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Bulletin of the Seismological Society of America; December 1996; v. 86; no. 6; p. 1853-1862
© 1996 Seismological Society of America
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A statistical technique for validating velocity models

Edwin S. Iversen, Jr. and Jonathan M. Lees

Institute for Statistics and Decision Sciences Duke University, Box 90251, Durham, North Carolina 27708-0251 iversen{at}isds.duke.edu
Department of Geology and Geophysics Kline Geology Laboratory Yale University, Box 208109, New Haven, Connecticut 06520-8109 lees{at}lamb.geology.yale.edu

Abstract

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 {lambda} 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 {lambda}(i) when the ith station is removed. For a single event, define a station's influence (SI) as a weighted difference between {lambda} and {lambda}(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.




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