Stochastic simulation of fully nonstationary aftershock ground motions from known preceding main shock

Abstract

Aftershocks can cause significant additional damage to a structure that already got damaged during the preceding main shock. Past studies showed that the ground motion characteristics of an aftershock, in statistical sense, are related to those of the preceding main shock. Hence, statistical assessment of additional damage during future aftershocks given a main shock requires conditional simulation of aftershock ground motions. In the present study, a methodology is proposed to obtain an ensemble of fully nonstationary aftershock ground motions at a site of interest from the known seismic scenarios of both the main shock and the anticipated aftershock. The proposed method is based on the Priestley process assumption in order to characterize both amplitude and frequency nonstationarities via some frequency-dependent deterministic amplitude modulations. The amplitude modulations of a probable aftershock process belonging to the anticipated aftershock seismic scenario are considered to be statistically dependent on those of the recorded main shock process. Since the amplitude modulation is obtained from the frequency-dependent energy arrival curves, a conditional scaling model for the energy arrival of aftershocks is newly proposed. An improved methodology is also proposed in order to extract the frequency-dependent amplitude modulations from the energy arrival curves, obtained either via the scaling model or from a recorded motion, as well as to generate process-specific random samples from the knowledge of such modulations. It is found that the simulated ground motion ensemble shows better agreement with the recorded aftershock process, especially for larger aftershocks, when the aftershock's dependency on its main shock (via the conditional scaling model) is considered than what it shows when the dependency is not considered.