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

ABSTRACT 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.

Spatial prediction of a scalar variable based on data of a functional random field

Kriging and cokriging and their several related versions are techniques widely known and used in spatial data analysis. However, when the spatial data are functions a bridge between functional data analysis and geostatistics has to be built. I give an overview to cokriging analysis and multivariable spatial prediction to the case where the observations at each sampling location consist of samples of random functions. I extend multivariable geostatistical methods to the functional context. Our cokriging method predicts one variable at a time as in a classical multivariable sense, but considering as auxiliary information curves instead of vectors. I also give an extension of multivariable kriging to the functional context where is defined a predictor of a whole curve based on samples of curves located at a neighborhood of the prediction site. In both cases a non-parametric approach based on basis function expansion is used to estimate the parameters, and I prove that both proposals coincide when using such an approach. A linear model of coregionalization is used to define the spatial dependence among the coefficients of the basis functions, and therefore for estimating the functional parameters. As an illustration the methodological proposals are applied to analyze two real data sets corresponding to average daily temperatures measured at 35 weather stations located in the Canadian Maritime Provinces, and penetration resistance data collected at 32 sampling sites of an experimental plot.