Automated parameterization of velocity pulses in near-fault ground motions

Proper parameterization of near-fault ground motions is of critical importance in earthquake engineering, and this process is traditionally performed by directly fitting an analytical pulse model to the original motion. Yet such a process is usually limited by the trial-and-error procedure, which is strongly dependent on the initial guesses and may converge to local rather than global minimums. In this study, we propose a progressive (step-by-step) iterative approach that can achieve a fully automated parameterization of the velocity pulse contained in near-fault motions. Assuming that a velocity pulse can be characterized by a pulse model with four key parameters, the approach is conducted by iteratively matching the pulse model to the smoothed ground motion, and the parameterized pulse is analytically derived by best fitting to the smoothed motion not only in the time domain but also in the spectral domain. Specifically, the velocity time history of interest is initially smoothed by a moving average filter so that the low-frequency content can be filtered out of the original motion, from which the pulse amplitude as well as its epoch is accordingly determined. The coherent velocity pulse is then progressively extracted by performing the nonlinear least-square-fitting of the pulse model to the filtered low-frequency content, during which the remaining parameters, that is, the pulse period, the number of cycles and the phase of the pulse, are estimated successively. Finally, the above procedure is applied repeatedly to the original ground motion by changing an empirical factor controlling the extent of smoothing of the motion so that convergence to local minimums that frequently occurs in the trial-and-error procedure could be largely avoided, and best match of the spectrum of the extracted pulse to that of the original motion can be acquired. Fitting quality of the velocity pulses is examined by comparing with existing methods. Prospective applications of the proposed procedure include the stochastic simulations of near-fault ground motions and parametric investigations of the influence of velocity pulses on various engineered structures.