REPLY BY D. RANKIN TO THE DISCUSSION BY J. T. WEAVER

Geophysics ◽  
1963 ◽  
Vol 28 (3) ◽  
pp. 490-490
Author(s):  
D. Rankin
Keyword(s):  
Electromagnetic Field ◽  
Plane Wave ◽  
Radiation Field ◽  
Free Space ◽  
Wave Incident ◽  
Induction Field ◽  
The Earth ◽  
Plane Wave Incident

I am indebted to Weaver if he has indeed clarified certain points which I had previously considered to be obvious. Cagniard (1953) states explicitly the magnitude of the wavelengths in free space and it is further implicit in the work of Rankin (1962) that it is indeed this same electromagnetic field which is being considered. The plane wave aspect of the problem arises from the extent of and not the distance from the source so that truly it is the induction field and not the radiation field that is under discussion. I had believed, until this note by Weaver, that d’Erceville and Kunetz (1962) also considered a plane wave incident on the earth and in fact that I was merely following both Cagniard and d’Erceville and Kunetz in this matter. The consistency of the results would tend to confirm this belief.

The wide-spacing approximation applied to multiple scattering and sloshing problems

1990 ◽  
Vol 210 ◽  
pp. 647-658 ◽  
Author(s):  
D. V. Evans
Keyword(s):  
Plane Wave ◽  
Closed Form ◽  
Multiple Scattering ◽  
Water Wave ◽  
Wave Incident ◽  
Reflection And Transmission ◽  
Wide Spacing ◽  
Plane Wave Incident ◽  
Rigid Walls

Linear water-wave theor is used in conjuctin with a wide-spacing approximation to develop closed-form expressions for the reflection and transmission coeffcients appropriate to a plane wave incident upon any number of identical equally spaced obstacles in two dimensins, and also to derive a real expressin from which the sloshing requencies, which occur when the bodies are bounded by rigid walls, can be determined. In each case the solutin is in terms of known properties of radiation problems associated with any one of the bodies in isolation.

scholarly journals Scattering from a Buried PEMC Cylinder Illuminated by a Normally Incident Plane Wave Propagating in Free Space

2018 ◽  
Vol 8 (1) ◽  
pp. 1-7 ◽  
Author(s):  
A. Hamid ◽  
F. Cooray
Keyword(s):  
Plane Wave ◽  
Half Space ◽  
Free Space ◽  
Transverse Magnetic ◽  
Planar Interface ◽  
Burial Depth ◽  
Multiple Reflections ◽  
Incident Plane ◽  
Plane Wave Incident ◽  
Expansion Coefficients

A rigorous solution is presented to the problem of scattering by a perfect electromagnetic conducting (PEMC) circular cylinder buried inside a dielectric half-space that is excited by a normally incident transverse magnetic (TM) plane wave propagating in free space. The plane wave incident on the planar interface separating the two media creates fields transmitting into the dielectric half- space becoming the known primary incident fields for the buried cylinder. When the fields scattered by the cylinder, in response to those fields incident on it, are incident at the interface, they generate fields reflected into the dielectric half-space and fields transmitted into free space. These fields, and the fields scattered by the cylinder are expressed in terms of appropriate cylindrical waves consisting of unknown expansion coefficients which are to be determined. Imposing boundary conditions at the surface of the cylinder and at a point on the planar interface, enables the evaluation of the unknown coefficients. This procedure is then replicated, by considering multiple reflections and transmissions at the planar interface, and multiple scattering by the cylinder, till a preset accuracy is obtained for the reflection coefficient at the particular point on the interface. The refection coefficient at this point is then computed for cylinders of different sizes, to show how it varies with the PEMC admittance of the cylinder, its burial depth, and the permittivity of the dielectric half-space.

REFLECTION FROM A WIRE GRID PARALLEL TO A CONDUCTING PLANE

1954 ◽  
Vol 32 (9) ◽  
pp. 571-579 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Plane Wave ◽  
Transmission Line ◽  
Incident Wave ◽  
Electric Vector ◽  
Wave Incident ◽  
Conducting Surface ◽  
Conducting Plane ◽  
Wire Grid ◽  
Parallel Wire ◽  
Plane Wave Incident

A solution is outlined for the problem of a plane wave incident obliquely on a parallel-wire grid which is backed by a plane conducting surface. The electric vector of the incident wave is taken to be parallel to the grid wires. The equivalent transmission line problem is pointed out. It is shown that, in certain cases, a resistive wire grid will absorb all the energy in the incident wave.

scholarly journals Квазистационарное приближение в задаче возбуждения низкочастотных электромагнитных полей в литосфере

2021 ◽  
Vol 91 (1) ◽  
pp. 82
Author(s):  
Е.Д. Терещенко ◽  
П.Е. Терещенко
Keyword(s):  
Electromagnetic Field ◽  
Plane Wave ◽  
Low Frequency ◽  
Wave Impedance ◽  
Frequency Range ◽  
Actual Surface ◽  
The Earth ◽  
Analytical Formulas ◽  
Lower Frequency Range ◽  
Stationary Approximation

The paper considers the excitation of a horizontal grounded antenna of the ELF-ELF electromagnetic field and a lower frequency range in a two-layer environment. Approximate analytical formulas are obtained that describe quite completely behavior of fields in the low-frequency range. The accuracy of using the quasi-stationary approximation is analyzed. The possibility of replacing the actual surface impedance with a plane wave impedance, normally falling on the interface. For a number of experiments carried out on the Kola Peninsula in the framework of the international cooperation (FENICS-2014, FENICS-2019), the frequency boundaries of the applicability of the approximate approach in assessing conductivity of the Earth.

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