Physics-based Stochastic Modeling And Simulation Of Earthquake Ground Motions With Temporal And Spectral Nonstationaryity

A site-based fully-nonstationary stochastic model for strong earthquake groundmotion is developed. The model employs filtering of a discretized whit-noise process.Nonstationarity is achieved by modulating the intensity and varying the filterproperties in time. The formulation has the important advantage of separating thetemporal and spectral nonstationary characteristics of the process, thereby allowingflexibility and ease in modeling and parameter estimation. The model is fitted torecorded ground motions by matching a set of statistical characteristics, including themean-square intensity, the mean zero-level up-crossing rate, and a measure of thebandwidth, all expressed as functions of time. These characteristics represent theevolving intensity and time-varying frequency content of the ground motion.Post-processing by a second filter assures zero residual velocity and displacement,and improves the match to response spectral ordinates for long periods.The proposed stochastic model is employed to develop a method for generatingan ensemble of synthetic ground motion time-histories for specified earthquake andsite characteristics. The stochastic model is fitted to a large number of recordedground motions taken from the PEER NGA database. Strong ground motionsrecorded on firm ground with source-to-site distance of at least10km are selected.Fitting to recorded ground motions results in sample observations of the stochasticmodel parameters. Using this sample, predictive equations are developed for themodel parameters in terms of the faulting mechanism, earthquake magnitude,source-to-site distance and the site shear-wave velocity. For any specified set of theseearthquake and site characteristics, sets of the model parameters are generated, whichare in turn used in the stochastic model to generate an ensemble of synthetic groundmotions. The resulting synthetic accelerations as well as corresponding velocity anddisplacement time-histories capture the main features of real earthquake groundmotions, including the intensity, duration, spectral content, and peak values.Furthermore, the statistics of their resulting elastic response spectra closely agreewith both the median and the variability of response spectra of recorded groundmotions, as reflected in existing prediction equations based on the NGA database.The proposed method can be used in seismic design and analysis in conjunction withor instead of recorded ground motions.