A PHENOMENOLOGICAL THEORY OF INDUCED ELECTRICAL POLARIZATION

1958 ◽  
Vol 36 (12) ◽  
pp. 1634-1644 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Current Flow ◽  
Effective Conductivity ◽  
Homogeneous Medium ◽  
Phenomenological Theory ◽  
Induced Polarization ◽  
Theoretical Derivation ◽  
Electrical Polarization ◽  
Partially Saturated ◽  
Layer Medium ◽  
Small Metal Particles

A brief theoretical derivation is presented for the effective conductivity and dielectric constant of a homogeneous medium loaded with a uniform distribution of spherical conducting particles. To account for the effect of induced polarization, the particles are taken to have a concentric membrane or film which has a blocking action to the current flow into the particle. The characteristics of this phenomenological model are very similar to the experimentally observed features of induced polarization in a block of compacted andesite particles which contains a dissemination of small metal particles and is partially saturated with a weak electrolyte.The theory is then extended to a two-layer medium where the lower region is polarizable. The results explain, at least in a qualitative way, the observed features of induced electrical polarization in rocks, soils, and clay.

DISCUSSIONS ON “A THEORETICAL STUDY OF INDUCED ELECTRICAL POLARIZATION”

Geophysics ◽  
1958 ◽  
Vol 23 (1) ◽  
pp. 144-148 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Dielectric Constant ◽  
Current Flow ◽  
Theoretical Study ◽  
Induced Polarization ◽  
Infinite Medium ◽  
Electrical Polarization ◽  
Polarization Response ◽  
Lower Semi

The analysis in the quoted paper is an attempt to calculate the induced polarization response of a two‐layer flat earth. The upper layer is a homogeneous overburden of thickness h with a resistivity [Formula: see text] and a dielectric constant of [Formula: see text]. The lower (semi‐infinite) medium which is the “aquifer” has a resistivity [Formula: see text] and dielectric constant [Formula: see text]. The value of the relaxation voltage as seen at the potential electrodes “immediately after” the current is shut off is designated Δϕ. The A’s of the above paper present a method for calculating the ratio Δϕ/V where V is the steady voltage across the potential electrodes during the time of current flow.

Inversion of induced polarization data

Geophysics ◽  
1994 ◽  
Vol 59 (9) ◽  
pp. 1327-1341 ◽  
Author(s):  
Douglas W. Oldenburg ◽  
Yaoguo Li
Keyword(s):  
Inverse Problem ◽  
Objective Function ◽  
Effective Conductivity ◽  
Optimization Theory ◽  
Induced Polarization ◽  
Dc Resistivity ◽  
Earth Structure ◽  
Nonlinear Inverse Problem ◽  
Polarization Data ◽  
The Earth

We develop three methods to invert induced polarization (IP) data. The foundation for our algorithms is an assumption that the ultimate effect of chargeability is to alter the effective conductivity when current is applied. This assumption, which was first put forth by Siegel and has been routinely adopted in the literature, permits the IP responses to be numerically modeled by carrying out two forward modelings using a DC resistivity algorithm. The intimate connection between DC and IP data means that inversion of IP data is a two‐step process. First, the DC potentials are inverted to recover a background conductivity. The distribution of chargeability can then be found by using any one of the three following techniques: (1) linearizing the IP data equation and solving a linear inverse problem, (2) manipulating the conductivities obtained after performing two DC resistivity inversions, and (3) solving a nonlinear inverse problem. Our procedure for performing the inversion is to divide the earth into rectangular prisms and to assume that the conductivity σ and chargeability η are constant in each cell. To emulate complicated earth structure we allow many cells, usually far more than there are data. The inverse problem, which has many solutions, is then solved as a problem in optimization theory. A model objective function is designed, and a “model” (either the distribution of σ or η)is sought that minimizes the objective function subject to adequately fitting the data. Generalized subspace methodologies are used to solve both inverse problems, and positivity constraints are included. The IP inversion procedures we design are generic and can be applied to 1-D, 2-D, or 3-D earth models and with any configuration of current and potential electrodes. We illustrate our methods by inverting synthetic DC/IP data taken over a 2-D earth structure and by inverting dipole‐dipole data taken in Quebec.

scholarly journals AN EXPERIMENTAL STUDY OF DIATHERMY

1927 ◽  
Vol 46 (5) ◽  
pp. 715-734 ◽  
Author(s):  
Ronald V. Christie ◽  
Carl A. L. Binger
Keyword(s):  
Electrical Resistance ◽  
High Frequency ◽  
Skin Effect ◽  
Current Flow ◽  
Homogeneous Medium ◽  
Local Heat ◽  
The Body ◽  
Technical Error ◽  
Theoretical Considerations ◽  
Maximal Heating

The principles governing the passage of high frequency currents through various conductors have been discussed and exemplified in experiments done on both non-living and living bodies. In Part I it was shown: (1) That the current takes the path of least electrical resistance rather than the shortest path; (2) that maximal heating occurs at the point of greatest concentration of the lines of current flow. In a homogeneous medium with parallel electrodes maximal heat production occurs in those portions of the medium adjoining the electrodes and the heat gradient is from without inward. Under these circumstances maximal heating never occurs at the center. In discussing the localization of heat not only the electrical resistance and current concentration, but also the cooling effect, must be considered. In experiments on the dog's cadaver no evidence of the so called "skin effect" could be demonstrated. This is in contradistinction to the findings of Bettman and Crohn, but the discrepancy is explained on the basis of what we believe to be a technical error in their work. The finding of no "skin effect" is in agreement with the conclusions of Dowse and Iredell, based on both experimental and theoretical considerations. In Part II three types of experiments were performed on the anesthetized dog. The conclusions to be derived from them are these: (1) The heat gradient of the body is reversed during diathermy and heating occurs from without inward; (2) deep heating during diathermy is greater than that which results from the application of local heat to the skin; (3) the lung can be heated by diathermy in spite of simultaneous cooling of the chest wall. These experiments we regard as satisfactory evidence of the passage of the current through the interior of the body.

