Astronomy and Astrophysics – Astronomy
Scientific paper
Jul 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007geoji.170..468z&link_type=abstract
Geophysical Journal International, Volume 170, Issue 1, pp. 468-478.
Astronomy and Astrophysics
Astronomy
Qp Wave, Symmetry Plane, The Voigt And Dilatational Matrices, Wa Parameters, Weak Anisotropy
Scientific paper
A procedure is proposed to obtain symmetry properties of weakly anisotropic (WA) elastic media by giving 15 WA parameters of qP wave in an arbitrary Cartesian coordinate system. The 15 WA parameters, which linearly depend on 21 elastic elements, form a complete set to determine the symmetry planes in WA materials. The procedure is based on the eigenvalue problems of two matrices. One of the matrices consists of the Voigt and dilatational matrices, and the other is an acoustic tensor defined by an irreducible, completely symmetric and traceless, fourth-rank tensor resulting from decomposition of the fourth-rank elastic tensor. If the eigenvectors are taken as the axes of a new coordinate system (called symmetry Cartesian coordinate system), the transformation of WA parameters from an arbitrary Cartesian coordinate system to a symmetry Cartesian coordinate system can reduce the number of distinct WA parameters of elastic materials except in triclinic medium.
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