We have estimated the spatial variation of site response using three- component accelerograms from the Yokohama High-Density Strong Motion network: 150 surface and 9 borehole accelerometers located in a 20 × 30 km2 area. The site response is the average from 28 earthquakes; 16 were recorded at all borehole stations. We inverted data recorded at the boreholes to determine (1) source parameters (seismic moment M0 and corner frequency fc) for each event, (2) Q(f) for the path, and (3) frequency-dependent site factors for the boreholes. The inversion scheme is independent of a reference station, that is, there are no a priori constraints about site response. For events with depths greater than 30 km, we find Q(f) almost independent of frequency, Q(f) = 285f 0.06; for the four shallow events that were analyzed, Q(f) = 70 f 0.28.
Having determined M0, fc, and Q(f) using the borehole data, we computed the site response for each of the 150 surface stations by dividing the observed surface spectrum by the path-modified source spectrum. We then averaged this ratio for all 24 events. To quantify the variability of the site response between sites we introduced a site-response ratio that depends on station separation and frequency. From this we computed cumulative probability functions for different frequencies for two cases: (1) the average Vs30 ratio is most similar for two sites with the same separation distance and (2) the average Vs30 ratio is least similar. When two sites have the most similar Vs30 ratio, these functions indicate that 95% of the time a frequency- dependent site response (f ≤ 1 Hz) can be predicted within a factor of two for a site up to 5 km from a site with a known site response, and 90% of the time the unknown response is within a factor of three for frequencies 1–10 Hz. When two sites have the least similar average Vs30 ratio, the cumulative probability functions have similar shapes for all frequencies above 0.5 Hz; for frequencies up to 10 Hz the site amplification can be predicted within a factor of three for 80% of the station pairs separated by as much as 5 km.