Elastic wavefield extrapolation in HTI media

Richard A. Bale and Gary F. Margrave

ABSTRACT

A wavefield extrapolation operator for elastic anisotropic media can be constructed from solutions of the one-way elastic-wave equation, solutions which are related to those of the Kelvin-Christoffel equation. Aside from an initial decomposition, which depends upon boundary conditions, the extrapolation is simply described by two matrix operations. The first, a diagonal matrix, applies the phase shift for each of the three elastic modes, P, S1 and S2. The second, a 3-by-3 "interface-propagator" matrix, describes the effects of crossing depth interfaces with changes in medium properties. These are sub-matrices of the general propagator matrices, conventionally used for two-way wavefield propagation. The interface-propagator matrix includes all forward-scattered mode-conversions in its full form. It can be modified in the extrapolation algorithm to select only those conversions of interest. In particular we consider the selection of only those conversions between shear-wave modes S1 and S2 which describe the onset of HTI type anisotropy. The result is an extrapolator which performs the equivalent of an Alford rotation valid at all angles of propagation. We consider two possible boundary conditions, one corresponding to a stress-free surface, and the other an infinite half-space.

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