FROM A POISSON PROCESS MODEL TO A LAPLACIAN MARTINGALE PROCESS FOR EARTHQUAKE FORECASTING IN A REGION IN THE PHILIPPINES

Abstract

The usual Poisson process for seismic hazard assessment is utilized as basis for constructing a Laplacian martingale process to respond to objections raised about the use of a Poisson model for forecasting earthquake occurrences. Seismic data from the Caraga Region of the Philippines were utilized in this study. The seismic signals themselves are shown to follow a power-law distribution with λ = 2.49915. Results show that the Laplacian martingale process predicted the arrival times of earthquakes with intensity 4 or greater with less than 1% relative error for the Caraga region. The unpredictability of the occurrence of earthquakes of such magnitudes appear to share the same unpredictability property with the occurrence of the nth prime in analytic number theory to Ph.D. as well as aligned teaching assignments, research outputs and other scholarly works.