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Earthquake location for small networks using the generalized inverse matrix

SEISMOGRAPHIC STATION DEPARTMENT OF GEOLOGY AND GEOPHYSICS UNIVERSITY OF CALIFORNIA, BERKELEY, CALIFORNIA

Abstract

The usual method of earthquake location which minimizes the sum of the squared residuals fails when the number of known arrival times is less than the number of location parameters. A generalized inverse matrix A exists which yields a solution Ab of minimum Euclidean length to the condition equations Ax = b. (This situation often arises in geodesy.) Because the rank of A equals the number of rows, which is one less than the number of columns, the computation of the appropriate A is very simple for only three stations. A worked example is given for the relocation of the trial position of an explosion using two stations.

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