WELL-TO-WELL (W2W) ELECTROMAGNETIC TOMOGRAPHY MODELING ADVANCEMENT: IMPROVING PRECISION AND EFFECTIVENESS WITH REGULARIZATION

Abstract

This research describes the direct and inverse problems of cross-well electromagnetic tomography. The model geometry has azimuthal symmetry, which simplifies the forward modeling and the inversion procedure. In the direct problem, the finite element method is used in the numerical solution of the Helmholtz equation. In the inverse problem, the study discusses the use of three stabilizer functionals: Global Smoothness (GS), Total Variation (TV), and Absolute Equality (AE). The first uses a smoothing function in the L2 norm, while the latter uses smoothing in the L1 norm, for it accepts abrupt changes between adjacent parameters. The results show that the TV method generated good estimates of both geometry and conductivity of the bodies, both for small and large conductivity contrast between the targets and the surrounding environment. Through the results, one can also observe that the regularization of the Total Variation presented a better estimate of the parameters than the Global Smoothness. In most of the synthetic models used in this work, the best estimates of the proposed model occurred when Absolute Equality constraints were used on the cells at the edges of the inversion grid, in addition to the stabilizer functional.