Electromagnetic Forward and Inverse Algorithms for 3-D Through-Casing Induction Mapping of Arbitrary Fractures

Abstract

This letter extends the axisymmetric version of the efficient forward and inverse algorithms to characterize and reconstruct arbitrary 3-D fractures in a cased borehole environment. We improve our previous hybrid distorted Born approximation and stabilized biconjugate gradient fast Fourier transform method as the 3-D forward modeling algorithm that can significantly reduce the computational cost in forward modeling. The bounding constraints and model parameter transformation functions are introduced to our previous axisymmetric variational Born iterative inverse method to effectively reconstruct 3-D fractures. Numerical results show orders of magnitude higher efficiency of the forward algorithm than the finite-element method, and the effectiveness of the inverse algorithm for through-casing 3-D fracture reconstruction.