Simulation of Strong Earthquake Ground Motions Based on the Phase Derivative

Abstract

A physical method for modeling the phase spectrum of earthquake ground motion is derived by defining relationships between the envelope delay and Fourier amplitude. In this method, two parameters with clear physical meanings, namely the median arrival time and strong shock duration, are introduced. These parameters provide a logical basis for modeling the phase spectrum in a physical sense. A simulation method for earthquake ground motions is introduced, based on a physical amplitude model and the proposed method for modeling the phase spectrum. To investigate the physical meaning of the phase spectrum of earthquake ground motion and to be used for simulating earthquake ground motions, two techniques based on the discrete Fourier transform (DFT) and the continuous Fourier transform (CFT) are employed to calculate the envelope delay. It is demonstrated that when using the DFT, the range of envelope delays is dependent on the duration of the earthquake ground motion, and the range of envelope delays corresponding to peak amplitudes is dependent on the time span of the strong shock in ground motions. This dependency is not observed with the CFT. The proposed simulation method for earthquake ground motions was used to regenerate two recorded earthquake acceleration time histories. Numerical results demonstrate that this method can accurately reproduce the main characteristics of strong earthquake ground motion recordings.