Extensão do critério de Barbieri em tomografia de tempos de trânsito não-linear.

Abstract

This work offers two methods to evaluate the quality of traveltime tomography with regularization by derivative matrices and also to improve velocity models. Both methods are based on Barbieri's work, originally developed in medical tomography. The first, Barbieri Criterion (BC), considers forward modeling by straight rays, while the second one, Modified Barbieri Criterion (MBC), is ruled by Fermat's principle. Both use filtering by singular value decomposition to suppress dominant eigenimages by assuming that inversion algorithm errors are randomly located. Simulations with synthetic data showed that both methods had improved the solution in model RMS sense, even if high Gaussian noise was added to data. In general, MBC requires greater regularization than standard inversion. When applied to real data from Dom João Field, Recôncavo Basin, both methods had recovered similar models and with a higher resolution than the standard approach. Real data results were validated by seismic reflection data. Forward modeling was performed by ray tracing, based on analytical solution for differential ray equation, and by graphs, which is a simple application of Fermat's principle. Graph modeling proved to be superior as it always links sources and receivers regardless of velocity model. Numerical inversion was performed by generalized inverse and by a conjugate gradient method, which presented a lower computational cost without losing quality. Solution was stabilized by regularization by derivative matrices. Regularization factors were selected by L-curve and sine-Theta-curve, the latter developed in this work as an extension to the former, or by generalized cross-validation.