A STOCHASTIC MODEL FOR SEQUENTIAL GROUND MOTIONS BASED ON THE COPULA THEORY

The existing ground motion physical stochastic model is extended to a stochastic model for sequential ground motions by considering the spatial correlation between the mainshock and aftershock. Considering the physical mechanism of ground motion generation and propagation, the sequential ground motions are represented by the Fourier model of 16 physical random variables. Meanwhile, considering the spatial correlation between the mainshock and aftershock, the model is more accurately represented by six two-dimensional random variables and two one-dimensional random variables based on the Copula theory. To describe the process of the ground motion propagation on local sites, a random field model of sequential ground motions is established. Based on 1038 pairs of measured sequential ground motions and five sets of ground motion array data, the probability distribution of each parameter is given by parameter identification and statistical analyses of physical random variables in the model combined with the Copula function. The comparison between the measured and the simulated ground motions shows that the proposed stochastic model for sequential ground motions can realistically reproduce both the spatial correlation of sequential ground motions and the wave traveling effect of ground motions at local sites.