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By using small-to-moderate earthquakes located within ∼200 km of San Francisco, we characterize the scaling of the ground motions for frequencies ranging between 0.25 and 20 Hz, obtaining results for geometric spreading, Q ( f ), and site parameters using the methods of Mayeda et al. (2005) and Malagnini et al. (2004). The results of the analysis show that, throughout the Bay Area, the average regional attenuation of the ground motion can be modeled with a bilinear geometric spreading function with a 30-km crossover distance, coupled to an anelastic function exp(− ϖfr / capital greek betaQ ( f ), where: Q ( f ) = 180 f 0.42 . A body-wave geometric spreading, g ( r ) = r −1.0 , is used at short hypocentral distances ( r g ( r ) = r −0.6 fits the attenuation of the spectral amplitudes at hypocentral distances beyond the crossover. The frequency-dependent site effects at twelve of the Berkeley Digital Seismic Network stations were evaluated in an absolute sense using coda-derived source spectra. Our results show the following. (1) The absolute site response for frequencies ranging between 0.3 Hz and 2.0 Hz correlate with independent estimates of the local magnitude residuals ( δM L ) for each of the stations. (2) Moment magnitudes ( M w ) derived from our path and site-corrected spectra are in excellent agreement with those independently derived using full-waveform modeling as well as coda-derived source spectra. (3) We use our weak-motion-based relationships to predict motions regionwide for the Loma Prieta earthquake, well above the maximum magnitude spanned by our data set, on a completely different set of stations. Results compare well with measurements taken at specific National Earthquake Hazards Reduction Program site classes. (4) An empirical, magnitude-dependent scaling was necessary for the Brune stress parameter to match the large-magnitude spectral accelerations and peak ground velocities with our weak-motion-based model. Online material: Tables of peak ground acceleration, peak ground velocity, and pseudo-spectral acceleration at 0.3 sec, 1.0 sec, and 3.0 sec.
Malagnini et al. (Fri,) studied this question.