Dependence Modeling for Tsunami and Earthquake Disasters in the Indonesian Megathrust Zones using Copula Models

The megathrust earthquake parameters that are related to the number of tsunami disasters (𝑍) are the number of earthquakes (𝑋) and the maximum earthquake magnitude (𝑌). The dependence property of these three random variables is stochastic due to the uncertainty of each event. This study provides the stochastic dependence model of (𝑋, 𝑍) and (𝑌, 𝑍) based on the historical data of tsunami and megathrust earthquake disasters occurring from 1905 to 2022 in five megathrust zones of Indonesia, namely the Sumatra, Java, Bali, Sulawesi and Papua zones. In this study, the stochastic dependence models applied are bivariate Copula models that are flexible under rigid assumptions. The data source is taken from the U.S. Geological Survey catalog. The results show that each megathrust zone has various responses to the earthquake and tsunami mechanisms; it can be seen from the probability functions of three random variables in each megathrust zone that they are significantly different. Furthermore, according to stochastic dependence modeling results, it is found that the Copula model selected for each zone varies in type and parameters. Moreover, the selected bivariate Copula models for each megathrust zone have better agreement with the data modeled than the conventional bivariate discrete models.