Parametric study of correlation of mainshock-aftershock ground motions based on Copula theory

Abstract

This study investigates the impact of aftershocks on hazard assessment and disaster prevention by examining three main characteristics of strong ground motions: amplitude, spectrum, and duration. A total of 6414 accelerograms were compiled from 26 selected mainshock-aftershock events in the Yalong River Basin, China, Japan, and Turkey. The aim is to investigate the correlation between mainshocks and aftershocks using Copula theory and seven representative intensity measures: peak ground acceleration (PGA), cumulative absolute velocity (CAV), peak ground velocity (PGV), Arias intensity, significant duration, mean frequency and predominant frequency of Fourier amplitude spectrum. The findings reveal a moderate to strong non-linear correlation among the seven intensity measures of mainshocks and aftershocks. This non-linear correlation can be effectively captured using Gumbel, Gaussian, and t-Copula functions. Under the conditions of the optimal Copula joint distribution model among the given intensity measures and the mainshock intensity measures, the Copula conditional prediction model for aftershocks accurately reflects the values of aftershock intensity measures. This approach demonstrates the effectiveness of Copula theory in studying the correlation between mainshock and aftershock intensity measures. It offers a novel method for determining aftershock intensity measures and investigating correlations among multivariate random variables.