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Investigation of anisotropic spatial correlations of intra-event residuals of multiple earthquake intensity measures using latent dimensions method


 Considering spatial correlation of multiple earthquake intensity measures (IMs) is of particular importance in loss assessment of spatially distributed assets. This subject has been investigated in previous studies under the assumption of isotropy. Considering the fact that the assumption of isotropy is not valid in general, the present study employs a non-separable covariance model based on latent dimensions method to investigate anisotropic properties of spatial correlations and cross-correlations of intra-event residuals of multiple earthquake IMs. This method leads to the generation of valid covariance matrix in order to model anisotropic spatially distributed multivariate random fields. Two sets of IMs are considered in this study; the first set consists of peak ground intensity values (acceleration, velocity, and displacement), and the second set consists of spectral accelerations at three different periods. Data of 10 earthquake events in California and Japan are utilized in this study to estimate parameters of marginal and cross-covariance models. Moreover, parameters of covariance model of regional site condition, which is considered as average shear wave velocity of top 30 m of soil profile (Vs30), are obtained in order to investigate the effect of local sited conditions on spatial correlations of IMs. It is shown that maximum range and anisotropy ratio of covariance models of intra-event residuals of IMs are correlated with those of Vs30 values. Also, it is observed that the anisotropy direction of residuals of IMs is consistent with anisotropy direction of Vs30 values. Finally, predictive models are proposed to obtain marginal and cross-covariance functions for different earthquake IMs considering anisotropy.