Barbieri Criterion for Solution Appraisal in Geophysical Diffraction Tomography

Abstract

Diffraction tomography provides a high resolution velocity image from the region under study. Because it is a type of ill-conditioned inverse problem, diffraction tomography requires some kind of regularization, such as regularization by derivative matrices. Quantitative or qualitative criteria for the solution appraisal of inverse problems are just as important as the solution itself. An effective criterion is the Barbieri approach, which is the main scope in this study. It is implemented in three steps: (i) the estimated model obtained through the inversion of the observed data (scattered acoustic field); (ii) a second inversion, this time of the complementary observed data which provides the complementary estimated model; (iii) the sum of the estimated model and complementary estimated model. If the inversion is exact, this sum must be a constant value for the whole vector. If this does not occur, the sum image indicates that the inversion was not satisfactory (quantitative effect) and in which regions the estimated model was not well recovered (qualitative effect). Simulations were performed on two synthetic models, one with well-to-well geometry and the other with surface seismics geometry. The results, confronted with the RMS deviation between the estimated and the true model, validated the use of the Barbieri criterion in diffraction tomography.