Confidence regions and error determinations for seismic event location

Abstract

A digital computer program has been written to locate seismic events and to determine the standard errors and joint confidence regions for the focal coordinates. Modified Jeffreys‐Bullen travel times are used, with surface focus travel times based on Nevada explosions. Results for eleven nuclear explosions in Nevada show a mean computed depth of focus of 39 ± 2 km. For these events, the displacement of the computed epicenter from the known epicenter is less than 20 km for all but three explosions when the Jeffreys‐Bullen travel times are used. The epicenter displacement is less than 15 km for all but the same three explosions when surface focus travel times are used. Linearized joint confidence regions for latitude and longitude were computed for all events; for all the Nevada explosions the semimajor axis of the 75% confidence region was less than 14 km. Exact confidence regions can be constructed for the focal coordinates. In a small neighborhood of the computed epicenter (10 to 20 km being sufficiently small), the linearized confidence region has the same statistical behavior as the exact confidence region. The axis ratio and orientation of the confidence region for latitude and longitude depends only on the distribution of the stations in distance and azimuth around the epicenter; the size of the confidence region depends also on the station residuals and the confidence level required. A quality factor for station distribution, varying between zero and unity, can be used to measure the capability of a given station network with respect to a given epicenter. This quality factor is related to the generalized variance of the estimates of focal coordinates. The statistical model used for earthquake location can be modified in several ways to take into account station time corrections, regional time corrections, travel time bias, etc., without basically altering the procedure for computing the confidence regions.