The aim of this project is the development and application of statistical techniques for describing earthquake catalogs, focusing primarily on spatial-temporal marked point process models and closely related objects such as tessellations and branching processes. The goals of the seismological application are the fitting, assessment, and improvement of models such as the epidemic-type aftershock sequence (ETAS) model, which are useful for describing earthquake catalogs, especially the geometric and spatial-temporal structure of earthquake faults, and the thorough investigation of errors in records of earthquake parameters and their impact on seismological inferences such as estimates of seismic hazard and standard errors for model parameters. In addition to the development of new useful stochastic models, the main statistical goals are the extension of assessment methods, especially point process residual analyses via rescaling and thinning, to the case of spatial-temporal marked point processes as well as other types of models such as tessellations and branching processes, and the development of tests for stationarity in the residuals that are powerful in the detection of departures from spatial homogeneity and from the assumption of spatial-temporal-magnitude separability.
Major earthquakes are catastrophic events that can cause numerous injuries, loss of lives, and billions of dollars in damages to public and private property. This project has the potential for very direct societal impact on the preparation for and response toward these potentially devastating occurrences. Seismic hazard estimation, defined as the quantification of the likelihood of an earthquake of at least a given size occurring in a certain region within a given time interval, is crucial to civil engineering, earthquake preparedness and response systems, and the determination of earthquake premiums which in turn influence governmental policy and property valuation. The refinement of spatial-temporal models for earthquake patterns described in this project is necessary for more precise estimation of seismic hazard..Further, the analysis of errors in earthquake catalogs and their impact on seismic hazard estimates is critical in order for proper awareness of uncertainties in earthquake forecasts among the public and scientific community. The statistical tools developed in this project are useful for other applications as well. In particular, spatial-temporal marked point process models are important for describing the occurrences of other natural phenomena besides earthquakes, such as wildfires, disease epidemics, hurricanes, and many others.
