Potential field of a stationary electric current in a stratified medium with a three-dimensional perturbing body

Hvoždara, M.; Petr, Václav

doi:10.1007/bf01582308

Cited by 19 publications

(10 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The scattering field can be described by a surface distribution of charges or potential on the body that is typically used for electrical resistivity modelling (Dieter, Paterson and Grant 1969;Snyder 1976;Eskola 1979;Hvozdara 1982Hvozdara , 1983Eloranta 1984). The body, within a homogeneous or layered halfspace, has an effect on the potential field which is commonly referred to as the scattering or secondary field.…”

Section: Basic Theorymentioning

confidence: 99%

“…The body, within a homogeneous or layered halfspace, has an effect on the potential field which is commonly referred to as the scattering or secondary field. The scattering field can be described by a surface distribution of charges or potential on the body that is typically used for electrical resistivity modelling (Dieter, Paterson and Grant 1969;Snyder 1976;Eskola 1979;Hvozdara 1982Hvozdara , 1983Eloranta 1984). The other method commonly used, especially in electromagnetic modelling, is to describe the scattering field by a volume distribution of current density or current dipole moment within the body (Hohmann 1971;Ting and Hohmann 1981;SanFilipo and Hohmann 1985;Robertson 1987).…”

Section: Basic Theorymentioning

confidence: 99%

See 1 more Smart Citation

EFFECTS OF WELL CASING ON POTENTIAL FIELD MEASUREMENTS USING DOWNHOLE CURRENT SOURCES¹

Schenkel

Morrison

1990

Geophysical Prospecting

View full text Add to dashboard Cite

A mathematical formulation for the electric potential from point current‐sources coaxial with a metal casing has been obtained. The excitation caused by the axial point‐sources will produce currents in the pipe. By assuming that the pipe can be divided into many cylindrical ring segments with constant axially‐directed current, the solution of the fields inside and outside the pipe can be formulated in an integral form. The integral equation applied to the segmented pipe yields a set of simultaneous linear equations which are solved for the currents in the pipe; these are then used to calculate the potentials anywhere outside the pipe in the medium. This solution has been used to study the distribution of the potentials in a half‐space for a single current‐source at and beyond the bottom of a finite length of casing. For a casing 0.1 m in radius and 0.006 m in wall thickness with a conductivity of 106 S/m, in a half‐space of 10‐2 S/m, it was found that only in a region very near the pipe does the pipe exert substantial influence on the fields of a point‐source 100 casing diameters beyond the end of the pipe. It appears that cross‐hole resistivity surveys can be implemented without corrections for the casing if the source is located at least 50–100 casing diameters beyond the end of the casing. Hole‐to‐surface surveys are much more affected by the pipe. For a pipe‐source separation of 100 casing diameters, the surface measurements must not be closer than a half pipe length for a 5% or less field distortion.

show abstract

Section: Basic Theorymentioning

confidence: 99%

Section: Basic Theorymentioning

confidence: 99%

EFFECTS OF WELL CASING ON POTENTIAL FIELD MEASUREMENTS USING DOWNHOLE CURRENT SOURCES¹

Schenkel

Morrison

1990

Geophysical Prospecting

View full text Add to dashboard Cite

show abstract

“…The method of BIE developed in the last 30 years has been shown as a very effective one for solving geoelectric potential fields in the layered medium containing 3D or 2D perturbing body; see e.g. Lee (1975); Okabe (1981); Hvoždara (1982Hvoždara ( , 1983; Schulz (1985); Eloranta (1986). In our earlier papers (Hvoždara, 1983(Hvoždara, , 1984 we have paid attention to the cases of a uniform exciting electric field, which approximates a telluric field for long periods.…”

Section: Introductionmentioning

confidence: 99%

The boundary integral method for the D.C. geoelectric problem in the 3-layered earth with a prismoid inhomogeneity in the second layer

