Entropia de Tsallis aplicada à inversão sísmica

Abstract

The growing global energy demand has increasingly demanded resources from oil, in this sense, the “easy exploration and production” reservoirs are running out. This has led to numerous studies that make it possible to remedy these deficiencies. Companies in the oil sector have invested in techniques that help in locating and drilling wells. One of the techniques used in oil exploration is post-stacking inversion. Here we study the role of Tsallis' generalized statistics in the inverse problem theory. This method is formulated as an optimization problem that aims to estimate the physical subsurface methods from indirect and partial permissions. In conventional approaches, the misfit function that will be minimized is based on the distance of the least squares between real data and modeled data, assuming that the noises follow a Gaussian distribution, however, in many real situations this does not happen and the error is usually non-Gaussian, which makes this technique fail. Our work studied the misfit function based on non-Gaussian distributions. The Gaussian 𝑞-distribution associated with the Maximum Entropy Principle in Tsallis' formalism. We propose and test our method on an inverse geophysical data problem, the post-stack inversion (PSI), which aims to estimate subsurface reflectivity (physical parameter) and results show that our method (𝑞-PSI) surpasses the conventional PSI, especially with noisy non-Gaussian data.