Expected shape of regressions for ground-motion parameters on rock

Probabilistic seismic-hazard assessments use attenuation relations that give some measure of earthquake ground motion as a function of distance, magnitude, and sometimes other parameters. Among the various relations that have been presented, an ambiguity exists with respect to whether the amplitudes of strong motion on rock show a distance-dependent magnitude saturation. Given a high degree of scatter in a limited number of observations, current empirical data cannot resolve this issue. Therefore, a series of synthetic ground-motion simulations have been conducted to elucidate the magnitude dependence of the distance decay for rock sites. Three different techniques are used: one based on empirical Green's functions, one based on theoretical Green's functions with a simple source representation, and one based on theoretical Green's functions with a composite source representation. All three techniques imply that ground motion decays less rapidly with distance for larger magnitude earthquakes, so that there is a distance-dependent magnitude saturation. Intuitively this can be explained as follows: at longer distances the Green's functions are more complex due to various arrivals spread out over a longer duration of time. A larger earthquake, with more subevents spread over a greater time period, will have constructive interference among the various arrivals from each subevent, and the longer durations of the subevent signals at larger distances will cause a proportionately greater increase in the amplitude than what typically occurs at shorter distances. Five different attenuation relations are evaluated on the basis of this prediction, and the implications with respect to probabilistic seismic-hazard assessment are tested in Field and Peterson (2000).