Facilitated estimation of ETAS

An approximation technique is introduced that greatly facilitates the estimation of the Epidemic-Type Aftershock Sequence (ETAS) model introduced by Ogata (1988), which is widely used to describe earthquake catalogs. The proposed approximation greatly simplifies the integral term in the log-likelihood, the computation of which is by far the greatest hurdle in maximum likelihood estimation. The approximation is close provided the observed region contains most of the aftershock activity caused by earthquakes within the observation region. Through simulations and an example involving earthquakes in Hector Mine, CA, the proposed method is shown to produce stable and accurate results, with rapid convergence.