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Two methods to improve location estimates—preliminary results

TELEDYNE GEOTECH, 314 MONTGOMERY STREET, ALEXANDRIA, VIRGINIA 22314

Abstract

Preliminary test results of two new seismic epicenter location methods show that the methods are quite effective in reducing location errors.

The first method assumes that a large part of the travel-time residuals is caused by differences between the actual structures at source and receiver, and the standard structure used in the program. To correct for both regions, tables of the differences between the half-way travel times from source to bottoming layer using the Herrin model, and various regional models, were computed. In application, the total travel-time correction for each source-to-station path is the sum of the down-ray correction of the source region and the up-ray correction of the receiver region. Resulting location errors are much smaller (about half) than the errors using the ordinary location method.

The second method considers the possibility that stations in close proximity may be measuring essentially the same travel-time residual, leading to a consistent stochastic bias. The assumption that the bias is stochastic can be modeled in terms of a correlation matrix for the residuals which varies according to the separation between two stations. The method adjusts the weighting of travel-time residuals in accordance with their overall intercorrelation matrix so that a large cluster of stations will not exert an inordinate effect on the estimated location. It thus becomes unnecessary to "balance" networks. Correlation coefficients estimated with 186 station residuals from LONGSHOT, were 0.7 for the O° to 5° distance range, 0.3 for the 5° to 10° range, and 0 for distances greater than 10°. For ease of computation, 184 stations were separated into nine geographical groupings. It was necessary to smooth the resulting correlation matrix to ensure a positive definite matrix. The LONGSHOT location error with the smoothed correlation matrix was reduced to 3.2 km, and the computational confidence intervals include the true location.

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