PS reflection moveout in a homogeneous anisotropic layer of arbitrary symmetry and tilt

Abstract

Use of unconverted reflected PP waves leads to moveout formulae, which relate the moveout to only a limited number of parameters specifying anisotropy. Use of converted reflected PS waves extends the number of parameters to, generally, a complete set of twenty-one parameters. It leads, on the other hand, to more complicated formulae and phenomena unknown from studies of unconverted PP waves. In anisotropic media one has to deal with the existence of two S waves and their singularities, acoustic approximation cannot be used. We present and test approximate formulae for the reflection moveout of PS waves converted at a horizontal reflector underlying a homogeneous layer of arbitrary anisotropy symmetry and orientation. For their derivation, we use the combination of weak-anisotropy approximation and A-parameters specifying anisotropy. The complete set of twenty-one A-parameters represents an alternative to twenty-one independent elements of the stiffness tensor. In addition to the moveout formulae for separate PS1 and PS2 waves, we also present moveout formula for a P to common S wave whose traveltimes represent an average of traveltimes of PS1 and PS2 waves. Use of the P to common S wave reflection leads to several simplifications. Presented tests indicate that for most offsets and models with P-wave anisotropy up-to to 26% and S-wave anisotropy over 25%, the relative traveltime errors do not exceed 2.5%.