A nonlinear inversion method for 3D electromagnetic imaging using adjoint fields

Electromagnetic imaging is modelled as an inverse problem for the 3D system of Maxwell's equations of which the isotropic conductivity distribution in the domain of interest has to be reconstructed. The main application we have in mind is the monitoring of conducting contaminant plumes out of surface and borehole electromagnetic imaging data. The essential feature of the method developed here is the use of adjoint fields for the reconstruction task, combined with a splitting of the data into smaller groups which define subproblems of the inversion problem. The method works iteratively, and can be considered as a nonlinear generalization of the algebraic reconstruction technique in x-ray tomography. Starting out from some initial guess for the conductivity distribution, an update for this guess is computed by solving one forward and one adjoint problem of the 3D Maxwell system at a time. Numerical experiments are performed for a layered background medium in which one or two localized (3D) inclusions are immersed. These have to be monitored out of surface to borehole and cross-borehole electromagnetic data. We show that the algorithm is able to recover a single inclusion in the earth which has high contrast to the background, and to distinguish between two separated inclusions in the earth given certain borehole geometries.