Greenhalgh, S.Mason, I.Zhou, B.2006-12-042006-12-042005Journal of Geophysics and Engineering, 2005; 2(1):8-151742-21321742-2140http://hdl.handle.net/2440/17879Copyright © 2005 Nanjing Institute of Geophysical ProspectingTriaxial 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. For the case of a perfectly polarized monochromatic signal, we interpret this to mean that the particle trajectory can only be elliptical. It seems as though particles can only move in a plane: they cannot move in three dimensions. In practice, the signal is made up of a band of frequencies, there are multiple arrivals in the time window of interest, and noise is invariably present, which causes the ellipse to wobble in a 3D orbit. Explicit analytical expressions are derived in this paper to yield the eigenvalues and eigenvectors of the coherency matrix in terms of the triaxial signal amplitudes and phases.encoherency matrixdirection findingeigenanalysismulti-component seismologyJournal article002005061110.1088/1742-2132/2/1/0020002288192000022-s2.0-2414449527654917