ZZ Resistivity Imaging Pty. Ltd.

An analytical treatment of single station triaxial seismic direction finding

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Triaxial seismic direction finding can be performed by eigenanalysis of the complex coherency matrix (or cross power matrix). By splitting the symmetric Hermitian coherency matrix C to D + E (where det(E) = 0 and D is diagonal), we shift unpolarized (or inter-channel uncorrelated) data into D and then E becomes 'random noise free'. Without placing any restrictions on the signal set—P, S, Rayleigh—matrix E has only one non-zero eigenvalue (at least for the case of a single mode arriving from a single direction). But for real data (polychromatic transients with correlated noise), it will have two non-zero eigenvalues. By rotating one axis of the triaxial geophone recorded signals to lie normal to the principal eigenvector, it is possible to reduce the coherency matrix from a 3 × 3 to a 2 × 2 matrix...

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