Calculation of Galvanic Effects by Means of the Method of Sub‐areas*

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.

Section: Introductionmentioning

confidence: 95%

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

Eloranta¹

1986

“…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%

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

Schenkel

Morrison

1990

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.

“…To solve the electric dc field problem of a three-dimensional model, Eskola (1979) introduced the method of sub-areas, whereby the surface integral equation of the field strength reduces into a set of simultaneous algebraic equations. For real conductivity the number of equations in the set is equal to the number of sub-areas; for complex conductivity it is twice that number.…”

Section: Introductionmentioning

confidence: 99%

The Solution of the Stationary Electric Field Strength and Potential of a Point Current Source in a 2 1/2‐ Dimensional Environment*

Eskola

Hongisto

1981

Self Cite

A method is given for solving the dc electric field problem of a point current source in an anisotropic 2 1/2‐dimensional structural model. The surface integral equation of the field strength is given. Parallel to the strike the field strength is represented by a Fourier series. On the plane perpendicular to the strike each term of the field strength series is solved by means of the method of sub‐sections, where linear behaviour of field strength over the sub‐sections is assumed. Some numerical examples for different galvanic effects are given.