23 September 1994 Generalized radon transform/amplitude versus angle (GRT/AVA) migration/inversion in anisotropic media
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Abstract
We investigate the inversion of seismic data for the recovery of combinations of elastic parameters. The theory is based on a single scattering and a high-frequency (stationary phase) approximation and maps the most singular part of the wave field onto the most singular part of the medium within this approximation. In this framework, it is assumed that the smooth constituents of the medium are known. Three asymptotic parameters play a role, one for propagation in the background medium, one for scattering in the medium perturbation, and one describing the smoothness of the medium perturbation itself. A procedure concerning what combinations of parameters can be determined given an acquisition geometry is discussed. The zero-offset case in particular simplifies the expressions but allows only one parameter to be reconstructed. We find that in anisotropic media we are forced to follow a `generalized' inverse approach, which we implement through a singular-value decomposition. Finally, we mention a simplification which is based on a micro-local analysis. Assuming that the medium jumps in a single direction only, and assuming that the associated dip can be estimated separately, the theory becomes essentially 1D and the inversion procedure reduces to an AVA analysis.
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Maarten V. de Hoop, Robert Burridge, Carl Spencer, Douglas Miller, "Generalized radon transform/amplitude versus angle (GRT/AVA) migration/inversion in anisotropic media", Proc. SPIE 2301, Mathematical Methods in Geophysical Imaging II, (23 September 1994); doi: 10.1117/12.187482; https://doi.org/10.1117/12.187482
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