A multi-modal analytical non-stationary spectral model for characterization and stochastic simulation of earthquake ground motions

Abstract A novel stochastic earthquake ground motion model is formulated in association with physically interpretable parameters that are capable of effectively characterizing the complex evolutionary nature of the phenomenon. A multi-modal, analytical, fully non-stationary spectral version of the Kanai–Tajimi model is introduced achieving a realistic description of the time-varying spectral energy distribution. The functional forms describing the temporal evolution of the model parameters can efficiently model highly non-stationary power spectral characteristics. The analysis space, where the analytical forms describing the evolution of the model parameters are established, is the energy domain instead of the typical use of the time domain. This space is used in conjunction with a newly defined energy-associated amplitude modulating function. The Spectral Representation Method can easily support the simulation of sample model realizations. A subset of the NGA database is selected in order to test the efficiency and versatility of the stochastic model. The complete selected database is thoroughly analyzed and sample observations of the model parameters are obtained by fitting the evolutionary model to its records. The natural variability of the entire set of seismic ground motions is depicted through the model parameters, and their resulting marginal probability distributions together with their estimated covariance structure effectively describe the evolutionary ground motion characteristics of the database and facilitate the characterization of the pertinent seismic risk. For illustration purposes, the developed evolutionary model is presented in detail for two example NGA seismic records together with their respective deterministic model parameter values.

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