Estimating permeability of sandstone samples by nuclear magnetic resonance and spectral-induced polarization

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. E215-E226 ◽  
Author(s):  
Andreas Weller ◽  
Sven Nordsiek ◽  
Wolfgang Debschütz
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Current Flow ◽  
Pore Space ◽  
Induced Polarization ◽  
Western Desert ◽  
Permeability Prediction ◽  
Spectral Induced Polarization ◽  
Space Geometry ◽  
Nuclear Magnetic

Two techniques to estimate permeability are compared in this paper: nuclear magnetic resonance (NMR) and spectral-induced polarization (SIP). Both methods are based on relaxation processes. NMR records the relaxation of hydrogen nuclei after excitation in an external magnetic field. The phenomenon of induced polarization can be characterized by a relaxation of ions after excitation by an electric field. Hydrogen nuclei are concentrated in the pore water, the current flow is restricted to the pore space for most reservoir rocks, and permeability is related to the pore space geometry. Based on the similarity between fluid movement and current flow in the pore space, different relations have been published linking parameters derived from NMRand SIP data to predict permeability. NMR, SIP and permeability data have been acquired on 53 sandstone samples of the cretaceous Bahariya Formation (Western Desert, Egypt) including 27 samples showing a lamination that causes anisotropy. We compare the applicability of known and generalized relations for permeability prediction including isotropic and anisotropic samples. Because NMR relaxation ignores directionality of pore space geometry, the known relations provide only a weak accuracy in permeability estimation. The integrating parameters derived from a Debye decomposition of SIP data are partly sensitive to anisotropy. A generalized power-law relation using resistivity, chargeability, and mean relaxation time provide a reliable permeability prediction for isotropic and anisotropic samples.

Generalized effective-medium theory of induced polarization

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. F197-F211 ◽  
Author(s):  
Michael Zhdanov
Keyword(s):  
Mathematical Model ◽  
Arbitrary Shape ◽  
Effective Conductivity ◽  
Effective Medium Theory ◽  
Induced Polarization ◽  
Effective Medium ◽  
Matrix Composition ◽  
Medium Theory ◽  
Rock Formations ◽  
The Matrix

A rigorous physical-mathematical model of heterogeneous conductive media is based on the effective-medium approach. A generalization of the classical effective-medium theory (EMT) consists of two major parts: (1) introduction of effective-conductivity models of heterogeneous, multiphase rock formations with inclusions of arbitrary shape and conductivity using the principles of the quasi-linear (QL) approximation within the framework of the EMT formalism and (2) development of the generalized effective-medium theory of induced polarization (GEMTIP), which takes into account electromagnetic-induction (EMI) and induced polarization (IP) effects related to the relaxation of polarized charges in rock formations. The new generalized EMT provides a unified mathematical model of heterogeneity, multiphase structure, and the polarizability of rocks. The geoelectric parameters of this model are determined by the intrinsic petrophysical and geometric characteristics of composite media: the mineralization and/or fluid content of rocks and the matrix composition, porosity, anisotropy, and polarizability of formations. The GEMTIP model allows one to find the effective conductivity of a medium with inclusions that have arbitrary shape and electrical properties. One fundamental IP model of an isotropic, multiphase, heterogeneous medium is filled with spherical inclusions. This model, because of its relative simplicity, makes it possible to explain the close relationships between the new GEMTIP conductivity-relaxation model and an empirical Cole-Cole model or classical Wait’s model of the IP effect.

Electrical response of a leak in a geomembrane liner

Geophysics ◽  
1988 ◽  
Vol 53 (11) ◽  
pp. 1445-1452 ◽  
Author(s):  
J. O. Parra
Keyword(s):  
Waste Disposal ◽  
Current Density ◽  
Current Flow ◽  
Electrical Response ◽  
Current Density Distribution ◽  
Waste Material ◽  
Disposal Site ◽  
Finite Region ◽  
Layer Medium ◽  
Flow Through

A leak in a geomembrane lined impoundment or landfill has a characteristic electrical response. I simulate the waste material, the liner, and the soil under the liner by infinite horizontal layers and express the secondary potential for a leak in the geomembrane liner in terms of a three‐layer medium Green’s function and the unknown current density distribution at the leak. The area of the leak is sufficiently small for the leak current density to be essentially uniform. I add the primary potential associated with a leak‐free liner to the secondary potential to form an integral equation and derive a general expression for the current density at the boundary between the waste material and the liner. From the expression for the current density, I determine the current flow through the leak by assuming that the total current distribution flows vertically across a finite region of the infinite, thin liner layer. This finite region has the same surface area as does the waste disposal site or landfill. My analysis implies that the current density is the most sensitive variable affecting the magnitude of current flow through the leak and the amplitude of the leak anomaly response. Multiple circular leaks in the thin resistive liner are included in the analysis. The potential anomaly of a leak is a localized response which is capable of providing a useful means for detecting and locating such leaks accurately in large waste disposal sites or landfills. Excellent agreement between experimental and model data shows my general solution is accurate in predicting leak signatures and suggests the solution may be useful to model field data acquired in geomembrane lined impoundments or landfills.

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