Ground motion attenuation with distance and the variation of excitation with magnitude are parameterized using three-component, 0.25 to 5.0-Hz earthquake ground motions recorded in the distance range of 15-500 km for southern California to define a consistent model that describes both peak ground motion and Fourier spectra observations. The data set consists of 820 three-component TERRAscope recordings from 140 earthquakes, recorded at 17 stations, with moment magnitudes between 3.1 and 6.7. Regression analysis uses a simple model to relate the logarithm of measured ground motion to excitation, site, and propagation effects. The peak motions are Fourier velocity spectra and peak velocities in selected narrow bandpass-filtered frequency ranges. Regression results for Fourier amplitude spectra and peak velocities are used to define a piecewise continuous geometrical spreading function, frequency dependent Q(f), and a distance dependent duration that can be used with random vibration theory (RVT) or stochastic simulations to predict other characteristics of the ground motion.
The duration results indicate that both the variation of the duration data with distance and its scattering decrease with increasing frequency. The ratio of horizontal to vertical component site terms is about √2 for all frequencies. However, this ratio is near unity for rock sites and is larger for soil sites.
Simple modeling indicates that the Fourier velocity spectra are best fit by bilinear geometrical spreading of r−1 for r < 40 km and r−1/2 for r > 40 km. The frequency-dependent quality factor is Q(f) = 180f0.45 for each of the three components and also for the combined three-component data sets. The T5%-75% duration window provides good agreement between observed and RVT predicted peak values.