A Modified Gaussian Model for Spectral Amplitude Variability of the SMART 1 Array Records

Abstract

Artificial ground motions, particularly conditional simulated artificial ground motions, are an essential complement to actual earthquake records when designing large-span structures, while considering the spatially varying properties of ground motions. Most existing methods, both conditional and unconditional forms, consider only the simulated ground motion complying with the power spectral densities and the coherence between the spectra of actual ground motions. In this study, the SMART 1 array’s records are regarded as conditional simulated ground motions from its central station. Their periodograms’ amplitude variation processes with the increased separation distance between two locations are studied. The analysis shows that the Gaussian model underestimates the periodograms’ amplitude variation, which can cause significant relative motions between structural supports and is detrimental to large-span structures. A random local power coefficient (LPC) is involved in modifying the Gaussian method. The LPC exhibits a noncentral Wishart distribution. Its statistical model as a function of the separation distance is derived. The LPC preserves the random field’s power spectral density and the spectral coherence relationships of the conventional Gaussian model. Simultaneously, the simulated random field’s periodogram variation complies with that of the SMART1 records. Monte Carlo simulations were conducted in the analysis and validated the modified Gaussian method.