Multi-taper S-transform method and its application in the EPSD and coherence estimation of earthquake ground motions

Abstract

Estimating the accurate evolutionary power spectral density (EPSD) and coherence of earthquake ground motions based on measured records is essential in earthquake engineering. This study introduces a multi-taper S-transform (MTST) method for estimating the EPSD and coherence of multi-variate non-stationary processes. With a set of orthogonal time-frequency Hermite windows, the MTST method can simultaneously achieve a sufficient resolution for the EPSD and coherence estimates and reduce their estimation variance. This method is applicable to the case of only one available record. Under the assumption that two univariate non-stationary processes are Gaussian and their auto-EPSDs have the same shape, the bias and variance of the EPSD and coherence estimators by the MTST method are provided. The usefulness and reliability of the MTST method are verified using both simulated earthquake ground motion accelerations with known target EPSD and coherence and field-measured records.