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Bulletin of the Seismological Society of America; February 1980; v. 70; no. 1; p. 149-170
© 1980 Seismological Society of America
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A probability model for regional focal mechanism solutions

D. R. BRILLINGER, A. UDIAS and B. A. BOLT

DEPARTMENT OF STATISTICS UNIVERSITY OF CALIFORNIA, BERKELEY, CALIFORNIA
CATEDRA DE GEOFISICA FACULTAD DE C. FISICAS UNIVERSIDAD COMPLUTENSE DE MADRID, MADRID 3, Spain
SEISMOGRAPHIC STATIONS UNIVERSITY OF CALIFORNIA, BERKELEY, CALIFORNIA

Abstract

The increase in the number of determinations of fault-plane solutions and their use for inferences on regional and local tectonics and stress fields makes it advisable to treat them in a standard way in groups on a regional basis. Probability models for joint group estimation of the shear dislocations, involving data from I earthquakes and J observations of the same region, are presented. The general model gives the probability {pi}ij of reading a compression (Yij = 1) for the P wave from event i at station j as

Formula
where {gamma} and {rho} are precision parameters and {Phi} is the normal cumulative.

This probability depends on Aij ({theta}), the theoretical amplitudes from a particular orientation of the greatest and least axes of principal stress for the regional solution. Estimates of the principal stress axes T and P and their variances are computed by constructing a loss function based on the likelihood. The algorithm allows for the estimation of a mean regional solution and one for each event. A treatment of measures of fit and the winnowing of clusters of solutions is given. The resulting program has been applied to the determination of the regional solution and exceptional mechanisms for the main shock and 25 aftershocks of the great 1964 Alaskan earthquake and 19 small earthquakes in Bear Valley, California.




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