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Harmonic decomposition of the anisotropic elastic tensor
R Baerheim and K Helbig Decomposition of the anisotropic
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2nd rank tensors anisotropic elastic tensor anisotropy axes axes axes Backus calculated classiﬁcation coefficients corresponding Cowin cubic symmetry decomposed deﬁned deﬁnition degree q deviation deviatoric diagonal dimension eigenvalues eigenvectors elastic components elastic constants equal to zero equation Exploration Geophysics expressed ﬁnd ﬁrst ﬁve fourth rank tensor Geophysical harmonic decomposition harmonic polynomial harmonic tensors Helbig hexagonal symmetry hierarchically symmetric tensor higher symmetry homogeneous polynomial ideal symmetry isotropic symmetry linear combination magnitude matrix Maxwell multipoles Mehrabadi non-totally symmetric norm number of independent orthonormal orthorhombic orthorhombic symmetry parallel perturbation polynomial of degree rank four rank harmonic tensor representation roots rotation scalars second-order tensor space directions speciﬁc Spherical Harmonics sum-vectors symm symmetry axis symmetry coordinate system symmetry plane tensor of order tensor of rank tensoren tensors derived tetragonal theory totally symmetric tensor traceless triclinic trigonal unique unit vectors vanish vector space wordt z-axis zijn