An empirical study of earthquake source spectra for California earthquakes

Abstract We generalize source, path, and site effects for California earthquakes as functions of magnitude and distance, based on regression analysis of 1000 Fourier acceleration spectra from 43 California earthquakes in the moment magnitude range from 4.4 to 7.4, recorded at rupture distances from 1 to 200 km. Empirically derived source spectra for California earthquakes are generally inconsistent with the spectral shape implied by a Brune (“omega-squared”) point-source model. This is manifested by magnitude- and frequency-dependence of the Brune model parameters. For example, the Brune stress parameter that best matches the data at high frequencies decreases from a value of about 120 bars at M5.5 to a value near 50 bars at M7.5. At frequencies below 1 Hz, though, source spectra have much lower spectral amplitudes than predicted by the Brune point-source model for these values of stress; this discrepancy grows with increasing magnitude. Finite-fault simulations indicate that this is a consequence of the breakdown of the validity of the point-source approximation for large ruptures. A stochastic finite-fault model, in which the fault is discretized as a number of subfaults, each of which is represented by a Brune omegasquared point source, correctly matches the observed spectral shapes and amplitudes. The spectral decay parameter kappa, representing average near-surface attenuation of high-frequency motion at rock sites, increases with increasing magnitude, from values near 0.035 sec at M5.5 to 0.050 sec at M7.5. Magnitude dependence of kappa may be interpreted as evidence of nonlinearity for typical California sites subjected to strong ground motion. Comparisons of our empirical source spectra for California to corresponding spectra for eastern North America suggest that the spectral amplitudes are similar in the two regions for low-frequency motions (f 2 Hz for M5.5, f 0.5 Hz for M7.5), for equivalent crustal conditions. The eastern events appear to have enhanced high-frequency near-source amplitudes relative to the California events; this is particularly pronounced for large-magnitude earthquakes.