A statistical technique for validating velocity models

This study investigates the use of a station influence statistic to identify velocity model shortcomings in the earthquake hypocenter location problem. Two groups of microearthquake events are examined. The first is a group of 81 events from the Mount St. Helens region that occurred between November 1987 and September 1991; the second, 110 well-located events from the 1992 Joshua Tree after-shock sequence. We describe a method for validating a postulated earth model. Let λ denote the hypocenter estimates that Geiger's method obtains. Systematically remove each station observation from the location problem, and recompute the location estimate. Call this estimate λ(i) when the ith station is removed. For a single event, define a station's influence (SI) as a weighted difference between λ and λ(i). Distributional summaries of SI statistics across events are used to identify model shortcomings: Given a specified velocity model, SI distributions that are not homogeneous across stations provide evidence of model inadequacies and/or failures in the weighting scheme. We show that velocity model shortcomings detected using SI statistics for the Mount St. Helens sequence under a one-dimensional model appear to correlate with known physical anomalies; while SI distributions evaluated under a three-dimensional model are more homogeneous and reflect a modest improvement over the one-dimensional model. SI distributions provide evidence of model failure for the Joshua Tree sequence under a one-dimensional model, but no evidence of failure under a three-dimensional model. Finally, the weighting scheme's validity is verified for the Joshua Tree sequence under the three-dimensional model.

Duke Scholars

Author Edwin Severin Iversen Jr. Statistical Science