Source Current Density Distribution Research Articles

Combining Electrical Resistivity, Induced Polarization, and Self-Potential for a Better Detection of Ore Bodies

Electrical resistivity (ER), induced polarization (IP), and self-potential (SP) are three geophysical methods that have been broadly used in the realm of mineral exploration. These geophysical methods provide complementary information, each exhibiting a distinct sensitivity to various types of mineral deposits. Considering the relationship among these three methods, we propose an integrated approach that merges their respective information to offer an improved localization technique for ore bodies. First, we invert the electrical conductivity distribution through electrical resistance tomography (ERT). Then, we use the inverted conductivity distribution to invert the IP and SP data in terms of chargeability and source current density distributions. Then, we normalize the inverted chargeability and source current density distributions and we combine them to obtain an ore body index (ORI) χ used to delineate the potential locations of ore deposits. We design this index to be sensitive to the presence of ore bodies, which are reflected by either strong and localized source current density (SP) and/or strong chargeability values (IP). The proposed method is first validated using a synthetic model with two distinct anomalies characterized by different properties. The results show the limitation of individual inversion, as each method exclusively detects one of these anomalies. The combined approach allows a better characterization of the target. Then, the approach is applied to a sandbox experiment in which two metallic bodies are buried in water-saturated sand used as the background. Again, the proposed methodology is successfully applied to the detection of the metallic targets, improving their localization compared with individual methods.

Thunderstorm generators operating as voltage sources in global electric circuit models

The description of global electric circuit (GEC) generators in continuous numerical models is analysed and discussed. It is shown that voltage-source generators, sometimes employed in simple lumped-element GEC models, have a consistent generalisation in continuous GEC models: just as current-source generators generalise to source current density distributions, voltage-source generators generalise to distributions of the relative potential on cloud boundaries. The difference between non-ideal and ideal current or voltage sources is investigated for both lumped-element and continuous GEC models. As in modern three-dimensional GEC models the formal generalisation of voltage-source thunderstorms turns out to be difficult to implement, two alternative approaches involving the replacement of voltage-source generators with equivalent current-source generators are developed. One approach is based upon a rough estimation of the source current producing the same contribution to the GEC as the original voltage source; the other approach uses the fact that each voltage-source generator can be shown to be a limiting case of a certain current-source generator with increased conductivity. For the first time voltage-source generators are implemented in a numerical GEC model (using both the direct generalisation and the suggested alternative approaches).

Induced polarization response of porous media with metallic particles — Part 3: A new approach to time-domain induced polarization tomography

The secondary voltage associated with time-domain induced polarization data of disseminated metallic particles (such as pyrite and magnetite) in a porous material can be treated as a transient self-potential problem. This self-potential field is associated with the generation of a secondary-source current density. This source current density is proportional to the gradient of the chemical potentials of the [Formula: see text]- and [Formula: see text]-charge carriers in the metallic particles or ionic charge carriers in the pore water including in the electrical double layer coating the surface of the metallic grains. This new way to treat the secondary voltages offers two advantages with respect to the classical approach. The first is a gain in terms of acquisition time. Indeed, the target can be illuminated with a few primary current sources, all the other electrodes being used simultaneously to record the secondary voltage distribution. The second advantage is with respect to the inversion of the obtained data. Indeed, the secondary (source) current is linearly related to the secondary voltage. Therefore, the inverse problem of inverting the secondary voltages is linear with respect to the source current density, and the inversion can be done in a single iteration. Several iterations are, however, required to compact the source current density distribution, still obtaining a tomogram much faster than inverting the apparent chargeability data using the classical Gauss-Newton approach. We have performed a sandbox experiment with pyrite grains locally mixed to sand at a specific location in the sandbox to demonstrate these new concepts. A method initially developed for self-potential tomography is applied to the inversion of the secondary voltages in terms of source current distribution. The final result compares favorably with the classical inversion of the time-domain induced polarization data in terms of chargeability, but it is much faster to perform.

