In one of my communications to the Cornwall Geological Society on the high temperature of the interior of the earth, I ventured to express a belief that mineral veins, and the internal heat, are connected with electrical action. This opinion, founded as it was on the curious arrangement of the veins, &c. in pri­mitive rocks, I have had the satisfaction to find confirmed by experiments made in some of the mines of Cornwall; and, I doubt not that the existence of electricity in metalliferous veins similarly circumstanced, and capable of con­ducting it, will prove to be as universal a fact, as the progressive increase of temperature under the earth’s surface is now admitted to be, much as my conclusions on this point were at one time controverted. In my first experiment I did not succeed in detecting any electricity; but in my second I had the gratification to observe considerable electrical action.

Laboratory measurements and field data indicate that self‐potential anomalies comparable to those observed in many areas of geothermal activity may be generated by thermoelectric or electrokinetic coupling processes. A study using an analytical technique based on concepts of irreversible thermodynamics indicates that, for a simple spherical source model, potentials generated by electrokinetic coupling may be of greater amplitude than those developed by thermoelectric coupling. Before more quantitative interpretations of potentials generated by geothermal activity can be made, analytical solutions for more realistic geometries must be developed, and values of in‐situ coupling coefficients must be obtained. If the measuring electrodes are not watered, and if telluric currents and changes in electrode polarization are monitored and corrections made for their effects, most self‐potential measurements are reproducible within about ±5 mV. Reproducible short‐wavelength geologic noise of as much as ±10 mV, primarily caused by variation in soil properties, is common in arid areas, with lower values in areas of uniform, moist soil. Because self‐potential variations may be produced by conductive mineral deposits, stray currents from cultural activity, and changes in geologic or geochemical conditions, self‐potential data must be analyzed carefully before a geothermal origin is assigned to observed anomalies. Self‐potential surveys conducted in a variety of geothermal areas show anomalies ranging from about 50 mV to over 2 V in amplitude over distances of about 100 m to 10 km. The polarity and waveform of the observed anomalies vary, with positive, negative, bipolar, and multipolar anomalies having been reported from different areas. Steep potential gradients often are seen over faults which are thought to act as conduits for thermal fluids. In some areas, anomalies several kilometers wide correlate with regions of known elevated thermal gradient or heat flow.

This paper is an extension of a previous study, in which the principles of self‐potential ground surface tomography were outlined. The new arguments which are here set forth are the proper accounting for the topographic effects and a robust approach to global 3D tomography. The 2D case is initially considered in order to facilitate a full understanding of the new method. In order to gauge the topographic distortions, the concepts of slope effect and surface regularization are introduced, as suitable means to compute point by point correction factors of the measured self‐potential data, prior to the recognition of the tomographic images of the primary and induced electric sources underground. The tomographic approach is then developed by introducing again the concepts of the scanning function and of the charge occurrence probability function, which were amply dealt with in the previous paper. The new approach to 3D global tomography means here the composition of charge occurrence probability functions related to any two orthogonal surface components of the natural electric field, in order to account fully for the total surface component of the self‐potential field and hence to elicit the greatest amount of information. Two field examples are presented to show the full effectiveness of the proposed method. They refer, respectively, to a near‐surface investigation for archaeological purposes and to a very deep investigation in an active volcanic area.

Ore deposits and buried metals like pipelines behave as dipolar electrical geobatteries in which the source is due to (1) variation of the redox potential with depth, (2) oxido‐reduction reactions acting at the ore body/groundwater contact, and (3) migration of electrons in the ore body itself between the reducing and oxidizing zones. This polarization mechanism is responsible for an electrical field at the ground surface, the so‐called self‐potential anomaly. A new quick‐look tomographic algorithm is developed to locate electrical dipolar sources in the subsurface of the Earth from the analysis of these self‐potential signals. We applied this model to the self‐potential anomaly discussed by Stoll et al. [1995] in the vicinity of the KTB‐boreholes drilled during the Continental Deep Drilling Project in Germany. The source of this self‐potential signal is related to the presence of massive graphite veins associated with steeply inclined fault zones within the gneisses and observed in the KTB‐boreholes.

Inversion of self‐potential data for source current density, js, in complex volcanic settings, yields hydrological information without the need for a prior groundwater flow model; js contains information about pH, pore saturation, and permeability, from which we infer the distribution of liquid and vapor phases. To understand the hydrothermal flow dynamics and hydraulic connectivity between surface thermal features at Mount Tongariro volcano, New Zealand, we undertook a reconnaissance scale self‐potential survey and developed an inversion routine for js, constrained by an existing 3‐D conductivity model from magnetotelluric measurements. The 3‐D distribution of js at Mount Tongariro reveals a discontinuous zero js zone interpreted as vapor or residually saturated pore space, surrounded by low to moderate js interpreted as circulating condensate liquid. Bounding faults act as conduits for down flowing groundwater or condensate, as well as barriers for the hydrothermal system. Localized small‐scale circulation associated with individual surface thermal features, rather than a single circulating system, accounts for the lack of widespread anomalous geochemical observations prior to the 2012 Te Maari eruption.

We take you on the journey from continuous equations to their discrete matrix representations using the finite-volume method for the direct current (DC) resistivity problem. These techniques are widely applicable across geophysical simulation types and have their parallels in finite element and finite difference. We show derivations visually, as you would on a whiteboard, and have provided an accompanying notebook at http://github.com/seg to explore the numerical results using SimPEG ( Cockett et al., 2015 ).

We develop a method of 3‐D magnetic anomaly inversion based on traditional Tikhonov regularization theory. We use a minimum support stabilizing functional to generate a sharp, focused inverse image. An iterative inversion process is constructed in the space of weighted model parameters that accelerates the convergence and robustness of the method. The weighting functions are selected based on sensitivity analysis. To speed up the computations and to decrease the size of memory required, we use a compression technique based on cubic interpolation.

We present a method for inverting surface magnetic data to recover 3-D susceptibility models. To allow the maximum flexibility for the model to represent geologically realistic structures, we discretize the 3-D model region into a set of rectangular cells, each having a constant susceptibility. The number of cells is generally far greater than the number of the data available, and thus we solve an underdetermined problem. Solutions are obtained by minimizing a global objective function composed of the model objective function and data misfit. The algorithm can incorporate a priori information into the model objective function by using one or more appropriate weighting functions. The model for inversion can be either susceptibility or its logarithm. If susceptibility is chosen, a positivity constraint is imposed to reduce the nonuniqueness and to maintain physical realizability. Our algorithm assumes that there is no remanent magnetization and that the magnetic data are produced by induced magnetization only. All minimizations are carried out with a subspace approach where only a small number of search vectors is used at each iteration. This obviates the need to solve a large system of equations directly, and hence earth models with many cells can be solved on a deskside workstation. The algorithm is tested on synthetic examples and on a field data set.