A Bayesian hierarchical method for multiple‐event seismic location

SUMMARY We formulate the multiple‐event seismic location problem as a Bayesian hierarchical statistical model (BAYHLoc). This statistical model has three distinct components: traveltime predictions, arrival‐time measurements, and an a priori statistical model for each aspect of the multiple‐event problem. The traveltime model is multifaceted, including both phase‐specific adjustments to traveltime curves to improve broad‐area prediction, as well as path/phase‐specific traveltime adjustments. The arrival‐time measurement model is decomposed into station, phase, and event components, allowing flexibility and physically interpretable error parameters. The prior model allows all available information to be brought to bear on the multiple event system. Prior knowledge on the probabilistic accuracy of event locations, traveltime predictions, and arrival‐time measurements can be specified. Bayesian methodology merges all three components of the hierarchical model into a joint probability formulation. The joint posterior distribution is, in essence, an inference of all parameters given the prior constraints, self‐consistency of the data set, and physics of traveltime calculation. We use the Markov Chain Monte Carlo method to draw realizations from the joint posterior distribution. The resulting samples can be used to estimate marginal distributions, for example epicentres and probability regions, as well as parameter correlations. We demonstrate BAYHLoc using the set of Nevada Test Site nuclear explosions, for which hypocentres are known, and phase measurements and traveltimes are well characterized. We find significant improvement in epicentre accuracy using BAYHLoc. Much of the improvement is attributed to the adaptive arrival‐time measurement model, which controls data weighting. Regardless of the initial traveltime model, the use of an adjustment to the traveltime curves produces a level of epicentre accuracy that is generally achieved only through meticulous analysis and data culling. Further, we find that accurate hypocentres (including depth and origin‐time) are achieved when either accurate traveltime curves with tight priors are used, or when prior information on a small subset of events is utilized.