Waveform joint inversion of seismograms and electrograms for moment tensor characterization of fracking events

Electromagnetic signals have been observed in association with fracking experiments in the laboratory, and in the field. We have developed a seismoelectric forward modeling approach to produce synthetic seismograms and electrograms generated by fracking events using the finite-element method with perfect matched-layer boundary conditions. The poroelastodynamic equations are solved in the frequency domain using a formulation based on the solid phase displacement and the pore pressure. These results are used to compute the electrical field disturbances of electrokinetic nature. Three types of electrical signals are generated: Type I disturbance is associated with the seismic source itself, Type II disturbance corresponds to seismoelectric conversions, and Type III corresponds to coseismic signals. This model is applied to simulate the seismic and electrical signals corresponding to the occurrence of a fracking event in a two-layers system. We perform a stochastic joint inversion of the seismograms and electrograms using the adaptive Metropolis algorithm (AMA) to obtain the posterior probability density functions of the parameters characterizing the seismic source assuming that the velocity model is perfectly known. The joint waveform inversion is performed on synthetic noise-free data and the AMA algorithm is successful in retrieving the true values of the unknown parameters. The proposed approach is then tested on the same synthetic data after being contaminated with 15% random noise with respect to the maximum amplitude of the signals. The model parameters are better determined for the joint inversion of seismic and electrical data by comparison with the inversion of the seismic time-series alone. We also propose a deterministic tomographic algorithm that is successful in locating the in situ source current density distribution for Types I and II anomalies from the electrical data alone.

Effects of Dextromethorphan/Quinidine on Auditory Event-Related Potentials in Multiple Sclerosis Patients With Pseudobulbar Affect

The purpose of this study was to characterize the brain activity and associated cortical structures involved in pseudobulbar affect (PBA), a condition characterized by uncontrollable episodes of laughing and/or crying in patients with multiple sclerosis before and after treatment with dextromethorphan/quinidine (DM/Q). Behavioral responses and event-related potentials (ERPs) in response to subjectively significant and neutral verbal stimuli were recorded from 2 groups: 6 multiple sclerosis patients with PBA before (PBA-preTx) and after (PBA-DM/Q) treatment with DM/Q and 6 healthy control (HC) subjects. Statistical nonparametric mapping comparisons of ERP source current density distributions between groups were conducted for subjectively significant and neutral stimuli separately before and after treatment with DM/Q. Treatment with DM/Q had a normalizing effect on the behavioral responses of PBA patients. Event-related potential waveform comparisons of PBA-preTx and PBA-DM/Q with HC, for both neutral and subjectively significant stimuli, revealed effects on early ERP components. Comparisons between PBA-preTx and HC, in response to subjectively significant stimuli, revealed both early and late effects. Source analysis comparisons between PBA-preTx and PBA-DM/Q indicated distinct activations in areas involved in emotional processing and high-level and associative visual processing in response to neutral stimuli and in areas involved in emotional, somatosensory, primary, and premotor processing in response to subjectively significant stimuli. In most cases, stimuli evoked higher current density in PBA-DM/Q compared with the other groups. In conclusion, differences in brain activity were observed before and after medication. Also, DM/Q administration resulted in normalization of behavioral and electrophysiological measures.

Brain responses to verbal stimuli among multiple sclerosis patients with pseudobulbar affect

To characterize the brain activity and associated cortical structures involved in pseudobulbar affect (PBA), a condition characterized by uncontrollable episodes of emotional lability in patients with multiple sclerosis (MS). Behavioral responses and event related potentials (ERP) in response to subjectively significant and neutral verbal stimuli were recorded from 33 subjects in 3 groups: 1) MS patients with PBA (MS+PBA); 2) MS patients without PBA (MS); 3) Healthy control subjects (HC). Statistical non-parametric mapping comparisons of ERP source current density distributions between groups were conducted separately for subjectively significant and for neutral stimuli. Behavioral responses showed more impulsive performance in patients with PBA. As expected, almost all ERP waveform comparisons between the MS groups and controls were significant. Source analysis indicated significantly distinct activation in MS+PBA in the vicinity of the somatosensory and motor areas in response to neutral stimuli, and at pre-motor and supplementary motor areas in response to subjectively significant stimuli. Both subjectively significant and neutral stimuli evoked higher current density in MS+PBA compared to both other groups. PBA of MS patients involves cortical structures related to sensory-motor and emotional processing, in addition to overactive involvement of motor cortical areas in response to neutral stimuli. These results may suggest that a 'disinhibition' of a "gate control"-type mechanism for emotional expression may lead to the lower emotional expression threshold of pseudobulbar affect.

