Modelling Evolutionary Power Spectral Density Functions of Strong Earthquakes Via Copulas

Abstract

This paper proposes a new approach for analyzing seismic accelerograms using the evolutionary Power Spectral Density function (ePSDF). The accelerogram of an earthquake can be accurately modeled and simulated from its spectrogram, based on the oscillatory stochastic processes theory. To adequately characterize a spectrogram that is consistent with the response spectra, a parametric model with 16 parameters is proposed. This model describes the square of the amplitude spectrum, an envelope of the square of the accelerogram, and a copula that constructs a time-frequency model from the time and frequency marginals. The use of copulas to model a bivariate probability distribution is a common practice in statistics, particularly when the marginal distributions are known. The periodogram can be viewed as an unnormalized probability density function, where the total energy serves as the normalization constant, since the total energy of a seismic motion is always finite. Additionally, a reduced model consisting of only 10 parameters is presented, which may be especially valuable when only shear wave effects are relevant.