Snell's law describes the relationship between phase an-gles and velocities during the reflection or transmission ofwaves. It states that horizontal slowness with respect to an in-terface is preserved during reflection or transmission. Evalu-ation of this relationship at an interface between two isotropicmedia is straightforward. For anisotropic media, it is a com-plicated problem because phase velocity depends on the an-gle; in the anisotropic reflection/transmission problem, nei-ther is known. Solving Snell's law in the anisotropic case re-quires a numerical solution for a sixth-order polynomial. Inaddition to finding the roots, they must be assigned to the cor-rect reflected or transmitted wave type. We show that if theanisotropy is weak, an approximate solution based on first-order perturbation theory can be obtained. This approach per-mits the computation of the full slowness vector and, thereby,the phase velocity and angle. In addition to replacing the needfor solving the sixth-order polynomial, the resulting expres-sions allow us to prescribe the desired reflected or transmittedwave type. The method is best implemented iteratively to in-crease accuracy. The result can be applied to anisotropic me-dia with arbitrary symmetry. It converges toward the weak-anisotropy solution and provides overall good accuracy formedia with weak to moderate anisotropy.
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