Hvoždara

2012

Contributions to Geophysics and Geodesy

Self Cite

View full text Add to dashboard Cite

The paper presents algorithm and numerical results for the boundary integral equations (BIE) method of the forward D.C. geoelectric problem for the three-layered earth which contains the prismoidal body with sloped faces in the second layer. This situation occurs in the sedimentary basins. Although the numerical calculations are more complicated in comparison with faces orthogonal to the x, y, z axes, the generalization to the sloped faces enables treatment of the anomalous fields for the bodies of more general shapes as rectangular prisms. The graphs with numerical results present isoline maps of the perturbing potential as well as the resistivity profiles when the source field is due to the pair of D.C. electrodes at the surface of the earth. Also presented apparent resistivity curves for the Schlumberger array AMNB sounding.

show abstract

“…The equations have been applied to the potential problem of a stationary current (Barthes and Vasseur 1978, Okabe 1981, Schulz 1983, HvoZdara 1982. Although our method is similar to that given by Barthes and Vasseur (1978), the motivation of this paper is to present a clear procedure for transforming the boundary value problem of the stationary electric current to equivalent Fredholm's integral equations of second kind formulated for potential.…”

Section: Introductionmentioning

confidence: 99%

Potential Field of a Stationary Electric Current Using Fredholm's Integral Equations of the Second Kind*

Eloranta¹

1986

Geophysical Prospecting

View full text Add to dashboard Cite

ELORANTA, E.H. 1986, Potential Field of a Stationary Electric Current Using Fredholm's Integral Equations of the Second Kind, Geophysical Prospecting 34,856-872.An integral equation method is described for solving the potential problem of a stationary electric current in a medium that is linear, isotropic and piecewise homogeneous in terms of electrical conductivity. The integral equations are Fredholm's equations of the 'second kind ' developed for the potential of the electric field. In this method the discontinuitysurfaces of electrical conductivity are divided into 'sub-areas' that are so small that the value of their potential can be regarded as constant.The equations are applied to 3-D galvanic modeling. In the numerical examples the convergence is examined. The results are also compared with solutions derived with other integral equations. Examples are given of anomalies of apparent resistivity and mise-i-lamasse methods, assuming finite conductivity contrast. We show that the numerical solutions converge more rapidly than compared to solutions published earlier for the electric field. This results from the fact that the potential (as a function of the location coordinate) behaves more regularly than the electric field. The equations are applicable to all cases where conductivity contrast is finite.

show abstract

Potential field of a stationary electric current in a stratified medium with a three-dimensional perturbing body

Cited by 19 publications

References 7 publications

EFFECTS OF WELL CASING ON POTENTIAL FIELD MEASUREMENTS USING DOWNHOLE CURRENT SOURCES¹

EFFECTS OF WELL CASING ON POTENTIAL FIELD MEASUREMENTS USING DOWNHOLE CURRENT SOURCES¹

The boundary integral method for the D.C. geoelectric problem in the 3-layered earth with a prismoid inhomogeneity in the second layer

Potential Field of a Stationary Electric Current Using Fredholm's Integral Equations of the Second Kind*

Contact Info

Product

Resources

About

Potential field of a stationary electric current in a stratified medium with a three-dimensional perturbing body

Cited by 19 publications

References 7 publications

EFFECTS OF WELL CASING ON POTENTIAL FIELD MEASUREMENTS USING DOWNHOLE CURRENT SOURCES1

EFFECTS OF WELL CASING ON POTENTIAL FIELD MEASUREMENTS USING DOWNHOLE CURRENT SOURCES1

The boundary integral method for the D.C. geoelectric problem in the 3-layered earth with a prismoid inhomogeneity in the second layer

Potential Field of a Stationary Electric Current Using Fredholm's Integral Equations of the Second Kind*

Contact Info

Product

Resources

About

EFFECTS OF WELL CASING ON POTENTIAL FIELD MEASUREMENTS USING DOWNHOLE CURRENT SOURCES¹

EFFECTS OF WELL CASING ON POTENTIAL FIELD MEASUREMENTS USING DOWNHOLE CURRENT SOURCES¹