Sets of ground motion records used for seismic hazard analyses typically have intensity measures corresponding to a particular hazard level for a site (perhaps conditioned on a particular intensity value and hazard). In many cases the number of available ground motions that match required spectral ordinates and other criteria (such as duration, fault rupture characteristics, and epicentral distance) may not be sufficient for high-resolution seismic hazard analysis. In such cases it is advantageous to generate additional ground motions using a parameterized statistical model calibrated to records of the smaller data set. This study presents a statistical parametric analysis of ground motion data sets that are classified according a seismic hazard level and a geographic region, and which have been used extensively for structural response and seismic hazard analyses. Parameters represent near-fault effects such as pulse velocity and pulse period, far field effects such as velocity amplitude and power spectral attributes, and envelope characteristics. A systematic fitting of parameterized pulse functions to the individual ground motion records, of parameterized envelopes to individual instantaneous ground motion amplitudes, and of parameterized power spectral density functions to averaged power spectra result in probability distributions for ground motion parameters representative of particular seismic hazard levels for specific geographical regions. This methodology presents a means to characterize the variability in a set of ground motions records in terms of physically meaningful parameters.
This paper presents statistical models for the generation of bi-axial earthquake ground motion time histories with spectra that match those from samples of ground motion records. The model parameters define near-field characteristics such as pulse velocity and pulse period, far-fault characteristics such as velocity amplitude and power spectral density, and envelope characteristics. The samples of ground motions used in this study were previously selected and scaled to be representative of particular hazard levels in particular geographical regions. A companion paper presents the fitting of the model to samples of ground motion waveforms. In this paper, the new concept of a parameter-response correlation spectrum establishes the period-dependence of the correlation between the response spectrum and ground motion parameters. Parameters that correlate to variability of the response spectra are retained as random variables and are then fit to mean and mean-plus-standard deviation of bi-axial response-spectra of the samples of historical records. Parameter statistics also include correlations between velocity amplitudes and pulse periods.
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