Following the 18 October 1989 Loma Prieta earthquake, triggered seismographs were deployed in and around the Marina District to investigate site amplification. In the 3 weeks after the mainshock, 16 aftershocks were recorded by two or more of these stations. Two additional stations, deployed in March 1990, recorded three earthquakes that occurred in Contra Costa County. By recasting the method of spectral ratios into a generalized inverse problem, we combine the shear-wave spectra from these 19 aftershocks to estimate the relative site amplification as a function of frequency. All five stations located in the Marina District are amplified by factors of 6 to 10 at 1 Hz and 2 to 4 at 3 Hz, relative to a station located on Franciscan sandstone at Fort Mason, irrespective of whether they are sited on artificial fill or beach sand. Two stations located on dune sand just outside the Marina District are amplified by factors of 2 to 4 for frequencies above 1 Hz. Four stations located on Franciscan sandstone in Pacific Heights, Nob Hill, Rincon Hill, and Diamond Heights show little relative amplification.
Conditional estimates of the mainshock spectra can be determined at stations that only recorded aftershocks, if they can be linked to stations that recorded the mainshock. These estimates are predicated on the assumption that the ground behaved linearly in the mainshock, an assumption that is clearly violated for those sites where there was ground failure. Using this method of extrapolation for a site in the Marina District that showed no evidence of ground failure yields mainshock spectra that are slightly greater than the mainshock spectra from the Outer Harbor Wharf in Oakland and near the Pacific Park Plaza in Emeryville and that significantly exceed the mainshock spectra from all the free-field accelerograms located in San Francisco.