A Note on the Mathematical Representation of the Source for Tubular Transmitting Antennas

Otto, D.

doi:10.1002/rds196838862

Cited by 8 publications

(7 citation statements)

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“…A practical example is the thick monopole driven from a coaxial line excited in the the TEu mode. For the rotationally symmetrical excitation in the TEM mode, which is included as a special case, the integral equation derived by King and Wu (1967) and again by Otto (1968) is, of course, obtained. Since the Seshadri-Wu method introduces neither a discontinuous potential nor a fictitious magnetic current source, it is no doubt the least "artificial.…”

Section: S Referencesmentioning

confidence: 98%

“…The approach taken by Otto (1968) is a familiar one. It was, in fact, suggested as an alternative by a reviewer who also seemed to be unfamiliar with, and anxious to avoid, the standard method for applying Green's theorem to a multiply connected region (Osgood, 1933).…”

Section: S Referencesmentioning

confidence: 99%

“…For thick antennas this is not necessarily true, especially when transverse as well as axial currents are excited. An analysis of the electrically thick tubular antenna in which scalar and vector potentials are not introduced has been published (Seshadri and Wu, 1967) but is not mentioned by Otto (1968). This analysis is concerned with the more general problem of a tubular antenna driven on the outside surface by a generator that is not necessarily rotationally symmetrical.…”

Section: S Referencesmentioning

confidence: 99%

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A Comment on “A Note on the Mathematical Representation of the Source for Tubular Transmitting Antennas” by D. V. Otto

King

1968

Radio Science

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Section: S Referencesmentioning

confidence: 98%

Section: S Referencesmentioning

confidence: 99%

Section: S Referencesmentioning

confidence: 99%

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A Comment on “A Note on the Mathematical Representation of the Source for Tubular Transmitting Antennas” by D. V. Otto

King

1968

Radio Science

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“…In early works, the solutions for the pipe response were obtained by making a simplifying assumption that it can be represented by a solid cylinder extented to infinity (Wait 1952 andSmythe 1968). Later, the cylindrical multi-layered infinite or semi-infinite pipe response was investigated for both direct cumnt (DC) and electromagnetic (EM) sources located inside or outside the pipe (Otto 1968, Gianzero and Rau 1977, and Wait 1982.…”

Section: Introductionmentioning

confidence: 99%

The electrical resistivity method in cased boreholes

Schenkel¹

1991

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!&e Govermient reserves for itself and others acting on its behalf a royalty free, nonexclusive, irrevocable, world-wide license for governmental purposes t o publish, distribute, translate, duplicate, exhibit, and perform any such data aopyrighted by the amtractor.The United States Department of Energy has the right to use this thesis for any purpose whatsoever, including the right to reproduce all or any part thereof. THE ELECTRICAL RESISTIVITY METHOD IN CASED BOREHOLES by CLIFFORD J. SCHENKEL AbstractThe resistivity method in cased boreholes with downhole current sources is investigated using the integral equation (IE) technique. The casing and other bodies are characterized as conductivity inhomogeneities in a half-space. For sources located along the casing axis, an axially symmetric Green's function is used to formulate the surface potential and electric field (E-field) volume integral equations. The situations involving off-axis current sources and three-dimensional (3-D) bodies is formulated using the surface potential IE method. The solution of the 3-D Green's function is presented in cylindrical and Cartesian coordinate systems.The methods of moments is used to solve the Fredholm integral equation of the second kind for the response due to the casing and other bodies.The numerical analysis revealed that the current in the casing can be approximated by its vertical component except near the source and the axial symmetric approximation of the casing is valid even for the 3-D problem. The E-field volume IE method is an effective and efficient technique to simulate the response of the casing in a half-space, whereas the surface potential approach is computationally better when multiple bodies are involved.Analyzing several configurations of the current source indicated that the casing response is influenced by four characteristic factors: conduction length, current source depth, casing depth, and casing length. The conduction length, the most important factor, relates the casing conductance with the conductivity of the host medium and is an indicator of the ability of the pipe to carry the current along its length. When the source is located within the casing, the characteristic parameters can be reduced to three ratios: the conduction length to casing length I (conduction ratio), the source position to casing length, and the casing depth to casing length.For a conduction ratio that is approximately greater than two. the fields from the casing are similar to those produced by a line source. When the source is located beneath the casing, the distortion of the fields is also dependent on the casing-source separation distance. For a current source near the casing (e 100 casing diameters), the casing greatly distorts the fields when compared to those produced by a pole source. When the source is greater than 100 casing diameters from the pipe, only the region near the casing is affected. The numerical simulations indicate that cross-hole and downhole to surface time monitoring studies may be conducted with ve...

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“…Later, the cylindrical multi-layered infinite or semiinfinite pipe response was investigated for both direct current (d.c.) and electromagnetic sources located inside or outside the pipe (e.g. Otto 1968;Gianzero and Rau 1977;Wait and Umashankar 1978/79;Wait 1982;Wait and Williams 1985).…”

Section: Introductionmentioning

confidence: 99%

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

Schenkel

Morrison

1990

Geophysical Prospecting

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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.

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A Note on the Mathematical Representation of the Source for Tubular Transmitting Antennas

Cited by 8 publications

References 5 publications

A Comment on “A Note on the Mathematical Representation of the Source for Tubular Transmitting Antennas” by D. V. Otto

A Comment on “A Note on the Mathematical Representation of the Source for Tubular Transmitting Antennas” by D. V. Otto

The electrical resistivity method in cased boreholes

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

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A Note on the Mathematical Representation of the Source for Tubular Transmitting Antennas

Cited by 8 publications

References 5 publications

A Comment on “A Note on the Mathematical Representation of the Source for Tubular Transmitting Antennas” by D. V. Otto

A Comment on “A Note on the Mathematical Representation of the Source for Tubular Transmitting Antennas” by D. V. Otto

The electrical resistivity method in cased boreholes

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

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