An Efficient, Analytic Solution Using Order Statistics for Probabilistic Seismic-Hazard Assessment without the Poisson Assumption

Standard approaches to probabilistic seismic-hazard assessment (PSHA) assume that earthquakes are random, independent events that follow a Poisson distribution of occurrences in a given time period (Cornell, 1968). To overcome the limitations of the Poisson assumption, such as ignoring earthquake clustering, we introduce an analytic method for PSHA that uses order statistics to allow for arbitrary distributions of earthquake occurrence. Cornell (1968) used the Poisson assumption to achieve a computationally efficient method that enables users to explore the impact of parameters used in earthquake occurrence and ground-motion models. We apply our order statistics method to the highly clustered seismicity associated with caldera collapses at Kilauea and explore the general implications of non-Poisson behavior for PSHA. We find that non-Poisson behavior has the greatest impact for high probabilities of exceedance, low-mean rates of occurrence, and multiple exceedances. Those conditions can be important for applications such as operating standards for buildings and infrastructure engineering, standards for temporary structures and during construction, the insurance industry, the design of earthquake early warning, and to assess hazards due to clustered processes such as aftershock sequences and earthquake swarms. The commonly used rate of exceedance hides the difference between the hazard due to a non-Poisson distribution and a Poisson distribution with the same mean rate of earthquakes. Thus, including non-Poisson behavior in PSHA means that we must plot and discuss PSHA results as the probability and not the rate of exceedance.