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Some statistical aspects of the estimation of seismic travel times

DALLAS SEISMOLOGICAL OBSERVATORY SOUTHERN METHODIST UNIVERSITY, DALLAS, TEXAS
SEISMOGRAPHIC STATION UNIVERSITY OF CALIFORNIA, BERKELEY, CALIFORNIA

Abstract

Some of the statistical aspects of estimating travel-time anomalies and station corrections are considered. In order to estimate these quantities using earthquake data the events themselves must first be located. We investigated the use of the Gauss-Newton iterative technique to obtain a least-squares epicenter location employing Monte Carlo methods. Results of these studies indicate that the Gauss-Newton process converges to an absolute minimum and that confidence ellipses computed by linear techniques are reliable for reasonable networks of well-distributed stations. Also the Monte Carlo studies indicate that a least-squares solution may be inaccurate if appreciable travel-time anomalies or station-error means exist. We then expanded the location procedure to include the estimation of travel-time anomalies and station corrections. In order to obtain these estimates data from some 278 large earthquakes were analyzed by using a modified Seidel iterative process.

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