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.

Recently, a new kind of sensor applicable in magnetoencephalography (MEG) has been presented: a solid-state yttrium-iron garnet magnetometer (YIGM). The feasibility of yttrium-iron garnet magnetometers (YIGMs) was demonstrated in an alpha-rhythm registration experiment. In this paper, we propose the analysis of lead-field matrices for different possible multi-channel on-scalp sensor layouts using YIGMs with respect to information theory. Real noise levels of the new sensor were used to compute signal-to-noise ratio (SNR) and total information capacity (TiC), and compared with corresponding metrics that can be obtained with well-established MEG systems based on superconducting quantum interference devices (SQUIDs) and optically pumped magnetometers (OPMs). The results showed that due to YIGMs’ proximity to the subject’s scalp, they outperform SQUIDs and OPMs at their respective noise levels in terms of SNR and TiC. However, the current noise levels of YIGM sensors are unfortunately insufficient for constructing a multichannel YIG-MEG system. This simulation study provides insight into the direction for further development of YIGM sensors to create a multi-channel MEG system, namely, by decreasing the noise levels of sensors.

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.

SUMMARY: The finite-element (FE) method is one of the most powerful numerical techniques for modelling 3-D electromagnetic fields. At the same time, there still exists the problem of efficient and economical solution of the respective system of FE equations in the frequency domain. In this paper, we concentrate on modelling with adapted hexahedral or logically rectangular grids. These grids are easy to generate, yet they are flexible enough to incorporate real topography and seismic horizons. The goal of this work is to show how a finite-difference (FD) solver can be used as a pre-conditioner for hexahedral FE modelling. Applying the lowest order Nédélec elements, we present a novel pre-conditioned iterative solver for the arising system of linear equations that combines an FD solver and simple smoothing procedure. The particular FD solver that we use relies on the implicit factorization of the horizontally layered earth matrix. We assessed runtime and accuracy of the presented approach on synthetic and real resistivity models (topography of the Black Sea continental slope). We further compared performance of our program versus publicly available Mare2DEM, ModEM and MUMPS programs/libraries. Our examples involve plane-wave and controlled source modelling. The numerical examples demonstrate that the presented approach is fast and robust for models with moderate contrast, supports highly deformed cells, and is quite memory-economical.