Imaging by wave-equation inversion.

摘要

Wave-equation inversion is a powerful technique able to build clean images with balanced amplitudes in complex subsurface areas relative to migration alone. The main contribution of this thesis is perform wave-equation inversion in image space without making any velocity model or acquisition geometry approximations. The method explicitly computes the least-squares Hessian matrix, defined from the modeling/migration operators, and uses an iterative solver to find the solution of the resulting system of equations. This technique is also 3-D, as it can handle 3-D data in a target-oriented fashion. This allows the method to improve the image where it is more important: in the neighborhood of the reservoir.; The Hessian matrix contains more information than just the amplitude of the diagonal elements; its rows are the point spread functions (PSFs) of the imaging system. In seismic imaging, the PSFs are non-stationary, due to the velocity model complexity, and the limited acquisition geometry. To make wave-equation inversion practical, I optimized the computation of the Hessian by taking advantage of the sparsity and structure of the matrix, the acquisition geometry, and the necessary frequency sampling. As a result, the computational savings can be of five orders of magnitude or grater compared to a direct implementation.; Wave-equation inversion in the presence of a complex overburden leads to an ill-conditioned system of equations that needs to be regularized to obtain a stable numerical solution. Regularization can be implemented in the poststack image-domain (zero subsurface offset), where the options for a regularization operator are limited to a customary damping, or in the prestack image-domain (subsurface offset), where a physically-inspired regularization operator (differential semblance) can be applied. Though the prestack image-domain inversion is more expensive than the poststack image-domain inversion, it can improve the reflectors continuity into the shadow zones with an enhanced signal-to-noise ratio. I demonstrate the utility of both these methods by improving the subsalt-sediment images of the Sigsbee2B synthetic and a 3-D Gulf of Mexico field data set.