Pulse-like ground motion simulation using wavelet-based Hilbert transforms

In areas near active faults, ground motions usually show a large pulse in velocity time history. These near-field pulse-like ground motions increase the structural failure and cause extensive damage to structures. Due to the limited number of pulse-like ground motion recorded in a range of magnitude and distance, there is a small set of possible earthquake scenarios for seismic engineering in a given area, especially in areas near the fault. A new method has been proposed in this paper for simulating near-field pulse-like ground motions using instantaneous feature modeling. The proposed method is introduced based on the time-frequency process which is necessary to consider non-stationary characteristics of ground motion. In this method of simulation, wavelet-based Hilbert transform is used to extract the non-stationary characteristics of original pulse-like ground motion. The stationary wavelet transform is first applied to decompose the original ground motion into a series of subband frequency, and then the instantaneous features are obtained by applying Hilbert transform on each subband frequency. Instantaneous frequencies are modeled by Gaussian distribution and the instantaneous amplitude fitted by Gaussian curves. Approximation coefficients obtained from the last level of wavelet transform are also simulated using the Gaussian curves. Pulse-like ground motion will be simulated using Hilbert and Wavelet inverse transforms and the new generated data for the instantaneous characteristics and approximation coefficients. In this study, four pulse-like ground motions of Imperial Valley1979 and Northridge 1994 were used to verify the effectiveness of this simulation method. Simulated ground motions were compared with the recorded pulse-like ground motions and various criteria were used to confirm the effectiveness of the proposed method. Peak ground acceleration, response spectrums, and arias curves which are important parameters of ground motion were used in this paper to validate the proposed method. Simulation results not only captured the main characteristics of the recorded pulse-like ground motion, but also preserved the effects of the pulse as well.