Linearity, resolution, and covariance in GRT inversions for anisotropic elastic moduli

Carl Spencer; Maarten V. de Hoop; Robert Burridge

doi:10.1117/12.218491

1 September 1995 Linearity, resolution, and covariance in GRT inversions for anisotropic elastic moduli

Carl Spencer, Maarten V. de Hoop, Robert Burridge

Proceedings Volume 2571, Mathematical Methods in Geophysical Imaging III; (1995) https://doi.org/10.1117/12.218491
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

This paper is concerned with the linearized inversion of elastic wave data using the Generalized Radon Transformation to give anisotropic medium parameters. Assumptions of linearity are examined by comparing linearized reflection coefficients calculated using the Born approximation with full plane-wave reflection coefficients. In typical sand/shale models we have found that the linearity assumption is valid only to approximately 60 degrees from the normal. Linear dependencies between the scattering patterns produced by individual moduli result in an ill-posed inverse problem. Utilizing P-wave data, we find that for the Transversely Isotropic case similarities in the C₅₅ and C₁₃ scattering directivity mean that they cannot be distinguished. C₁₁ is best observed at wide-angle and hence estimates made using limited aperture data are subject to large error. Quasi-Monte Carlo techniques are adapted to carry out the 4D inversion integral.

Citation Download Citation

Carl Spencer, Maarten V. de Hoop, and Robert Burridge "Linearity, resolution, and covariance in GRT inversions for anisotropic elastic moduli", Proc. SPIE 2571, Mathematical Methods in Geophysical Imaging III, (1 September 1995); https://doi.org/10.1117/12.218491

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