For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. Critical‐angle phenomena are described naturally by this approach. The reflection coefficient at grazing incidence is shown to be unity, as in the isotropic case. In particular, it is shown that the incident wave vector for grazing incidence may be greater or less than 90°: The domain of incident wave‐vector angles can actually split into disjoint pieces. It is much more natural to consider intensity–conversion ratios, rather than amplitude–conversion ratios, showing the important role of ray (rather than wave‐vector) directions in describing phenomena such as grazing angles. Energy conversion coefficients are shown to satisfy reciprocity relations which are formulated. General features of the numerical results are discussed. Consideration of wave propagation in an acoustic‐axis direction is included in the general algorithm, so results can be obtained both generally and for planes of symmetry, including planes of isotropy. Christoffel equations and boundary conditions for both anisotropic media in coordinate systems formed by incident and interface planes, rather than in crystallographic coordinates, are considered. This algorithm could be used in seismic processing, migration, and inversion of seismic data in anisotropic media.Ī unified approach to the study of reflection and refraction of elastic waves in general anisotropic media is presented. We have tested this algorithm in some of the most computationally difficult models to ensure there is no energy leakage in the system of calculations. With this information, the algorithm solves system of equations incorporating the imposed boundary conditions to arrive at the scattered wave amplitudes. Second, the algorithm determines the reflection and transmission angles of all of the possible scattered modes followed by their respective velocities and polarization vectors. In the first step, the plane-wave velocities and polarizations of all three orthogonal wave modes are calculated for a given incidence angle. To achieve this, the algorithm solves for polarization, amplitude and slowness of all the wave modes generated by a plane wave incident to the interface. This algorithm has been written to extend these capabilities to the general case of reflectivity from the interface between two anisotropic slabs of arbitrary symmetry and orientation. To date, these issues have been ameliorated by using approximations to the full solutions for wave propagation and reflectivity for special material symmetries. Elastic anisotropy in the Earth causes many artifacts in an isotropic seismic processing and interpretation.
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