Tomografia eletromagnética poço-a-poço usando os reguladores de suavidade global e de variação total

Abstract

In this work, we describe the forward and inverse problems of Crosswell electromagnetic tomography. The model geometry has azimuthal symmetry, which significantly simplifies both the forward modeling and the inversion processing, reducing a 3-D tensor equation to a scalar two-dimensional form. In the forward problem we use the finite element method for the numerical solution of the Helmholtz equation. In the inverse problem, we discuss the use of three stabilizing functionals: Global smoothness (GS), Total Variation (TV), and Absolute Equality (AI). The first one uses a smoothing function on L2 norm, while the second uses smoothing on the L1 norm, which accepts abrupt changes between adjacent parameters. Our results show that the use the TV method generated good estimates of the geometry and conductivity of bodies, both for small and for large conductivity contrasts between the targets and the surrounding environment. We also note that the Total Variation regularization showed a better estimate of the parameters, compared to Global Smoothness. In most of the synthetic models used in this work, we obtained a better estimate of the bodies when we used Absolute Equality constraints to the cells at the edges of the inversion grid, in addition to the stabilizing functionals.