Inhomogeneous ETAS Models for Seismic Data Analysis of Southern California

Abstract:

Modern earthquake catalogs are often analyzed using spatial-temporal point process models. This work applies the special-temporal ETAS (Epidemic-Type Aftershock Sequence) model of Ogata to regional seismicity of Southern California. Events between 1973 and 2015 with magnitude 4.0 or above are included for statistical analysis. The Preliminary Determination of Epicenters (PDE) data used are in space window between 114^oW and 122^oW in longitude, and between 30^oN and 38^oN in latitude. Three different types of models are implemented and compared: a homogeneous model, several inhomogeneous models with rectangular grids to partition the region, and several inhomogeneous models with simple polygons generated using Voronoi tessellation (Dirichlet tessellation) with events of large magnitudes as the polygon’s centers. Predicted intensity rate is obtained based on the model parameters’ MLEs (maximum likelihood estimates). Model comparisons and diagnostics are discussed using AIC (Akaike’s Information Criterion). It is observed that background rate plays an important role in inhomogeneous model fitting, and a trend of better fit appears in the models fit using Voronoi polygons. In addition to results of statistical modeling, computation aspects like computing environment setup of Java and R, and remedy of divergence are discussed. Spatial issues that may affect convergence and model selection are discussed.