A New Spatial Variation Model for Ground-Motion Intensities Combined with Correlation and Coherency

Regional seismic risk or loss assessments generally require simulation of spatially distributed ground motions using multiple intensity measures. Hence, in this study, ground-motion model estimation is performed with a spatial correlation. Previously, many researchers have analyzed spatial correlations and developed empirical models using ground-motion recordings. In this study, ground motions occurring in California between 2019 and 2023 were used to analyze spatial correlations using semivariograms for the peak ground acceleration and pseudospectral acceleration in various spectral periods. Based on the analysis results, two aspects need to be revised in the conventional correlation model: (1) the empirical exponential model cannot reasonably reflect the target spatial correlation at a separation distance <10 km, and (2) the variation in the spatial correlation ground-motion intensity cannot be described at a small separation distance <1 km. Owing to these limitations, we revised the fitting model of the semivariogram to better characterize the spatial correlation. In the model, another function called coherency, replaced the spatial correlation to characterize the variation in the Fourier phase rather than the intensity within a separation distance <1 km. This research shows that the spatial variation in any region can be analyzed by combining the coherence and correlation functions for practical seismic-risk or loss assessment problems.