Modeling the Phase Spectrum Characteristics of Ground Motion Considering Source, Propagation Path and Local Site Effect Amplification

The design earthquake motion is often defined by response spectra. To check the seismic capacity of designed structures, however, it is necessary to perform dynamic analysis using earthquake motion (time history) which is compatible with the design spectra. In this regard, the phase characteristic of earthquake motion is one of the most important issues in addition to that of the amplitude characteristic. Early-stage research has been performed to simulate design earthquake motion. One rudimentary method is to use an envelope function [1] and multiply it to the stationary wave form simulated using a random phase criterion. Another approach is to use the phase spectrum of a particular instance of observed earthquake motion [2]. However, these methods do not clarify the phase characteristics of earthquake motion. We have previously pointed out that the phase characteristic of earthquake motion strongly controls its nonstationary nature, and have developed methods to model the phase characteristics of earthquake motion [3, 4]. One of these is an empirical approach by which regression equations for the mean and standard deviation of group delay times of earthquake motion have been derived as functions of earthquake magnitude and epicentral distance [3]. Another one is a theoretical approach through which we have developed a method to model the group delay time for near-source earthquake motion by assuming that the rupture process of an earthquake fault can be expressed by a train of impulses and that the minimum phase concept is effective in evaluating phase shift caused by wave propagation [4]. In the empirical method, regression equations were introduced based on the assumption that the group delay time of earthquake motion can be represented as a product of the source, the path and the local site effects. However, it subsequently became clear that this assumption did not hold for the mechanism of earthquakes. In addition, the equations could not be used to estimate phase spectra in near-source regions because the assumption of a single-source-mechanism is adopted. The theoretical method used only direct S-wave motion, and it was concluded that this approach is not suitable for taking the effect of surface wave motion on the group delay time into account. We therefore developed a new method to model phase spectra in order to consider the earthquake mechanism and offer a wider range of applicability than our past methods. We also demonstrated its efficiency in synthesizing earthquake motion.