupture extends to the northern small segment (#4 in Fig. 2), which is shifted from the main fault, depends on the stress field around the fault. Since all 4 fault segments were ruptured in the kinematic source model, the principal maximum stress direction of N105°E is the most probable, which is also consistent with the result of stress tensor inversion [Fukuyama et al. (2003a); Kubo and Fukuyama (2004)] (N107°E). The above simulations indicate that once the frictional property of the fault, stress field around the fault and the geometry of the fault are all obtained, we are able to estimate a scenario for earthquake rupture [Fukuyama (2003a, b)].

For the Landers earthquake, surface faults are very accurately traced [Hart et al. (1993)] (Fig. 1). The coseismic slip distribution was well estimated using near-field and teleseismic waveforms as well as using GPS data [Wald and Heaton (1994)]. Thus the fault model is constructed based on the surface fault traces. Since there is no information on the friction law, typical relations obtained in the laboratory were applied. For the stress field, principal stress directions were searched by trial and error.

Figure 8 shows the result of simulation of the Landers earthquake [Aochi (1999); Aochi and Fukuyama (2002)]. A uniform stress field cannot make the rupture propagate along several fault segments as obtained by the kinematic waveform inversion. In order to propagate through the Kickapoo fault (Fig. 1), the stress field should be different in the northern and southern regions. In this computation the most optimum solution was that with the stress rotated clockwise [Aochi and Fukuyama (2002)]. This is consistent with the fact that the northern and southern part of the faults belong to the different geological block, in which the stress field might be different [Unruh et al. (1994)].

total slip slip velocity total slip slip velocity

Slip Velocity

Fig. 8 Result of dynamic rupture simulation of the 1992 Landers earthquake. Snapshots of slip and slip velocity are shown in left and right columns, respectively. nE, K, CR, HV, nJV, sJV stand for northern Emerson, Kickapoo, Camp Rock, Homestead Valley, northern and southern Johnson Valley faults, respectively [after Aochi (1999)].

Fig. 8 Result of dynamic rupture simulation of the 1992 Landers earthquake. Snapshots of slip and slip velocity are shown in left and right columns, respectively. nE, K, CR, HV, nJV, sJV stand for northern Emerson, Kickapoo, Camp Rock, Homestead Valley, northern and southern Johnson Valley faults, respectively [after Aochi (1999)].

In both cases, a complete set of initial and boundary conditions could not be used to compute dynamic rupture propagation. Some of the parameters had to be assumed. However, this kind of situation is very common and how to assume the missing information will be important if this is applied to the prediction of future earthquake dynamic rupture.

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