S‐wave kinematics in acoustic transversely isotropic media with a vertical symmetry axis

Abstract

Acoustic transversely isotropic models are widely used in seismic exploration for P‐wave processing and analysis. In isotropic acoustic media only P‐wave can propagate, while in an acoustic transversely isotropic medium both P and S waves propagate. In this paper, we focus on kinematic properties of S‐wave in acoustic transversely isotropic media. We define new parameters better suited for S‐wave kinematics analysis. We also establish the travel time and relative geometrical spreading equations and analyse their properties. To illustrate the behaviour of the S‐wave in multi‐layered acoustic transversely isotropic media, we define the Dix‐type equations that are different from the ones widely used for the P‐wave propagation.

S‐wave in 2D acoustic transversely isotropic media with a tilted symmetry axis

“…The S‐wave slowness surface equation in acoustic transversely isotropic media with a vertical symmetry axis (acoustic VTI) is given by (Jin and Stovas ) where η is the anellipticity parameter (Alkhalifah and Tsvankin ), p and q are, respectively, the horizontal slowness and vertical slowness in acoustic VTI media. The S‐wave vertical group velocity and normal moveout (NMO) velocity in acoustic VTI media can be defined as where and are P‐wave vertical velocity and NMO velocity in acoustic VTI media, respectively.…”

“…Although the acoustic VTI medium was initially introduced by manually setting the vertical S‐wave phase velocity to be zero (Alkhalifah ), the acoustic VTI medium can be practical from the upscaling point of view. One such practical acoustic VTI medium, taken as the equivalent medium for a stack of finely interlayered plane isotropic solid and fluid layers, was introduced in Appendix D in Jin and Stovas (). Although this is a binary medium, based on the long wave equivalent theory (Backus ), more general practical acoustic VTI media can be obtained for a stack of thin isotropic and/or VTI layers if one or more layers have zero S‐wave vertical phase velocity (Grechka, Zhang and Rector ).…”

“…). Jin and Stovas () defined S‐wave parameters in acoustic VTI media and analysed its kinematic properties.…”

“…This paper is a sequel for the Jin and Stovas () and focus on the kinematics of S‐wave in two‐dimensional (2D) acoustic TTI media. The slowness vector is constrained to be in the vertical plane containing the symmetry axis.…”

Pure P‐ and S‐wave equations in transversely isotropic media

“…The standard used approach, better known as acoustic approximation, is based on setting the vertical shear wave phase velocity to zero (Alkhalifah, 1998, 2000). Despite its reasonable accuracy, the approximation suffers from shear wave artefacts (Grechka et al ., 2004; Jin and Stovas, 2018, 2020). For the S‐wave equations, we cannot exclude vertical P‐wave phase velocity and all anisotropy parameters are needed.…”