Electrical Potential Due to a Point Current Source Over an Inhomogeneous Anisotropic Earth*

Pal, Barun Prosad; Dasgupta, Sujit

doi:10.1111/j.1365-2478.1984.tb00748.x

Cited by 9 publications

(4 citation statements)

References 17 publications

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“…On p. 948, (19), Pal and Dasgupta (1984) have given, for a special case, a simple expression of the potential on the free surface, viz.,…”

Section: The Potential a N D I T S Physical Dimensionmentioning

confidence: 99%

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Comment on “Electrical Potential Due to a Point Current Source Over an Inhomogeneous Anisotropic Earth” Barun Prosad Pal and S. P. Dasgupta*

Patella

1986

Geophysical Prospecting

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Pal and Dasgupta (1984) intended to present the results of a theoretical study about the conventional Wenner and Schlumberger vertical geoelectric sounding over a highly specialized inhomogeneous anisotropic subsurface. In a subsequent paper (Pal and Dasgupta 1985) they applied their previous study to a simplified model satisfying the same basic assumptions.I was at once attracted by the unusual titles, of the two papers. However, I was surprised at the total fallacy of the study. My criticism is detailed below. T H E MODELThe authors assume a transverse conductivity c,., that varies with the distance r according to the law cr,.=ct(r/P)", where n, p, 6, are suitably chosen constants. The coefficient p must have the dimension of a length (see the authors' fig. 1). Obviously the transverse conductivity model has cylindrical symmetry around a vertical z-axis passing through a surface point 0, the location of the current source A , of direct current with intensity + I , i.e. A E 0.My criticism starts with the following preliminary questions.1. Which geological and geophysical observations can be approximated by that particular transverse conductivity model? 2. What is the material and/or physical significance of the vertical axis of symmetry (r = 0), where the transverse conductivity drastically reduces to zero when n is positive, or reaches infinity when n is negative? 3. How could one recognize, in the field, this axis, and in particular the location of point 0 in order to locate the current source A?Without an answer to these questions even the expert reader has difficulties to apply the ideas the authors have intended to propose.

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“…On p. 948, (19), Pal and Dasgupta (1984) have given, for a special case, a simple expression of the potential on the free surface, viz.,…”

Section: The Potential a N D I T S Physical Dimensionmentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

Comment on “Electrical Potential Due to a Point Current Source Over an Inhomogeneous Anisotropic Earth” Barun Prosad Pal and S. P. Dasgupta*

Patella

1986

Geophysical Prospecting

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“…Several authors have extended the treatment for an anisotropic half space. The integral equation approach was used by PAL and DASGUPTA (1984) to derive the electric potential due to a surface point source over an inhomogeneous, anisotropic half space of the simple vertical transversely isotropic (VTI) type. A modification of this was made by PAL and MUKHERJEE (1986) who dealt with a layered conducting earth with dipping anisotropy.…”

Section: Introductionmentioning

confidence: 99%

Electric Potential and Fréchet Derivatives for a Uniform Anisotropic Medium with a Tilted Axis of Symmetry

Greenhalgh

Marescot

Zhou

et al. 2009

Pure appl. geophys.

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In this paper we develop analytic solutions for the electric potential, current density and Fréchet derivatives at any interior point within a 3-D transversely isotropic medium having a tilted axis of symmetry. The current electrode is assumed to be on the surface of the Earth and the plane of stratification given arbitrary strike and dip. Profiles can be computed for any azimuth. The equipotentials exhibit an elliptical pattern and are not orthogonal to the current density vectors, which are strongly angle dependent. Current density reaches its maximum value in a direction parallel to the longitudinal conductivity direction. Illustrative examples of the Fréchet derivatives are given for the 2.5-D problem, in which the profile is taken perpendicular to strike. All three derivatives of the Green's function with respect to longitudinal conductivity, transverse resistivity and dip angle of the symmetry axis (dG/dr l , dG/dr t , dG/dh 0 ) show a strongly asymmetric pattern compared to the isotropic case. The patterns are aligned in the direction of the tilt angle. Such sensitivity patterns are useful in real-time experimental design as well as in the fast inversion of resistivity data collected over an anisotropic earth.

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“…Asten [1] obtained an analytical solution for the potential due to a point source in a homogeneous anisotropic half-space, where one of the principal axes of the conductivity tensor is parallel to the ground surface. Pal and Dasgupta [16] also studied a special case of the electrical potential in an inhomogeneous anisotropic half-space. An extension of this was made by Pal and Mukherjee [17] who considered a two-layered conducting earth with dipping anisotropy.…”

Section: Introductionmentioning

confidence: 99%

Direct current electric potential in an anisotropic half‐space with vertical contact containing a conductive 3D body

Stagnitti

2004

Mathematical Problems in Engineering

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Detailed studies of anomalous conductors in otherwise homogeneous media have been modelled. Vertical contacts form common geometries in galvanic studies when describing geological formations with different electrical conductivities on either side. However, previous studies of vertical discontinuities have been mainly concerned with isotropic environments. In this paper, we deal with the effect on the electric potentials, such as mise-à-la-masse anomalies, due to a conductor near a vertical contact between two anisotropic regions. We also demonstrate the interactive effects when the conductive body is placed across the vertical contact. This problem is normally very difficult to solve by the traditional numerical methods. The integral equations for the electric potential in anisotropic half-spaces are established. Green's function is obtained using the reflection and transmission image method in which five images are needed to fit the boundary conditions on the vertical interface and the air-earth surface. The effects of the anisotropy of the environments and the conductive body on the electric potential are illustrated with the aid of several numerical examples.

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Electrical Potential Due to a Point Current Source Over an Inhomogeneous Anisotropic Earth*

Cited by 9 publications

References 17 publications

Comment on “Electrical Potential Due to a Point Current Source Over an Inhomogeneous Anisotropic Earth” Barun Prosad Pal and S. P. Dasgupta*

Comment on “Electrical Potential Due to a Point Current Source Over an Inhomogeneous Anisotropic Earth” Barun Prosad Pal and S. P. Dasgupta*

Electric Potential and Fréchet Derivatives for a Uniform Anisotropic Medium with a Tilted Axis of Symmetry

Direct current electric potential in an anisotropic half‐space with vertical contact containing a conductive 3D body

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