Amin Bassrei
Instituto de Física/UFBA and CPGG/UFBA

This work has three parts: first, we present a new numerical technique for the solution of geophysical linear ill-posed inverse problems, in the case of discrete data and discrete model parameters. The Landweber’s (1951) algorithm is applied to invert synthetic tomographic data corrupted by noise. When using an iterative algorithm one has to investigate: the existence of a solution, the uniqueness of this solution, the speed of convergence, and the properties of the solution. At this stage we are more interested in the speed of convergence. This "new" iterative method is in general faster than the Algebraic Reconstruction Technique (ART), as showed in the numerical simulations. Second, we apply the Generalized Simulated Annealing (GSA) approach to the inversion of gravity data for 2-D density distributions. The tests with synthetic data (Mundim, Lemaire and Bassrei, 1998) show the promising application of GSA in gravity inversion. The results obtained suggest us that the GSA approach enables to find quickest machines than the two conventional ones (Boltzmann and Cauchy machines). Third, in the solution of inverse problems we are never sure about the validity of the results. In the case of seismic tomography for instance, we cannot guarantee our 2-D or 3-D reconstructed images. We can only be certain in the so called artificial or synthetic examples, where the true model (or image), given by the vector of model parameters m, is known. Based on Barbieri (1974), we have the alternative approach for evaluating the inversion process where the final step is a constant or in fact pseudo-constant image where we can check and observe in what regions of the model the inversion was not successful. We show some simulations with synthetic data in traveltime tomography.