Analysis of the correction factor in the spreading-resistance technique for monitoring epitaxial silicon

The range of applicability of the mixed-boundary-value method for calculating spreading resistance for a homogeneous slab with an effective contact-radius source and backed by a substrate of arbitrary but finite resistivity is investigated. Solutions are presented in terms of the correction factor and the source current density distributions for a slab of varying thickness and with various high-resistivity substrates. The correction factors for different schemes of calculation are correctly obtained by means of introducing an additional current source of opposite sign, but with the same absolute value, located at the drain point contact. This combination of source and drain currents gives the true value for the potential distribution along the surface of the semiconductor. This, in turn, leads to new terms in the equations obtained for the correction factors, which have been omitted in previously published works. A comparison between several schemes of calculation is presented. Within the framework of “uniform” and “variable” current distributions underneath the contact probe, there are two limits for the correction factor. A model based on a combination of these approaches is discussed, and a comparison between the proposed method and the Schumann–Gardner formulation is made.

Low-resolution electrical tomography of the brain during psychometrically matched verbal and spatial cognitive tasks.

EEGs were recorded from 75 normal, young, female subjects during psychometrically matched verbal (WF) and spatial (DL) cognitive tasks to elicit the differences in the electrical source distribution inside the brain. Recordings were obtained using 43 EEG and 3 guard electrodes then visually edited and spatially filtered to remove extracerebral artifacts. Twenty 1-sec artifact-free epochs were obtained and analyzed from 42 and 60 subjects during WF and DL respectively. Of these subjects, 20 were placed in a training set and the remainder into a test set. The baseline for the comparison of the two tasks was established by factoring the average cross-spectral matrices of the training-set EEGs, computed in the theta, alpha, and beta frequency bands into spatial patterns common to the two tasks. Only those spatial patterns that contributed to the correct classification of subjects in the test set were included in the source analysis. The source-current density distributions were obtained using the LORETA-KEY algorithm. The results show that the source-current density distribution is related to the putative functional activity in the brain in all three frequency bands. The electrical effects of the tasks are both most highly localized and lateralized in the theta band. The effects in the alpha and beta bands are much more generalized and are strongly lateralized only during one and the other of the tasks respectively. The conclusion is that WF is mainly a left central and bilateral frontal cerebral process while DL is mainly a right central and bilateral posterior cerebral process.

New expressions for depolarization dyadics in uniaxial dielectric-magnetic media

We present some novel expressions for the depolarization dyadics in uniaxial dielectric-magnetic media. These expressions were obtained by generalizing the Fikioris approach for extracting the singular behaviour of integrals involving the dyadic Green functions and the source current density distributions. Cubical, cylindrical and spherical geometries serve as examples for a discussion of the depolarization dyadics' dependence on geometry and anisotropy.

High resolution three-dimensional microwave imaging of antennas

A procedure for imaging antenna currents that uses a relationship between the radiated far-field hemisphere and the Fourier transform domain of the source current density distribution is presented. The technique is applied to an array of two orthogonal waveguides, a slotted waveguide array and a reflector antenna. In each case the radiated far-field hemisphere is inverted to produce a high-resolution volumetric image of the antenna currents. Polarization discrimination is demonstrated as is the ability of the technique to 'see behind' blockages by defocusing the foreground. It is shown that accurate distribution is available from the reconstructed image. Selective editing of the Fourier domain of the current distribution is performed to suppress unwanted artifacts in the reconstruction. >

