Stochastic simulation of velocity pulses of near-fault ground motions based on multivariate copula modeling

Due to the featured high-amplitude, long-period pulses in velocity or displacement time-history, the near-fault ground motion may have a stronger destructive effect on engineering structures. Therefore, studying velocity pulses modeling of near-fault ground motions has been an important topic in the earthquake engineering community. However, the variability and probabilistic correlation of pulse model parameters have not received enough attention. To this end, an elegant method for stochastic simulation of velocity pulses of near-fault ground motions is proposed based on the classical Gabor wavelet modeling and probabilistic correlation analysis of associated model parameters by multivariate copula modeling. Especially, an efficient scheme of iteratively determining the optimal copulas pertinent to edges of a complex vine structure is developed, and two parameters relevant to the near-fault ground motion records, i.e., the rupture distance and the strongest pulse orientation, are introduced which provides a physical basis for addressing the dependence structure among variables. For illustrative purposes, the ground accelerograms recorded by near-fault instruments in the 1999 Chi-Chi earthquake are used. It is shown that the multivariate copula modeling enables the efficient representation of probabilistic correlation between model parameters which is consistent with their physical mechanism. The time histories and spectral characteristics of velocity pulses of near-fault ground motions and their stochastic fluctuations with respect to the rupture distance are well simulated. While the empirical linear regression model does not meet the requirements of random vibration analysis and thus cannot guide the safety design of seismic structures.