Spatial Cross-Correlation Models for Absolute and Relative Spectral Input Energy Parameters Based on Geostatistical Tools

In recent years, energy-based seismic design methodology has received increasing attention because it takes into account not only the force and displacement behavior of a structure but also the cumulative damage effect caused by seismic loading. Specifically, as a fundamental parameter, input energy parameters (both absolute and relative measures) are directly related to the cumulative damage potential; therefore, they are commonly used in energy-based seismic design and seismic risk assessment. This study thus proposes new spatial cross-correlation models for absolute and relative elastic input energy parameters, using 2219 ground-motion records selected from 12 earthquake events. The normalized within-event residuals for both absolute and relative measures are first calculated. Semivariogram analysis is then conducted to quantify the spatial correlation of residuals for the input energy parameters at multiple sites and multiple periods. The linear model of coregionalization (LMC) approach is adopted to fit the empirical data; it is observed that the proposed LMC-based function performs reasonably well in capturing the spatial variability of the input energy measures. The influence of regional site conditions on the spatial cross correlation of input energy parameters is also investigated, and generic models are proposed using the averaged standardized coregionalization matrices of 12 events. The spatial cross-correlation models developed for input energy parameters can be used in regional seismic risk assessment within an energy-based framework.