abstract

A simple model for estimating Fourier amplitude spectra (FS) is calibrated using the horizontal components of 70 strong-motion records from California, chosen so that the results are not biased by the effects of one earthquake nor by the effects of a single site. An exponential dependence of FS on magnitude M, a geometric dependence of FS on source-to-site distance R, and a soil amplification term Ys are included in the model, using the form

 
FS(T)=exp(b1+b2M+b4Ys)Rb3

where the coefficients b1, b2, b3, and b4 are determined for each period T of interest. The trends indicate that: (1) larger magnitudes imply relatively more energy content at long periods; (2) source-to-site distance has an important effect on spectral shape, because high frequency spectral amplitudes attenuate faster with distance than do long-period spectral amplitudes; and (3) alluviumsite conditions amplify long-period (>1 sec) amplitudes over those recorded at rock sites by a factor of about 1.6, but decrease short-period (≃0.1 sec) amplitudes. Values of FS calculated from strong-motion records are lognormally distributed about the values predicted from this model. The accuracy of the model, as measured by the dispersion in observed values, is as good as the accuracy implied by the model proposed by Trifunac (1976). Moreover, the model used here reflects a realistic change in frequency content with distance, which the Trifunac model does not; hence, extrapolation of this model to estimate spectral amplitudes for large magnitudes at close distances is more reliable than is extrapolation of the Trifunac model. The model estimates approximately the horizontal spectral amplitudes of the records obtained at Pacoima Dam in 1971 and El Centro in 1940, although these records were not used in the calibration procedure and hence the estimation of their spectral amplitudes constitutes an independent prediction. Investigation of possible nonlinear dependence of In FS on M, using a form similar to that proposed by Trifunac

 
FS(T)=exp(b1+b2M+b5M2+b4Ys)Rb3

reveals that the M2 term does not appreciably improve the accuracy of the model, nor does it greatly change values of predicted spectra for the magnitude range of available data (5 to 7.7). Significance of the M2 term depends solely on records obtained during the 1952 Kern County earthquake; thus, use of models of this type, calibrated with available California strong-motion records, implies the assumption that the Kern County records are typical of a magnitude 7.7 shock.

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