Practical Aspects in the Estimation of Space-time Branching Point Process Models for Earthquake Occurrences
Advisor: Rick Paik Schoenberg
This dissertation presents practical aspects in the estimation of space-time branching point process models for earthquake occurrences. Branching point process models such as the ETAS (Epidemic-Type Aftershock Sequence) models introduced by Ogata (1988, 1998) are often used in the description, characterization, simulation, and declustering of modern earthquake catalogs. Earthquake catalogs often have issues of incompleteness and other inaccuracies for earthquakes of magnitude below a certain threshold, and such earthquakes are typically removed prior to ﬁtting a point process model. Among the two applications of ETAS models this dissertation presents, the ﬁrst applications investigates the bias in the parameters in ETAS models introduced by the removal of the smallest events. It is shown that, in the case of most of the ETAS parameters, the bias increases approximately exponentially as a function of the lower magnitude cutoff.
The second application investigates how the parameters in these models vary across different tectonic zones. After considering divisions of the surface of the Earth into several zones based on the plate boundary model of Bird (2003), ETAS models are ﬁt to the occurrence times and locations of shallow earthquakes within each zone. The ﬁts and variations in parameter estimates for distinct zones are compared. Seismological explanations for the differences between the parameter estimates for the various zones are considered, and implications for seismic hazard estimation and earthquake forecasting are discussed.