Abstract

The method of estimating coverage ellipses on epicenters is now often modified to try and allow for possible epicenter bias. Usually this is done by replacing the a priori variance of the measurement error used to calculate such ellipses by an a priori variance that is the sum of two variances, one for measurement error and the other for travel-time error. This procedure cannot work; the only statistical quantity in epicenter estimation is measurement error. All that a coverage ellipse can specify (for a given level of probability) is the precision of the estimate: that is the area within which the estimated epicenters of a series of earthquakes or explosions will lie, for a given source region, station network, and size of measurement error. Correcting for the bias turns the ellipse into a measure of accuracy, rather than precision, with the orientation and area unchanged. The differences between precision and accuracy are illustrated here with the epicenters estimated by Myers and Schultz. The results obtained suggest that the precision of the biased epicenters and the effectiveness of the bias corrections derived by Myers and Schultz are better than claimed in their article.

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