A physiochemical model for the complex dielectric response of sedimentary rocks is used to invert broadband dielectric spectra for effective grain size distributions. The complex dielectric response of each grain within the “water‐wet” granular matrix is obtained by superimposing the polarization of the electrochemical double layer, which is assumed to surround each grain, with the complex dielectric response of the dry mineral grain. The effective complex dielectric response of the water‐wet matrix (grains and surface phase) is obtained by volume averaging over the entire distribution of particle sizes. The complex dielectric response of the total mixture (water‐wet matrix and bulk pore solution) is obtained using the Bruggeman‐Hanai‐Sen effective medium theory. Studies of Berea sandstone show that the grain size distribution, obtained by inverting the real part of the complex dielectric spectra, is similar to the grain size distribution obtained from optical images of the sample in thin section. The current model, however, does not account for surface roughness effects or the polarization of counterions over multiple grain lengths; therefore the grain size distribution obtained by dielectric spectroscopy is broader than the image‐derived distribution. The dielectric‐derived grain size distribution can be fit with two separate power laws that crossover at R ≅ 1 μm, which corresponds to a relaxation frequency of 2 kHz. The low‐frequency dielectric response (f < 2 kHz) is primarily controlled by the macroscopic grain fraction (mainly quartz grains), which has a fractal dimension of d = 1.84±0.05. The high‐frequency dielectric response (f > 2 kHz) is primarily controlled by the clay size grains and surface roughness, which has a fractal dimension of d = 2.48±0.07. At very low frequencies (f < 0.1 Hz) the dielectric response appears to be controlled by the electrochemical polarization of counterions over multiple grain lengths. A more general model should account for the effects of surface roughness and grain interactions on the dielectric response. It would also be useful to develop a simplified version of this model, perhaps similar in form to the empirically derived Cole‐Cole response, which could be more easily used to model and interpret electrical geophysical field surveys (e.g., induced‐polarization, ground‐penetrating radar, and time domain reflectometery measurements).

This paper reports on laboratory measurements of the streaming potential properties of common minerals and in particular of Westerly granite. Data are presented for these solids in contact with simple electrolytic solutions and in one case for temperature variation in the range 5°–70°C. For 1:1 electrolytes the ratio of the streaming potential coupling coefficient to fluid resistivity was approximately −4 mV/(atm Ωm) and for 2:1 electrolytes −2 mV/(atm Ωm). The effect of temperature was small (0.05 mV/°C temperature increase) and indicates that the zeta potential was independent of temperature. Preliminary experimental results using mixed electrolytic solutions (NaCl + CaCl2) and two‐phase fluid flow are also described. Two‐phase flow can enhance streaming potentials by as much as a factor of 3 or 4. The laboratory data are used to interpret streaming potentials in geological problems, such as earthquake prediction, geothermal prospecting using the self‐potential method, and surface conductivity contribution to the electrical resistivity of rocks.

The equations of motion and stress/strain relations for the linear dynamics of a two-phase, fluid/solid, isotropic, porous material have been derived by a direct volume averaging of the equations of motion and stress/strain relations known to apply in each phase. The equations thus obtained are shown to be consistent with Biot’s equations of motion and stress/strain relations; however, the effective fluid density in the equation of relative flow has an unambiguous definition in terms of the tractions acting on the pore walls. The stress/strain relations of the theory correspond to ‘‘quasistatic’’ stressing (i.e., inertial effects are ignored). It is demonstrated that using such quasistatic stress/strain relations in the equations of motion is justified whenever the wavelengths are greater than a length characteristic of the averaging volume size.

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When a fluid electrolyte moves relative to a solid, an electric field is generated that migrates ions and thus dissipates energy. This “electrokinetic” dissipation is theoretically compared to the viscous shear dissipation for fluid flow generated by a fixed time harmonic pressure gradient in a planar quartz duct. It is shown that, regardless of frequency, it is safe to ignore the electrokinetic losses when the electrolyte molarity is on the order of 0.1 M or greater. For low molarity electrolytes [Formula: see text], however, the electrokinetic losses do become significant compared to the viscous losses for flow in sufficiently tight pores. The ratio of electrokinetic dissipation [Formula: see text] to viscous dissipation [Formula: see text] is always a maximum when the electrokinetic radius (the duct haft‐width divided by the Debye length) is ≈1.5. The maximum value of [Formula: see text] does not exceed 0.5 for the NaCl, KCl, and quartz systems considered. The generated electric field pushes on the excess ions in the duct in a direction opposite to the applied pressure gradient, thus giving rise to an apparent viscosity enhancement. This enhancement is ⩽45 percent for the systems considered here, and can be directly obtained from the [Formula: see text] ratio. Indeed, the central effect of a large [Formula: see text] ratio is that the amount of relative fluid flow is reduced, and thus, the amount of wave attenuation is reduced.

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Despite over 2 decades of international and national monitoring of electrical signals with the hope of detecting precursors to earthquakes, the scientific community is no closer to understanding why precursors are observed only in some cases. Laboratory measurements have demonstrated conclusively that self potentials develop owing to fluid flow and that both resistivity and magnetization change when rocks are stressed. However, field experiments have had much less success. Many purported observations of low‐frequency electrical precursors are much larger than expectations based on laboratory results. In some cases, no precursors occurred prior to earthquakes, or precursory signals were reported with no corresponding coseismic signals. Nonetheless, the field experiments are in approximate agreement with laboratory measurements. Maximum resistivity changes of a few percent have been observed prior to some earthquakes in China, but the mechanism causing those changes is still unknown. Anomalous electric and magnetic fields associated with fluid flow prior to earthquakes may have been observed. Finally, piezomagnetic signals associated with stress release in earthquakes have been documented in measurements of magnetic fields.

[ 1 ] The self-potential (SP) method has long been used for av ariety of geophysical applications because of its ease of acquisition, but has suffered from difficulty in interpretation of the data. Self-potential signals result from as ource term that is coupled with the earth resistivity and appropriate boundary conditions. This work describes an inversion methodology for determining the self-potential sources from measured SP and resistivity data. The SP source inversion is al inear problem, though it is complicated by nonuniqueness that is common to potential-field problems. The linear operator is also poorly conditioned because of the limited set of measurements, which are often constrained to the earth'ssurface. Our approach utilizes model regularization that selects a class of solutions which fit the data with sources that are spatially compact. Large variations in sensitivity due to distance and resistivity structure throughout the model are addressed through the use of ascaling term derived from the Green'sfunctions that define the linear operator.Asignificant benefit of these methods is the resolution of targets at depth from surface measurements alone. This inversion technique is first illustrated with a simple synthetic data set. In as econd example we apply this approach to af ield data set taken from previously published literature and investigate the effects of different resistivity structure assumptions on the inversion results. The spatial distribution of sources provides useful information that can subsequently be interpreted in terms of physical processes that generate the SP data.