Aftershocks of the 1989 Loma Prieta, California, earthquake are used to estimate site response in a 12-km2 area centered on downtown Santa Cruz. A total of 258 S-wave records from 36 aftershocks recorded at 33 sites are used in a linear inversion for site-response spectra. The inversion scheme takes advantage of the redundancy of the large data set for which several aftershocks are recorded at each site. The scheme decomposes the observed spectra into source, path, and site terms. The path term is specified before the inversion. The undetermined degree of freedom in the decomposition into source and site spectra is removed by specifying the site-response factor to be approximately 1.0 at two sites on crystalline bedrock. The S-wave site responses correlate well with the surficial geology and observed damage pattern of the mainshock. The site-response spectra of the floodplain sites, which include the heavily damaged downtown area, exhibit significant peaks. The largest peaks are between 1 and 4 Hz. Five floodplain sites have amplification factors of 10 or greater. Most of the floodplain site-response spectra also have a smaller secondary peak between 6 and 8 Hz. Residential areas built on marine terraces above the floodplain experienced much less severe damage. Site-response spectra for these areas also have their largest peaks between 1 and 4 Hz, but the amplification is generally below 6. Several of these sites also have a secondary peak between 6 and 8 Hz. The response peaks seen at nearly all sites between 1 and 4 Hz are probably caused by the natural resonance of the sedimentary rock column. The higher amplifications at floodplain sites may be caused by surface waves generated at the basin margins. The secondary peak between 6 and 8 Hz at many sites may be a harmonic of the 1- to 4-Hz peaks.
We used waveforms from a seven-station approximately linear array located on the floodplain to calculate the apparent velocity and azimuth of propagation of coherent arrivals within moving windows of the S-wave codas. The initial windows give results that are consistent with direct S-wave arrivals. The apparent velocities are high (greater than 4.0 km/sec), and azimuths are from the source. Waves arriving later than 2 sec after the direct S waves have apparent velocities of less than 1 km/sec, indicating that they are surface waves, and arrive from divergent azimuths. This analysis indicates that after the direct S-wave arrival, long-duration shaking comes from surface waves that are generated at the basin margin and reverberate in the floodplain sediments.