In order to improve computer simulations of earthquakes and computations of ground motions, the primary goals of this study are to: (1) examine the effect of a range of kinematic rupture models and rupture parameters on synthesized seismograms, (2) examine the theoretical relationship between rupture models and synthesized seismograms, and (3) demonstrate that simple kinematic earthquake models, used with empirical Green's functions, can be used to predict very realistic seismograms.
Earthquake models and synthesized seismograms are examined by computing ground motion for the 1971 San Fernando earthquake (ML = 6.4) and for two aftershocks (ML = 3.3 and 3.5). Well-constrained source parameters and Green's functions allow a controlled examination of rupture models and rupture parameters. Seismograms are synthesized for the full wave train on three components and for frequencies of 0.5 to 25.0 Hz and are compared to observed seismograms as a guide to indicate whether the models are realistic. The examination of rupture models and rupture parameters show that: (1) variations in modeled rupture velocity and rise times most greatly affect the waveforms and amplitudes of synthesized waveforms; (2) the shape of the slip function is not critical to match observed seismograms; (3) only a narrow range of rupture parameters results in realistic synthetic seismograms; (4) simple source models are sufficient to provide good matches to observed seismograms; (5) a simple interpolation scheme for empirical Green's functions is sufficient to match observed seismograms; and (6) the best rupture model for simulating earthquakes is a Kostrov slip model with healing that results in a smooth variation of slip amplitudes, and a distribution of rise times that results in a constant stress drop for most of the fault surface; randomly distributed areas of shortened rise times, resulting in higher stress drops, improve synthesis above 10 Hz.
Theoretical and numerical solutions for the representation relation show that: (1) spectral fall-off of the synthesized seismograms is controlled by the phase delays resulting from rupture parameters; (2) moderately complicated source pulse shapes result from simple rupture models, and the high complexity of synthesized seismograms is primarily a result of the empirical Green's functions; (3) high-frequency arrivals are generated by simple fault rupture models that violate accepted hypotheses that require spatial variations in either stress drop, rupture velocity, or slip rate; and (4) only Haskell rupture models are subject to previously published results that the empirical Green's function synthesis method leads to deficiencies of the Fourier amplitude spectra.