The scaling of seismic sources according to Brune (1970, 1971), with a stress drop of 100 bars, allows accurate prediction of average Fourier spectra of seismic shear waves in the far-field for the frequency band 1 to 10 Hz. Random vibration theory under the assumption of stationary response accurately predicts average linear-elastic response spectrum amplitudes in this same frequency band. These conclusions are reached through comparison of theoretical estimates with strong motion observations during a wide range of California earthquakes (local magnitudes 4.0 to 7.2, distances 9 to 130 km). Thus, these models are an accurate, physically based method of estimating high-frequency strong ground motion for a range of earthquake magnitudes and distances, and offer the advantage (over purely empirical methods) of a physical basis for extrapolating to predict ground motions for magnitudes and distances which are poorly documented with data.

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