  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.
