Three-Dimensional Electromagnetic Modelling and Inversion from Theory to Application

• Published in: Surveys in geophysics Vol. 26; no. 6; pp. 767 - 799
• Main Author: Avdeev, Dmitry B.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.11.2005
• Subjects: Aquatic reptiles; Computation; Electromagnetic induction; Equations; Finite difference method; Integral equations; Inverse problems; Inversion; Linear equations; Mathematical models; Modelling; Optimization; Preconditioning; Studies; Three dimensional models
• ISSN: 0169-3298; 1573-0956
• DOI: 10.1007/s10712-005-1836-x

The whole subject of three-dimensional (3-D) electromagnetic (EM) modelling and inversion has experienced a tremendous progress in the last decade. Accordingly there is an increased need for reviewing the recent, and not so recent, achievements in the field. In the first part of this review paper I consider the finite-difference, finite-element and integral equation approaches that are presently applied for the rigorous numerical solution of fully 3-D EM forward problems. I mention the merits and drawbacks of these approaches, and focus on the most essential aspects of numerical implementations, such as preconditioning and solving the resulting systems of linear equations. I refer to some of the most advanced, state-of-the-art, solvers that are today available for such important geophysical applications as induction logging, airborne and controlled-source EM, magnetotellurics, and global induction studies. Then, in the second part of the paper, I review some of the methods that are commonly used to solve 3-D EM inverse problems and analyse current implementations of the methods available. In particular, I also address the important aspects of nonlinear Newton-type optimisation techniques and computation of gradients and sensitivities associated with these problems.