Abstract

Standard single-component spectral ratios used to estimate localized site effects may be generalized by using a 3×3 matrix transfer function between the three-component motion observed at a reference (rock) site and that at a nearby soil site. This complex matrix (G matrix) represents the complete three-dimensional site-response within the linear regime. No prior knowledge of the geology at the soil site is required, and G may be computed directly from the spectral responses of earthquakes recorded at both sites. Earthquakes from different hypocentral locations may be used but must be selected so that the body-wave incidence at both stations is nearly vertical and must be time-windowed to avoid surface waves. G is calculated using a stochastic inverse of the observed response spectra and corresponding noise covariance for each response. This method of analysis depends on the availability of a good quality reference (rock) site, as do standard spectral ratio techniques that compare rock and soil site records. We have applied this method to determine site effects to data recorded by strong ground motion seismographs near Wellington, North Island, New Zealand. Magnitudes of the diagonal elements of G are similar to standard single-component spectral ratios, and large values of the off-diagonal matrix elements are seen at some locations. At these locations the maximum response is better estimated from the principal values of the transfer function matrix. The orientation at which the maximum amplification (up to 14 in one case) occurs varies widely according to location.

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