Stochastic Modeling and Simulation of Ground Motions for Performance-Based Earthquake Engineering, PEER Report 2010-02


A fully nonstationary stochastic model for strong earthquake ground motion is developed. The model employs filtering of a discretized white-noise process.
Nonstationarity is achieved by varying the filter properties and modulating the intensity of the process in time. Separation of the spectral and temporal nonstationary characteristics of the process allows flexibility and ease in modeling and parameter estimation. The evolving intensity and time-varying frequency content of the process are characterized by a set of statistical measures including the mean-square intensity, the mean zero-level up-crossing rate, and a measure of the bandwidth. Model parameters are identified by matching these measures with those of a target accelerogram. Post- processing of simulated ground motions by a second filter assures zero residual velocity and displacement, and improves the response spectral ordinates for long periods.

By identifying the parameters of the stochastic model for a large sample of recorded accelerograms drawn from the NGA database, predictive equations are developed that empirically relate the model parameters to a set of earthquake and site characteristics. For specified earthquake and site characteristics, sets of the model parameters are generated that are used in the stochastic model to generate an ensemble of synthetic ground motions. The resulting synthetic acceleration, as well as corresponding velocity and displacement time-histories, captures the main features of real earthquake ground motions, including the evolving intensity, duration, spectral content, natural variability, and peak values. Furthermore, the statistics of their resulting elastic response spectra, i.e., the median and logarith mic standard deviation, closely agree with the values predicted by the NGA ground motion prediction equations. The synthetic motions can be used with or in place of recorded motions in seismic design and analysis, particularly in the context of performance-based earthquake engineering.

The proposed method is extended to simulate the orthogonal horizontal components of ground motion for specified earthquake and site characteristics. This is achieved by taking advantage of the notion of principal axes directions, along which the two components are statistically independent, and by properly accounting for the correlations among the model parameters of the two components.

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Sanaz Rezaeian
Armen Der Kiureghian
Publication date: 
August 7, 2010
Publication type: 
Technical Report
Rezaeian, S., & Der Kiureghian, A. (2010). Stochastic Modeling and Simulation of Ground Motions for Performance-Based Earthquake Engineering, PEER Report 2010-02. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA.