Finite-Source Modeling of the 22 December 2003 San Simeon
Earthquake

Douglas Dreger

Introduction

The $M_{w}$ 6.5 San Simeon earthquake, which occurred in the central California Coast Ranges on December 22, 2003 was analyzed with our automated finite-source procedure the day of the earthquake. The derived source information was used to incorporate rupture finiteness into the ShakeMap greatly improving its representation of near-fault ground motions as well as those in the heavily struck community of Paso Robles, about 35 km to the SE of the earthquake.

In this report the initial line-source modeling, and its application toward improving published ShakeMaps is described. In addition, the current preferred model that combineds GPS and seismic waveform data is presented, and the implications of the model in terms of central Coast Range ground motion hazard is discussed.

Line Source Modeling and ShakeMap

The seismic moment tensor was obtained automatically and the reviewed results were emailed within an hour after the event. The moment tensor result upward revised the magnitude from $M_{L}$6.4 to $M_{w}$6.5. The ShakeMap was updated with the new value automatically.

Subsequent analysis focussed on inverting broadband waveform data from the BDSN to test the two moment tensor nodal planes to determine the orientation of the causative fault. The method employed is based on Hartzell and Heaton's (1983) inverse scheme for kinematic rupture parameters such as slip distribution, slip rise time and rupture velocity. Dreger and Kaverina (2000) showed that it was possible to use a similar approach to determine key finite-source parameters quickly after an earthquake using the near-realtime broadband data stream. The Dreger and Kaverina (2000) method was developed by modeling the 1992 $M_{w}$7.3 Landers and $M_{w}$6.7 Northridge earthquakes. Although the system was not yet automated its application at the time of the Hector Mine earthquake, $M_{w}$ 7.1, showed that the approach was feasible in the short time frame required for emergency response applications. The application of this method in the 2003 San Simeon earthquake is the first "live fire" test of the system, and the first time that near-realtime finite-source information was used to update ShakeMap (see Hardebeck et al., 2004).

The first stage of the Dreger and Kaverina (2000) method is to test line-source models with the orientations of the two moment tensor nodal planes. In this analysis the east dipping plane (strike=290, dip=56, rake=74) was found to fit the broadband data slightly better, though it could not be shown to be a statistically significant improvement in fit. Aftershocks, however, confirmed that the east dipping nodal plane was the causative structure. The line-source inversion results for both planes indicated that the main slip was located substantially SE of the hypocenter, extending as much as 20 km to the SE. Figure 13.1 shows the analyst reviewed line-source model for the east-dipping mechanism.

Figure 13.1: Analyst reviewed line-source model of the 2003 San Simeon earthquake
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The line-source information was used to incorporate source finiteness into the ShakeMap (Figure 13.2). In this calculation the distance used to model the ground motion attenuation, in areas where actual ground motion data was not available, was the closest distance to the extended fault rupture rather than to the epicenter as is typically done. The effect of this modification is an extension of the near-fault area of strongest shaking to the SE, elevating estimated ground motions in the Paso Robles region to instrumental intensity VII-VIII. This intensity is more consistent with the observed damage in the region. (e.g. Hardebeck et al., 2004).

In Figure 13.2 it is shown how the ShakeMaps vary as additional information is added. Figure 13.2a shows the original ShakeMap. This map has only a few contributing stations, which are located far from the event and the afflicted region. The distribution of instrumental intensity therefore tends to be centered on the epicenter with radial decay. Estimated intensity in the vicinity of Paso Robles is only V-VI. Figure 13.2b shows the map after adjustment by adding the finite-source information. Several days after the event as additional near-fault, non-realtime, ground motion recordings became available the ShakeMap was updated. Figure 13.2c shows the map obtained with the additional ground motion information. Note how the maps in Figures 13.2b and 13.2c agree. The former has no near-fault data, but does have the the finite-rupture information obtained by inverting regional data for the rupture process, and the latter includes only the additonal near-fault recordings. This comparison demonstrates the utility of incorporating either rupture finiteness or even directivity information in ShakeMaps to improve performance in regions where there may be few strong motion records or cases in which the near-fault data may not be immediately available. Finally, Figure 13.2d shows the final ShakeMap that includes all available near-fault observations as well as the finite extent of the rupture.

Figure 13.2: Evolution of instrumental intensity ShakeMaps (Wald et al., 1999) for the 2003 San Simeon earthquake. The star shows the epicenter, triangles the stations used, and thick line the finite extent of rupture. A), upper left, initial map based on $M_{w}$ and realtime data. B), upper right, modification accounting for rupture finiteness. C), lower left, map with all available data including non reltime data. D), lower right, preferred map that combines available data and rupture finiteness.
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Combined Slip Model and Ground Motion Simulation

Three-component displacement data at 8 regional and local stations, and three-component velocity records at the Parkfield site (PKD) were combined with 36 GPS permanent ground deformation vectors to invert for the detailed kinematic rupture process. This data is described in detail in Chapter III. Figure 14.2 shows the fit to the seismic waveform data, and Figure 14.3 shows the fit to the GPS vectors. The fit to both data sets is very good. Figure 13.3. shows the slip distribution that was obtained.

