A Spatially Varying Ground Motion Model with an Evolving Energy Spectrum

Abstract

Besides phase variability, amplitude variability is one of the two manifestations of the spatially varying ground motion (SVGM) in the frequency domain. Neglecting the amplitude variability of the earthquake spectra can result in an underestimation of the structural responses. Few existing amplitude variability models can be used for estimating spectra at a distance from a reference location. In this paper, a new amplitude variability model describing the evolution of the energy spectra is developed based on records of five earthquake events acquired from the SMART 1 array. The similarity between the spectra of two locations is used as a metric for measuring the spectrum changes. The energy spectra at a distance from a reference location are found to be composed of two parts, including the averaged spectra and the random variation part. In the new model, the former is estimated by the moving average of the reference spectrum, while the envelope of the latter is approximated by the wavelet approximation of the reference spectrum’s Fourier amplitude spectrum. The parameters of five models for each event and a general model for all five events are identified. Monte Carlo simulations are used for testing the models. The results validate the new model in terms of capturing the similarity changes of actual earthquakes.