Linearized quantities in T.I. media

P. F. Daley

ABSTRACT

When describing transversely isotropic (T.I.) media it has become common to use, apart from reference qP and qS V velocities, α and β, the two parameters, ε and δ, to account for the deviation of the coupled qP and qS V modes of wave propagation from the isotropic case. The prefix "q" denotes "quasi", and is used to distinguish anisotropic from isotropic media as different inherent concepts, not explicitly obvious in the isotropic case, are required to be addressed when dealing with anisotropic media of any degree of complexity. The dimensionless quantity, ε, is a measure of the ellipticity of the qP wavefront and δ, the "strange" parameter, is employed as a measure of deviation of the qP wavefront or slowness surface from the ellipsoidal and also of the qS V wavefront or slowness surface from the spherical. As the parameter, δ, has been described in the literature as "conceptually inaccessible", it would seem a logical progression to attempt to determine an alternative parameterization in physically realizable quantities. It is that topic which is dealt with in this note. The linearized qP and qS V phase (wavefront normal) velocities and the linearized PP and S V S V reflection coefficients to first order accuracy at an interface between two T.I. media are examined in this regard. The solution proposed involves a simple reorganizing of terms in the linearized expressions for the two phase velocities and reflection coefficients resulting from the introduction of the parameter σ. This quantity is used in a modified form here compared with that used by other authors, usually when discussing qS V wave propagation in a T.I. medium.

The parameterization of this media type in (ε, σ ) rather than (ε ,δ ) is transparent from a numerical perspective as little if any changes would be required in any related software.

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