Implementing Inter-Frequency Correlations into the SDSU Broadband Ground Motion Method

Nan Wang, Rumi Takedatsu, Kim B. Olsen, & Steven M. Day

Submitted August 6, 2018, SCEC Contribution #8292, 2018 SCEC Annual Meeting Poster #010

Earthquake ground motion records reveal frequency-dependent correlations, which has implication for seismic risk (Bayless and Abrahamson, 2017). The empirical inter-frequency correlation model of within-event residual for the Effective Amplitude Spectrum (EAS) computed from the PEER NGA-West2 database shows correlation of ground motions between nearby frequencies. We attempt to incorporate such correlation as a post-processing method into the current San Diego State University (SDSU) Broadband (BB) ground motion generator module, which combines deterministic (low-frequency) and stochastic (high-frequency) components. We first apply Cholesky decomposition of the regressed inter-frequency covariance model (C) and multiply it with an uncorrelated normal random variable with zero mean to generate a correlated random variable (zero mean, covariance is proportional to C) for different realizations, which are then multiplied with the Fourier amplitude of the high-frequency ground motion synthetics calculated using Zeng et al. (1991)’s scattering theory. Using our improved method, the BB results for 7 western U.S. events with Mw5.0-7.2 show that the empirical inter-frequency correlations of EAS are well predicted in the SDSU module for a large number of realizations from a single event with unbiased goodness-of-fit of the spectral accelerations in the presence of correlated synthetics. This post-processing method can also be extended to improve frequency-dependent spatial correlations.

Wang, N., Takedatsu, R., Olsen, K. B., & Day, S. M. (2018, 08). Implementing Inter-Frequency Correlations into the SDSU Broadband Ground Motion Method. Poster Presentation at 2018 SCEC Annual Meeting.

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