SUMMARY: This paper presents a feasibility study of using the controlled-source frequency-domain electromagnetic (CSEM) method in mineral exploration. The method has been widely applied for offshore hydrocarbon exploration; however, nowadays this method is rarely used on land. In order to conduct this study, we have developed a fully parallelized forward modelling finite-difference (FD) code based on the iterative solver with contraction-operator preconditioner. The regularized inversion algorithm uses the Gauss–Newton method to minimize the Tikhonov parametric functional with the Laplacian-type stabilizer. A 3-D parallel inversion code, based on the iterative finite-difference solver with the contraction-operator preconditioner, has been evaluated for the solution of the large-scale inverse problems. Using the computer simulation for a synthetic model of Sukhoi Log gold deposit, we have compared the CSEM method with the conventional direct current sounding and the CSEM survey with a single remote transmitter. Our results suggest that, a properly designed electromagnetic survey together with modern 3-D inversion could provide detailed information about the geoelectrical structure of the mineral deposit.

We propose an approach and the numerical algorithm for mapping the electroencephalographic (EEG) data from the scalp to the cortex. The algorithm is based on the solution of ill-posed Cauchy problem for the Laplace’s equation using tetrahedral finite elements. The FEM-based scheme allows to calculate the volumetric distribution of a potential over the head volume. We demonstrate the usage of the the algorithm for accurate estimation of the depth of electric sources in the head. The algorithm sufficiently increases the spatial resolution of the EEG technique making it comparable with intracranial techniques.

For interpretation of electroencephalography (EEG) and magnetoencephalography (MEG) data, multiple solutions of the respective forward problems are needed. In this paper, we assess performance of the mixed-hybrid finite element method (MHFEM) applied to EEG and MEG modeling. The method provides an approximate potential and induced currents and results in a system with a positive semi-definite matrix. The system thus can be solved with a variety of standard methods (e.g. the preconditioned conjugate gradient method). The induced currents satisfy discrete charge conservation law making the method conservative. We studied its performance on unstructured tetrahedral grids for a layered spherical head model as well as a realistic head model. We also compared its accuracy versus the conventional nodal finite element method (P1 FEM). To avoid modeling singular sources, we completed our computations with a subtraction approach; the derived expression for the MEG response different from earlier published and involves integration of finite quantities only. We conclude that although the MHFEM is more computationally demanding than the P1 FEM, its use is justified for EEG and MEG modeling on low-resolution head models where P1 FEM loses accuracy.