Resistivity and Induced Polarization Responses of Arbitrarily Shaped 3‐d Bodies in a Two‐layered Earth*

Das, U. C.; Parasnis, D.S.

doi:10.1111/j.1365-2478.1987.tb00805.x

Cited by 14 publications

(12 citation statements)

References 10 publications

(8 reference statements)

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“…Different choices are possible: the charge density may be assumed to be concentrated as a point charge located at the centre of gravity of the element; it may be assumed constant or linearly varying over the element; or it may be represented by some higher-order polynomial. Substitution of the representation for the charge density into the integral equation Das and Parasnis 1987).…”

Section: Numerical Examples Of Charge Distributionmentioning

confidence: 99%

ASPECTS OF CHARGE ACCUMULATION IN d. c. RESISTIVITY EXPERIMENTS¹

Oldenburg

1991

Geophysical Prospecting

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LI, Y. and OLDENBURG, D.W. 1991. Aspects of charge accumulation in d.c. resistivity experiments. Geophysical Prospecting 39, 803-826. When an electric current is introduced to the earth, it sets up a distribution of charges both on and beneath the earth's surface. These charges give rise to the anomalous potential measured in the d.c. resistivity experiment. We investigate different aspects of charge accumulation and its fundamental role in d.c. experiments. The basic equations and boundary conditions for the d.c. problem are first presented with emphasis on the terms involving accumulated charges which occur wherever there is a non-zero component of electric field parallel to the gradient of conductivity. In the case of a polarizable medium, the polarization charges are also present due to the applied electric field, yet they do not change the final field distribution. We investigate the precise role of the permittivity of the medium. The charge buildup alters the electric fields and causes the refraction of current lines; this results in the well-known phenomenon of current channelling. We demonstrate this by using charge density to derive the refraction formula at a boundary. An integral equation for charge density is presented for whole-space models where the upper half-space is treated as an inhomogeneity with zero conductivity. The integral equation provides a tool with which the charge accumulation can be examined quantitatively and employed in the practical forward modelling. With the aid of this equation, we investigate the effect of accumulated charges on the earth's surface and show the equivalence between the half-space and whole-space formulations of the problem. Two analytic examples are presented to illustrate the charge accumulation and its role in the d.c. problem. We investigate the relationship between the solution for the potential via the image method and via the charge density. We show that the essence of the image method solution to the potential problem is to derive a set of fictitious sources which produce the same potential as does the true charge distribution. It follows that the image method is viable only when the conductivity structure is such that the effect of the accumulated charge can be represented by a set of point images. As numerical examples, we evaluate quantitatively the charge density on the earth's surface that arises because of topography and the charge density on a buried conductive prism. By these means, we demonstrate the use of the boundary element technique and charge density in d.c. forward modelling problems.

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Section: Numerical Examples Of Charge Distributionmentioning

confidence: 99%

ASPECTS OF CHARGE ACCUMULATION IN d. c. RESISTIVITY EXPERIMENTS¹

Oldenburg

1991

Geophysical Prospecting

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“…The moment method was proposed by Harrington (1961). A 3D electromagnetic modelling code was developed by Tabbagh (1985) and was adapted to the electrical problem (Das and Parasnis 1987; Dabas et al . 1994).…”

Section: Control With 3d Modellingmentioning

confidence: 99%

On the effectiveness of 2D electrical inversion results: an agricultural case study

Panissod

Michot²,

Benderitter

et al. 2001

Geophysical Prospecting

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Electrical resistivity tomography was used in Beauce (France) to assess the water extraction by corn plants (evapotranspiration). The acquired pseudosections show conductive anomalies under the plants. A 2D inversion of measurements led us to identify clear resistive features associated with the water losses under the corn‐plant rows. New models have been calculated with two different 3D algorithms (finite‐difference and moment‐method) to take into account 3D structure of the ground and to confirm that periodic resistive features may generate shifted apparent‐resistivity anomalies.

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“…We prefer to use another approach, in which the anomalous bodies are replaced by an equivalent distribution of current sources (Das & Parasnis 1987). The theoretical basis is the same as in the case of the moment method used in electromagnetism (Raiche 1974;Hohmann 1975;Tabbagh 1985).…”

Section: -D Forward Modellingmentioning

confidence: 99%

3-D Inversion In Subsurface Electrical Surveying-I. Theory

Dabas

Tabbagh

1994

Geophysical Journal International

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S U M M A R YThe problem of 3-D inverse modelling in Direct Current (DC) surveys is addressed in this paper. First, forward modelling of the response of 3-D bodies in DC surveys is carried out by the moment method. It consists of dividing a volume into N small cells, equivalent to 3N dipoles. The numerical code is checked against published results obtained through algorithms that use either equivalent surface charge densities or a finite-difference approach. Good agreement is found between these methods and a maximum discrepancy of 3 per cent is computed on a widely published test model.Secondly, inverse modelling is carried out by a classical least-squares (LS) scheme that includes the Levenberg-Marquardt constraints formalism. We have tested two approximations: Born, and localized non-linear (LN). The difference between resistivities calculated with and without these approximations is found to be too large for inverse modelling, especially in the case of conductive bodies. We use this inversion scheme for different theoretical 3-D models that consist of two layers (34 cells) under an overburden. It is found, in the case of a vertical contrast, that, when a resistive feature overlays a conductive one, resistivities are resolved very accurately, with a low number of iterations and with a better accuracy than in the case where the conductive feature overlays the resistive one. Despite a slower convergence rate, in the case of both vertical and lateral constrasts, the shape of the body is well resolved, even if a slight discrepancy in the absolute values is noticed, especially for conductive cells. Finally, the stability of the inversion is tested with noisy data.

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Resistivity and Induced Polarization Responses of Arbitrarily Shaped 3‐d Bodies in a Two‐layered Earth*

Cited by 14 publications

References 10 publications

ASPECTS OF CHARGE ACCUMULATION IN d. c. RESISTIVITY EXPERIMENTS¹

ASPECTS OF CHARGE ACCUMULATION IN d. c. RESISTIVITY EXPERIMENTS¹

On the effectiveness of 2D electrical inversion results: an agricultural case study

3-D Inversion In Subsurface Electrical Surveying-I. Theory

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Resistivity and Induced Polarization Responses of Arbitrarily Shaped 3‐d Bodies in a Two‐layered Earth*

Cited by 14 publications

References 10 publications

ASPECTS OF CHARGE ACCUMULATION IN d. c. RESISTIVITY EXPERIMENTS1

ASPECTS OF CHARGE ACCUMULATION IN d. c. RESISTIVITY EXPERIMENTS1

On the effectiveness of 2D electrical inversion results: an agricultural case study

3-D Inversion In Subsurface Electrical Surveying-I. Theory

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Product

Resources

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ASPECTS OF CHARGE ACCUMULATION IN d. c. RESISTIVITY EXPERIMENTS¹

ASPECTS OF CHARGE ACCUMULATION IN d. c. RESISTIVITY EXPERIMENTS¹