- Introduction
- Finite Fault Inversion for Slip Distribution
- Strong Motion Simulation
- Site Corrections
- Generation of a ShakeMap
- Acknowledgments
- References

This project focused on the development of methodology for the near-real-time estimation of earthquake strong ground motion with the objective of providing this information on a regional (statewide) scale. A critical objective of our development was to provide seamless implementation and uniform performance in varied network coverage. To accomplish this goal we: 1) refined a finite fault inverse method to determine fault slip using regional distance stations; 2) developed a strong motion simulation procedure that uses finite source information as input; 3) investigated the incorporation of site type correction factors, 4) and investigated alternative methods to improve the simulation of high frequency strong ground motions. We have successfully completed these tasks and have developed software that calculates model-based estimates of strong shaking that include the focussing effects due to source directivity. The method we have developed estimates PGA, PGV and spectral acceleration at periods of 0.3, 1.0 and 3.0 seconds. These model predictions may be used to interpolate actual strong motion observations (when available) in the same manner as the southern California TriNet ShakeMap (Wald et al. 1999), and we provide examples of data/model shakemaps for the Landers and Northridge earthquakes. These examples show that it is possible to calculate robust shakemaps even in extremely sparse coverage.

We extensively tested the algorithms with data recorded for the 1992 Landers and 1994 Northridge earthquakes, and compared our regionally derived fault slip maps with those obtained using local strong motion recordings. Favorable comparisons indicate that our methodology is capable of uniquely determining the causative fault plane of the earthquake, the slip dimension (both along strike and down dip), the earthquake rupture velocity, and a reasonable characterization of the gross slip distribution, suggesting that the derived source parameters may be used to simulate near- source strong ground motions. The code will be integrated into the Rapid Earthquake Data Integration (REDI) system (Gee et al., 1996) operated by the Berkeley Seismological Laboratory. Our preliminary testing indicates that the essential source information may be obtained within 4 to 20 minutes following the determination of a seismic moment tensor solution depending upon the level of approximation required.

The focus of this task was to use the regionally derived fault slip maps to simulate the distribution of near-source strong ground motion, and to compare the model predictions with observations to calibrate the methodology. Additionally, we tested method of hybrid Green's function (Kamae et al., 1998), the composite source (Zeng, 1994) method and empirical attenuation relationship (Somerville et al., 1997) to attempt to better simulate higher frequency ground motions. Our basic method of ground motion simulation is one we developed in which fault slip is deterministically integrated using appropriate local Green's functions. We found that this deterministic approach performed reasonably well in the comparisons of PGV, however the Sa comparisons had mixed results. The PGA, PGV and Sa maps were all found to be successful in outlining the area of observed large ground motions, however there were varying degrees of misfit of the location of predicted and observed maximal values. The methods of Kamae et al. (1998) and Zeng (1994) improved the results somewhat but not to a degree that offsets their higher computational expense. PGA and Sa (0.3, 1.0 and 3.0 seconds) were well modeled using the approach of Somerville et al. (1997), which utilized the regionally derived finite source information as input. The empirical approach is also extremely fast and requires information available after the initial fault plane and rupture velocity inversion, which is also relatively fast. The best shakemaps for the two study events were obtained by taking the larger of the two values from the deterministic and the empirical maps. We call this map our 'conservative shakemap'. The empirical component of the conservative shakemap is found to explain the mean attenuation of the observed strong motions very well and the deterministic component provides a better estimate of the large near-fault ground motions.

We explored ways to improve the predicted strong motion parameters by applying site corrections to the synthetic ground motions. Implementation of the empirical site corrections applied to Quaternary, Tertiary and Mesozoic sites (Borcherdt, 1994; Park and Elrick, 1998; Wald, 1999) improved the agreement with the observations but not enough to offset a systematic under prediction at LA basin sites. A second method used two 1D velocity models to characterize rock and soil sites. The application of site specific Green's functions provided a noticeable improvement in the predicted shakemap but stations located within the LA Basin remain underpredicted.

We have developed a multi-staged algorithm to generate a shakemap. First, line source or course planar inversions are performed to determine the rupture velocity, causative fault plane and slip dimension of an earthquake. This information may then be used to generate a shakemap using an attenuation relationship (e.g. Somerville et al. 1997) sensitive to directivity and site class. If local strong motion data is available it may be integrated with the empirical values to develop a data/model shakemap. With relatively dense coverage the map would be data driven with model predictions contributing only in the regions where there are gaps in coverage. Following the determination of the causative fault plane and rupture velocity, processing may be continued to determine a higher resolution picture of the distribution of fault slip. The higher resolution slip map is then used to simulate near-source synthetic time histories from which values of PGA, PGV and spectral acceleration may be measured. We then combine the larger of the simulated and the empirical ground motions to produce a 'conservative shakemap'. As in the first stage of processing available data may be integrated into the shakemap, where model predictions are used to interpolate only in areas where there are no observations (Figure 14.1). A common multi-parametric attenuation relationship provides seamless transition from one level of approximation to another as more data and model information becomes available.

Many thanks to Arben Pitarka for performing strong motion calculations at our request and to Yuehua Zeng for providing his programs to us.

Borcherdt, R. D., Estimates of site-dependent response spectra for design (methodology and justification), *Earthquake Spectra, * *10, * 617-654, 1994.

Zeng, Yuehua, A composite source model for computing realistic synthetic strong ground motions, *Geophys.Res.Lett.,* *21*, 725-728, 1994.

Gee, L. S., Real-time seismology at UC Berkeley; the Rapid Earthquake Data Integration Project, *Bull. Seism. Soc. Am.,* *86,* 1037-1106, 1996.

Somerville, P. G., N. Smith, R. Graves and N. Abrahamson, Modification of empirical strong ground motion attenuation relations to include the amplitude and duration effects of rupture directivity, *Seism.Res.Lett.,* *68,* 199-222, 1997.

Kamae K., Irikura K. and A. Pitarka, A technique for simulating strong ground motion using hybrid Green's function, *Bull. Seism. Soc. Am.,* *88,* 357-367,1998.

Park, S. and S. Elrick, Predictions of shear-wave velocities in Southern California using surface geology, *Bull. Seism. Soc. Am.,* *88,* 677-685, 1998.

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*, 537-556, 1999.

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