Structural constraints for image-based inversion methods

Abstract

This thesis presents two methodologies of structural regularization for Wave-Equation Migration Velocity Analysis and Joint Migration Inversion: cross-gradient regularization and filtering with morphological operators. In Wave-Equation Migration Velocity Analysis, the cross-gradient regularization aims to constrain the velocity contrasts with the reflectivity map by parallelization of the velocity gradient vector and the image gradient vector. We propose a version with cross-gradient of the objective functions: Differential Semblance, Stack Power and Partial Stack Power. We combine the Partial Stack Power with its version of cross-gradient, in order to gradually increase the resolution of the velocity model without compromising the adjustment of the long wavelengths of the velocity model. In Joint Migration Inversion, we propose to apply morphological operators of erosion and dilation in the preconditioning of the velocity model in each iteration. Operators use the reflectivity map to mark the regions with the same value of physical property. They homogenize the geological layer and accentuate the velocity contrast at the edges. Structural constraints do not only reduce the ambiguity in estimating a velocity model, but also make the migration/inversion methods more stable, reducing artifacts, delineating geologically plausible solutions, and accelerating the convergence of the objective function.