Errata: Reflection and transmission coefficients in T.I. media
P. F. Daley
As the two papers that will be dealt with here, Daley and Hron (1977) [paper 1] and Graebner (1992) [paper 2], involve essentially the same topic, placement of typographical and other errors within these papers in a common location would seem appropriate. Both papers deal with particle displacement reflection and transmission coefficients at a solid/solid interface between two transversely isotropic (T.I.) media. The axes of rotational invariance in both the upper (1) and lower (2) media, separated by a plane interface, are aligned perpendicular to the plane interface.
The paper by Daley and Hron (1977) was written both to obtain reflection and transmission coefficients for this medium type for a fairly specific purpose and to show that plan-wave coefficients are associated with the zero-order approximation of an infinite asymptotic series. The 1992 paper published by Graebner, presents a much more general and possibly useful plane-wave approximation for the reflection and transmission coefficients in terms of the horizontal slowness, p, in a manner similar to those derived for isotropic media by Aki and Richards (1980). No analytic expressions for individual coefficients are given in paper 2 for the solid/solid case. Rather, the problem is set up in a manner to be solved by numerical methods using block partitioning of the original 4x4 matrix. This allows the generally complex value of a specified coefficient of the 16 possible reflection and transmission coefficients at this type of interface to be obtained over a range of slownesses.
In this report, apart from correcting the typographic errors in paper 1, the derivation of the polarization vectors in a T.I. in paper 2 will be re-examined.