The slip in the San Simeon earthquake is unusual in three respects. First, the distribution is elongated along strike, extending as much as 20 to 25 km SE of the hypocenter. This is in contrast to the primarily updip rupture of other reverse mechanism events such as the 1971 San Fernando (Heaton, 1982) and 1994 Northridge ( Dreger, 1997) earthquakes. The San Simeon earthquake is similar to the much larger 1999 $M_{w}$ 7.6 Chi-Chi, Taiwan earthquake in terms of the extensive along strike rupture. Secondly for a $M_{w}$ 6.5 event the peak and average slip is high. Although, the peak slip is dependent upon the weight of the smoothing that is applied, all of the models show that over much of the fault the slip is between 1-3 m. Empirical relationships for average slip as a function of moment indicate that on average $M_{w}$ 6.5 events have about 70 cm of average slip (e.g. Somerville et al., 1999). Third the event also has a relatively long slip rise time function that is variable over the rupture surface with an average of about 3 seconds. On average $M_{w}$ 6.5 events have an average rise time of about 0.8 seconds (Somerville et al., 1999).

Figure 13.3: Fault normal projection of slip distribution. The black circle marks position of the hypocenter. The Fault orientation and slip vector are the same as obtained from the moment tensor analysis and used in the line-source calculation.
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Central Coast Ground Motion
Hazard Implications

From the derived kinematic source description it is possible to spatially and temporally integrate the slip using near-fault Green's functions to predict the distribution of near-fault strong shaking (Dreger and Kaverina, 2000). Figure 13.4a shows the results of such a calculation. The plot clearly shows the southeastward extension of ground motion contours due to the source finiteness and directivity. The two lobes of elevated ground velocity extending due east and due south of the earthquake are the directivity-amplified SH lobes of the reverse mechanism.

Whether the observed ground motions from the 2003 $M_{w}$ 6.5 event are representative of all central Coast Range magnitude 6.5 earthquakes is an important question. There are strike-slip faults in the region, and the last large nearby earthquake, the 1952 Bryson event, was predominently strike-slip (Dehlinger and Bolt, 1987). In order to address this question the kinematic source description that was obtained for the 2003 San Simeon earthquake was used to simulate near-fault ground motions for a hypothetical vertically dipping right-lateral strike-slip fault. The results of the calculation shows that for the vertical strike-slip fault the effect of directivity is greatly enhanced. In some areas the peak ground velocity can be three times greater, and the area receiving greater than 10 cm/s is four times larger than the reverse slip case. Fortunately in the 2003 San Simeon earthquake the slip direction was perpendicular to the rupture direction producing a relatively mild directivity effect. These calculations show however that while the recorded ground motions from the 2003 San Simeon earthquake are useful for chacterizing earthquake hazard in the central Coast Ranges similar sized strike-slip earthquakes could be significantly more damaging.

Figure 13.4: Simulated peak ground velocity assuming the obtained kinematic source description. Contours are in intervals of 5 cm/s beginning with 5 cm/s. The surface projection of slip is shown. A) Simulated PGV for the actual reverse slip mechanism. B) Simulated PGV for a vertical right-lateral strike-slip mechanism.
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References

Dehlinger, P., and B. Bolt, Earthquakes and associated tectonics in a part of coastal central California, Bull. Seis. Soc. Am., 77, 2056-2073, 1 987.

Dreger, D. S. The large aftershocks of the Northridge earthquake and their relationship to mainshock slip and fault-zone complexity, Bull. Seism. Soc. Am., 87, 1259-1266, 1997.

Dreger, D., and A. Kaverina , Seismic remote sensing for the earthquake source process and near-source strong shaking: A case study of the October 16, 1999 hector mine earthquake, Geophys. Res. Lett., 27, 1941-1944, 2000.

Hardebeck, J.L., J. Boatwright, D. Dreger, R. Goel, V. Graizer, K. Hudnut, C. Ji, L. Jones, J. Langbein, J. Lin, E. Roeloffs, R. Simpson, K. Stark, R. Stein, J.C. Tinsley, Preliminary report on the 22 December 2003, M 6.5 San Simeon, California earthquake Seism. Res. Lett., 75, 155-172, 2004.

Hartzell, S. H., and T. H. Heaton, Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake, Bull. Seism. Soc. Am., 73, 1553-1583, 1983.

Heaton, Y. H. The 1971 San Fernando earthquake: a double event?, Bull. Seism. Soc. Am., 72, 2037-2062, 1982.

Somerville, P. G., K. Irikura, R. Graves, S. Sawada, D. Wald, N. Abrahamson, Y. Iwasaki, T. Kagawa, N. Smith, and A. Kowada. Characterizing crustal earthquake slip models for the prediction of strong ground motion, Seism. Res. Lett., 70, 59-80, 1999.

Wald, D. J., V. Quitoriano, T. H. Heaton, H. Kanamori, C. W. Scrivner, and C. B. Worden. TriNet ShakeMaps: Rapid generation of instrumental ground motion and intensity maps for earthquakes in southern California, Earthquake Spectra, 15, 537-555, 1999.

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