Effective Sampling of Spatially Correlated Intensity Maps Using Hazard Quantization: Application to Seismic Events

Abstract

The paper presents a methodology for the selection of an optimal set of stochastic intensity measure (IM) maps representing the regional hazard over a geographic area, which can subsequently be used for the analysis of spatially distributed infrastructure systems. A key characteristic of the proposed approach, named Hazard Quantization (HQ), is that it embraces the nature of regional IM maps as two-dimensional (2D) random fields, and therefore uses a methodology for the optimal representation of non-Gaussian and nonhomogeneous random fields with a limited number of samples. In HQ, the representation of the regional hazard is supported by proofs of optimality. In particular, HQ ensures mean-square convergence of the ensemble of representative IM maps to the complete portfolio of possible hazard events, which is a particularly important property for risk analysis. HQ does not require the use of specialized simulation techniques, such as importance sampling or hierarchical sampling of the involved parameters, making the method simple to use. Other desirable characteristics make the method robust and applicable to a variety of hazard sources. In this paper, HQ is demonstrated for the regional seismic hazard analysis of the Charleston, South Carolina, region. A small set of IM maps and their associated probabilities resulting from the application of HQ are evaluated at all points and all pairs of points, on their ability to correctly represent the hazard curve and autocorrelation. Finally, a detailed comparison of the proposed technique with other popular methodologies in the same field is presented.