Reflection and transmission coefficients at the interface between two transversely isotropic media (Matlab software)

P.F. Daley

ABSTRACT

Derivations and related closed form expressions for reflection and transmission coefficients at the interface between two transversely isotropic (TI) media have been available in the literature for several decades. However, the progression from a set of equations to software that produces accurate results is often less obvious than might be expected. This is true for this problem as there are a number of related or ancillary inconveniences related to the original problem that must be addressed. These require either extensive algebraic manipulations or the development of numerical algorithms that deal with the additional points. These are supplemented by typographic errors which may be present in the original works as well as having to acquire an appreciation of at least the basic concepts of wave propagation in an anisotropic medium. This report discusses the use of software for the numerical computation and graphical display of the reflection and transmission coefficients for the media type indicated above using the Matlab programming language. The procedure is initially presented at a fairly basic level for the computation and graphical presentation of the generally complex valued coefficients (amplitude and phase versus incident phase angle). Other options are available to display the coefficients versus the reflected or transmitted phase angle, or the horizontal component of the slowness vector or the incident and reflected or transmitted group angles.

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