Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra

Abstract

Theoretical predictions of seismic motions as a function of sourcestrength are often expressed as frequency-domain scaling models.The observations of interest to strong-motion seismology, however,are usually in the time domain (e.g., various peak motions, includingmagnitude). The method of simulation presented here makes use ofboth domains; its essence is to filter a suite of windowed, stochastictime series so that the amplitude spectra are equal, on the average,to the specified spectra. Because of its success in predicting peakand rms accelerations (Hanks and McGuire, 1981), anomega -squaredspectrum with a high-frequency cutoff (fm), in addition to the usualwhole-path anelastic attenuation, and with a constant stress parameter(Deltasigma) has been used in the applications of the simulationmethod. With these assumptions, the model is particularly simple:the scaling with source size depends on only one parameter-seismicmoment or, equivalently, moment magnitude. Besides peak acceleration,the model gives a good fit to a number of ground motion amplitudemeasures derived from previous analyses of hundreds of recordingsfrom earthquakes in western North America, ranging from a momentmagnitude of 5.0 to 7.7. These measures of ground motion includepeak velocity, Wood-Anderson instrument response, and response spectra.The model also fits peak velocities and peak accelerations for SouthAfrican earthquakes with moment magnitudes of 0.4 to 2.4 (with fm= 400 Hz and Deltasigma = 50 bars, compared to fm = 15 Hz and Deltasigma= 100 bars for the western North America data). Remarkably, the modelseems to fit all essential aspects of high-frequency ground motionsfor earthquakes over a very large magnitude range. Although the simulationmethod is useful for applications requiring one or more time series,a simpler, less costly method based on various formulas from randomvibration theory will often suffice for applications requiring onlypeak motions. Hanks and McGuire (1981) used such an approach in theirprediction of peak acceleration. This paper contains a generalizationof their approach; the formulas used depend on the moments (in thestatistical sense) of the squared amplitude spectra, and thereforecan be applied to any time series having a stochastic character,including ground acceleration, velocity, and the oscillator outputson which response spectra and magnitude are based.