State-of-the-Art for Assessing Earthquake Hazards in the United States. Report 23. Empirical Study of Attenuation and Spectral Scaling Relations of Response Spectra for Western United States Earthquakes.

This report is concerned with an empirical study so the response spectra of western United States earthquakes, principally in California. The basic data are logarithms of response spectral velocity as a function of period. They are the arithmetic average of the logarithm of the response spectral values for the two horizontal components of motion for 5 percent damping. The anelastic attention id determined empirically from the response spectra. It satisfies the relation Qf 150 times f to the 0.6 power, where Qf is the specific quality factor at a frequency of f. The coefficient of anelastic attenuation kf is related to Qf by kf pi times fv Qf, where V is the velocity of the wave. Observed response spectra are extrapolated to a reference distance of 50 km for earthquakes of different magnitude. From these spectra a scaling relation is determined, which is expressed in the form of a set of equations. These equations enable one to predict response spectra for any body-wave magnitude for distances greater than 50 km. The predicted values agree well with observed ones at distances greater than 50 km, but show more variations at distance less than 50 km.