Contact resistance calculations based on a variational method

Noble's variational method is used to solve the contact resistance problem that arises when a circular disc source electrode is in contact with a semiconductor slab through an infinitesimally thin layer of resistive material. The method assumes that the source current density distribution J( r) has the form K 1(1 − r 2) −μ + K 2(1 − r 2) 1 2 + K 3(1 − r 2) 3 2 , where the parameters K 1, K 2, K 3 and μ are determined by variational principles. Calculations of the source current density and the total slab resistance, performed for a wide range of contact resistivities, show that the results are practically indistinguishable from those derived from an exact mixed boundary value method proposed earlier by us. Whilst this method of using an optimised μ is very accurate, it is computationally slow. By fixing μ at a constant value of 1 4 , we find that we can drastically reduce the computation time for each calculation of the total slab resistance to 1.5 s on an Apple II microcomputer, and still achieve an overall accuracy of 1%. Tables of the abscissas and weights required for implementation of the numerical scheme are provided in the paper.

The contact resistance at the interface between a disc electrode and an infinite slab: Mixed-boundary-value solutions

We consider the contact-resistance problem that arises when a circular-disc electrode is in imperfect contact with a semiconductor slab, the imperfect contact being modelled by an infinitely thin layer of resistive material at the interface between the disc electrode and the slab. The resulting mixed-boundary-value problem is solved through the use of basis functions that satisfy the boundary conditions outside the source region identically. Calculations of the source current-density and the total slab resistance (including the effect of the contact resistance) are performed for homogeneous slabs of different thicknesses and with different substrate resistivities, for a wide range of values of the contact resistivity of the interface layer. The results obtained show that the presence of a contact resistance tends to make the source current density distribution more uniform. They also confirm the existence of upper and lower bounds for the difference between the total slab resistance and the layer contact-resistance, as predicted by Foxhall and Lewis. Although applied only to slabs of uniform resistivity, the method can be readily extended to slabs of nonuniform resistivity.

The spreading resistance of a homogeneous slab on a high-resistivity substrate: Mixed boundary value solutions

The range of applicability of the mixed boundary value method for calculating spreading resistance is extended to a homogeneous slab with a disc contact source and backed by a substrate of arbitrary, but finite resistivity. Solutions are presented in terms of the spreading resistance correction factors and the source current density distributions for a slab of varying thickness and with various high resistivity substrates. In particular, the results for a thin slab indicate that, as the substrate resistivity increases, more and more of the source current is concentrated near the edge of the disc electrode. A comparison is made of the source current density and potential corresponding to the mixed boundary value method with those given by the uniform flux and the variable flux (power-loss) method. It is found that, except for large slab thicknesses, the source potential distributions for a slab with a high resistivity substrate are not strongly influenced by the particular form of the source current density distribution assumed in either the uniform flux or the variable flux method. In consequence, both these two methods yield correction factors which agree quite closely with those derived from the mixed boundary value method.

The role of source boundary condition in spreading resistance calculations

Solutions are presented for the current density distribution at an equipotential disc electrode in contact with a slab backed by a perfect conductor. These exact solutions provide a basis for testing the validity of the two forms of source current density distribution assumed in approximate calculations of spreading resistance correction factors, viz. a uniform distribution and the distribution given by the classical solution for the infinitely thick slab. By using the latter distribution and the power loss definition for spreading resistance, a new correction factor integral has been obtained. Correction factors have been calculated by using this integral and those given by Schumann and Gardner, by Lee and by assuming a uniform current distribution. Except for Schumann and Gardner's method, all the methods yield results consistent with those obtained for the current density distributions. In the case of Schumann and Gardner's method, the correction factors obtained for thin slabs agree closely with those given by the exact method, despite the fact that the assumed source current distribution is in gross disagreement with the exact distribution. The close agreement in correction factors is fortuitous and is a consequence of the definition that Schumann and Gardner used for the spreading resistance. For a slab with a perfectly insulating substrate, exact solutions are not available. A comparative study has therefore been made in this case between the correction factors obtained by the four approximate methods themselves. The overall conclusion is that of the approximate methods, the uniform current density method is the most satisfactory from the point of view of self-consistency and overall accuracy.