Nonstationary Spatial Correlation of Earthquake Ground Motions in California

Assessing seismic risk to spatially distributed infrastructure systems requires realistic representations of spatially correlated ground motions. Existing models for the spatial correlations of ground motions rely on strong second‐order stationarity assumptions, under which the correlation structure is assumed to be invariant across space, potentially masking regional variations. Because repeatable site and path effects can vary spatially, the resulting correlation structure is likely to be nonstationary. We propose a nonstationary spatial correlation method that captures geographically varying correlation decay behavior. We compute site‐to‐site Pearson correlations of within‐event residuals using earthquakes recorded at both sites in each site pair and model the resulting spatial correlation using a generalized exponential form with a parameter that controls the decay of correlation with distance. Spatially varying decay parameters are estimated using a Bayesian regression framework. To account for sampling uncertainty arising from finite numbers of paired recordings, we incorporate Fisher's z ‐transformation to stabilize variability in the observed site‐to‐site correlations. We implement the method using a 50‐km grid‐based discretization to develop a nonstationary spatial correlation model for California and find that the resulting model reduces correlation residual variance by 36% relative to a statewide stationary approach. Grid cells with high rates of decay of spatial correlation were observed in the San Francisco Bay Area and the Greater Los Angeles Area. A simulation‐based verification study shows that the observed high decay rates in these two areas reflect genuine spatial variability rather than being artifacts of dense sampling.