A Sample Generation of Scenario Earthquake Shaking Maps via a Combination of Modal Decomposition and Empirical Copula toward Seismic Hazard Assessment

ABSTRACT To quantify variations in seismic hazard assessment, a large number of scenario earthquake shaking maps (hereafter referred to as s-EQ maps for short) are required. In this article, we propose a method to easily generate a large number of s-EQ maps by combining modal decomposition and empirical copula. First, by applying modal decomposition to a set of existing s-EQ maps, we identify a scenario set with a parameter space to reduce the dimensionality of models. Next, we model a probability distribution of the modal coordinates, which we regard as random variables to allow us to induce a probability measure on the parameter space. By applying an empirical copula for modeling the probability distributions, the dependence structure between modal coordinates and the probability distribution of an individual modal coordinate can be discussed independently. Some simulations show that the dependence structure between modal coordinates is important to not distort the seismic hazard assessment. The proposed method can be applied to actual existing s-EQ maps to easily generate a large number of new s-EQ maps that follow the original probability distribution. We also show that variations can be added to the newly generated s-EQ maps by adjusting the empirical copula. Furthermore, we give a generalization of the proposed method to cases with nonequal probabilities of occurrence of existing scenarios.