A phase model of earthquake motions based on stochastic differential equation

Abstract

In this paper, a method is proposed to simulate Group Delay Time (GDT) of earthquake ground motion by using Stochastic Differential Equation (SDE). The random characteristic of GDT is expressed by a stochastic differential equation whose mean and variance processes are defined by ordinary differential equations. An algorithm is developed to identify the coefficients of the ordinary differential equations. Regression surfaces of the coefficients are developed as functions of earthquake magnitude, epicentral distance and frequency. The Milstein approximation scheme is used to solve the stochastic differential equation of GDT. The efficiency of the developed method is demonstrated by comparing the simulated result with the original one.

The normal distribution fitting method for frequency distribution characteristics of peak arrival time of earthquake

“…23 The nonrepeatability and unpredictability of natural seismic waves mean that the above fitting methods often fail to produce satisfactory frequency distribution characteristics in the artificial phase difference spectrum. 24 The research results show that the physical meaning of the phase difference spectrum of natural seismic wave can be expressed as peak arrival time. Moreover, the variation laws of acceleration time-history curve of natural seismic wave can be transformed into its energy distribution characteristics in the time domain.…”

Definition of Yield Seismic Coefficient Spectrum Considering the Uncertainty of the Earthquake Motion Phase

“…Boore [22] used the stochastic differential equation to simulate the GDT. Additionally, Zhang et al [23] developed a method to apply the stochastic differential equation in relation to earthquake magnitude, epicenter distance, and local soil conditions. Chai et al [24] used the GDT concept to model phase spectra according to the compact support of the Meyer wavelet.…”