Fast Probabilistic Seismic Hazard Analysis through Adaptive Importance Sampling

Abstract

Probabilistic Seismic Hazard Analysis (PSHA) relies on two widely utilized approaches with high computational demands: (a) Riemann sum and (b) conventional Monte Carlo (MC) integration. The first requires sufficiently fine slices across magnitude, distance, and ground motion, and the second requires extensive synthetic earthquake catalogs to compute seismic hazards accurately. These approaches are notably resource-intensive for low-probability seismic hazards, e.g., up to 10⁸ MC samples for a hazard with 10^-4 probability to achieve coefficient of variation (COV) of 1%. Here, we present a novel framework to compute hazard and deaggregation with unprecedented computational efficiency. We formulate Adaptive Importance Sampling (AIS) PSHA to approximate optimal important sampling (IS) distributions and dramatically reduce the size of synthetic earthquake catalogs (i.e., number of MC samples) to estimate hazards. We evaluate the effectiveness and reliability of our proposed method using comprehensive test problems from the Pacific Earthquake Engineering Research Center (PEER) for PSHA benchmarks, encompassing various seismic source types, including areal, fault, and combined ones. Our findings indicate that this novel approach significantly outpaces Riemann sum and traditional MC methods with computations up to >10⁵ and 7.8x10³ times faster, respectively, while maintaining an standard deviation of the estimate below 2%. Moreover, we show theoretically that optimal IS distributions are equivalent to hazard deaggregation distributions. Empirically, we show our approximated optimal IS and the deaggregation distributions are closely alike, e.g., with a Kolmogorov–Smirnovstatistic between 0.017 and 0.113. We developed our methodology to have broad applicability in PSHA practices, especially in cases requiring extensive computational resources to navigate numerous logic tree scenarios addressing epistemic uncertainty.