Conditional Intensity Function of Stress Release Model: Estimation and Its Application on Earthquake Data

Relating to the occurrence of earthquakes, elastic rebound theory shows the accumulated elastic pressure in the seismic region due to the movement of plate tectonics which is released when the pressure exceeds the plate strength limit. On the basis of this theory, the point process is constructed into a stress release model. The stress release model considers the increased pressure in an area and the pressure released during an earthquake over a period of time. It is possible to measure the probability of earthquake occurrence using the conditional intensity function of the stress release model. Thus, this research aims to estimate conditional intensity function of stress release model and apply it to earthquake data in Indonesia, especially Java Island and Sumatra Island. These two areas are the most earthquake-prone areas in Indonesia. We use data from January 1993 to December 2016 obtained from the United States Geological Survey. The maximum likelihood method is needed to estimate parameters of conditional intensity function. The conditional intensity function of the stress release model is a nonlinear equation obtained from hazard function of accumulation of pressure released from earthquakes over a time period. In application, we show that probability of earthquake occurrence in Java and Sumatra is almost the same. The southern regions of the Java Island have higher earthquake intensity than the northern, while the western regions of the Sumatra Island have higher earthquake intensity than the eastern.