Aftershock recordings from 10 digital seismographs deployed along the axis of the San Francisco Peninsula from the epicenter of the 18 October 1989 Loma Prieta earthquake to San Francisco provide the data for a joint inversion for source, wave propagation, and site effects. The inversion procedure is a least-squares method using the singular-value decomposition algorithm and is done in two parts: The first solves only for the source and attenuation terms for all events, and the second projects the residuals from the first inversion onto the site terms. The coefficient of geometrical spreading is solved for as part of the model of attenuation. Residuals, plotted versus distance and frequency, provide a check on the appropriateness of the attenuation model.
The earthquakes are all located near the San Andreas fault, mostly in the aftershock zone of the Loma Prieta mainshock, but some area near Daly City on the Peninsula. The data set, provided by GEOS recorders, consists of 148 digital seismograms for 33 events from 10 sites that form a linear profile from the epicentral region to the city of San Francisco, a distance of approximately 100 km. Strong-motion accelerograms are also available for the larger events. Body-wave spectra are fit surprisingly well by our model, especially at distances beyond about 20 km where differences due to radiation pattern effects and changes in angle of incidence become less important. Results from the inversion show that estimates of moment are only 1% higher for the P waves compared to the S waves. Apparently, there are no major biases in the estimates, as each is determined independently of the other. P-wave corner frequencies are 1.5 times higher than S-wave corner frequencies on average. Stress drops with an average of 176 bars for events that range in magnitude from 1.7 to 4.2 are higher than those found in previous studies where site and path were not explicitly taken into account. The exponents of geometrical spreading are very close to one (1.019 for P waves and 1.017 for S waves) for this data set, which extends to about 100 km. The whole path Q (assumed to be frequency independent) was about 800 for both P and S waves (specifically, 790 for P waves and 830 for S waves). The average P-wave attenuation at all sites is quantified by a t* of 0.020 sec, which compares to 0.03 sec for S waves. t* determined for each site range from a low of 0.008 sec at San Bruno Mountain, a hard-rock site, to a high of 0.065 sec at Corralitos in the epicentral area. Residuals of the model fits, which are distance dependent, show larger amplitudes near the epicenter, but fall-off with a minimum at about 30 km where amplitudes are about 30 to 60% lower than average. At distances farther than 30 km, amplitudes rise out to the limit of the data at about 105 km where amplitudes are about average at frequencies less than 10 Hz, but are slightly above average for higher frequencies. The location of this low in amplitude can be explained as the boundary between the amplitude decay of direct arrivals and the emergence of wide-angle reflections from the lower crust and Moho, which increase in amplitude beyond 30 km. These amplitudes correlate with damage patterns from the mainshock, as less damage was observed along the Peninsula but appeared to increase towards San Francisco, even when damage in the Marina and China Basin districts of San Francisco are not included in the damage census.