Modeling of phase spectrum to simulate design ground motions

Abstract

In this paper, the concept of group delay time is used to model the phase spectrum on each separated frequency range according to the compact support of Meyer wavelet. The regression equations to predict the mean value and standard deviation of group delay times can be developed on the basis of the recorded earthquake set. Based on the predicted mean value and standard deviation for a target site, the sample of group delay time at a certain discrete frequency can be either generated randomly by a specified probability density function or simulated conditionally by applying the Kalman filtering technique to consist of the earthquake data observed at nearby stations. Then, the phase spectrum can be modeled by integrating the simulated group delay times. On the basis of the modeled phase spectrum, the design ground motion can be simulated by the iteration process of modifying the Fourier amplitude, such that the associated spectral response acceleration will be compatible with the design response spectrum as specified by the seismic design code.