Reflection and transmission coefficients in TI media: exact and linearized phase velocities, eikonals and polarization vectors

P.F. Daley and E.S. Krebes and Laurence R. Lines

ABSTRACT

Reflection and transmission coefficients which partition energy due to plane wave incidence at the interface between two transversely isotropic (TI ) media are considered. The basic forms of these coefficients employed use expressions for certain quantities that may be classified as either exact or linearized. Phase velocities and the related slowness vectors, as well as the polarization vectors for the incident and the four possible reflected or transmitted wave types, are investigated for both levels of accuracy mentioned above. Computed results for these precision types should be compared graphically for what has been termed weak anisotropy (WA ) . However, liberties will be taken and at least one of the media will be chosen to be strongly anisotropic, to determine the possible limits of the degree of anisotropy which may be considered without a major compromise of results. The results suggest that the degree of anisotropy, for which the linearized quantities are assumed to provide reasonably accurate results, may be larger than that typically associated with "weakly anisotropic" media. A full sensitivity study is not done here as the prime motivation for this work was to develop the linearized formulation of reflection and transmission coefficients, given that the exact solutions are known. This is one of the motivations for undertaking this study, as a linearized algorithm to determine reflection and transmission coefficients for more complex anisotropic media is a future objective.

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