Elastic wave-equation migration for laterally varying isotropic and HTI media

Richard A. Bale and Gary F. Margrave

ABSTRACT

Prestack wave-equation migration of isotropic or anisotropic elastic seismic data is described as vector wavefield extrapolation, plus an imaging condition for combinations of shot and receiver wave-modes. For azimuthally anisotropic data, the effect is to combine the (normally separate) steps of shear-wave splitting correction and migration into a single migration step. This enables a more accurate correction of the shear waves based upon the local propagation direction. The algorithm is extended to laterally varying medium with two different forms of generalized phase shift operators. The first, which we call "phase shift plus adaptive windowing" (PSPAW), is appropriate for anisotropic media described by several parameters. The second, based on conventional phase shift plus interpolation (PSPI), has been formulated for isotropic media, but is computationally intractable for general anisotropic media. In both cases, the spatial interpolation methodology is applied both to the phase shift and to the modal decomposition and recomposition steps.

The PSPAW algorithm has been applied to modelled data, first for a faulted isotropic model, and then for a model with a faulted layer which is transversely isotropic with a horizontal symmetry axis (HTI). The anisotropic elastic migration unravels the effect of shear-wave splitting as a natural consequence, a task which we show isotropic migration fails to do.

The isotropic PSPI algorithm has recently been applied to a new elastic version of the well-known Marmousi model, to test the ability of this algorithm with highly variable media. The preliminary results are encouraging, especially for the shallow imaging of the converted wave data.

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