Asymptotic approximation of waves due to a dipole on a two‐layer medium

W. C. Chew, J. A. Kong

Research output: Contribution to journalArticle

Abstract

The TM wave due to a horizontal magnetic dipole is first expanded in terms of a series of integrals, each of which is interpreted as due to an image source. Each of the image source integrals possesses a branch point and a high‐order pole which can be close to the saddle point. To facilitate uniform asymptotic approximation, the branch point is first removed by a transformation, which results in an integral with a high‐order pole near three saddle points. The uniform asymptotic approximation of such an integral is obtained through the use of the generalized Weber's function. The result agrees with numerical integration much better than the geometrical optics approximations (GOA). For the case of TE waves, the pole is far away, and our analysis reduces to the three‐saddle‐point analysis where the behavior of the wave can be approximated by parabolic cylinder functions. We show that in such a case our result agrees better with the experiment than GOA. The uniform asymptotic approximation of the waves extends the domain of validity of the image source representation, which is extremely useful when the layer is thick.

Original languageEnglish (US)
Pages (from-to)509-513
Number of pages5
JournalRadio Science
Volume17
Issue number3
DOIs
StatePublished - Jan 1 1982

Fingerprint

dipoles
Geometrical optics
Poles
approximation
poles
geometrical optics
saddle points
numerical integration
magnetic dipoles
experiment
Experiments
analysis

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Earth and Planetary Sciences(all)
  • Electrical and Electronic Engineering

Cite this

Asymptotic approximation of waves due to a dipole on a two‐layer medium. / Chew, W. C.; Kong, J. A.

In: Radio Science, Vol. 17, No. 3, 01.01.1982, p. 509-513.

Research output: Contribution to journalArticle

Chew, W. C. ; Kong, J. A. / Asymptotic approximation of waves due to a dipole on a two‐layer medium. In: Radio Science. 1982 ; Vol. 17, No. 3. pp. 509-513.
@article{7c694b2a28454c418daa4c0c69e742d6,
title = "Asymptotic approximation of waves due to a dipole on a two‐layer medium",
abstract = "The TM wave due to a horizontal magnetic dipole is first expanded in terms of a series of integrals, each of which is interpreted as due to an image source. Each of the image source integrals possesses a branch point and a high‐order pole which can be close to the saddle point. To facilitate uniform asymptotic approximation, the branch point is first removed by a transformation, which results in an integral with a high‐order pole near three saddle points. The uniform asymptotic approximation of such an integral is obtained through the use of the generalized Weber's function. The result agrees with numerical integration much better than the geometrical optics approximations (GOA). For the case of TE waves, the pole is far away, and our analysis reduces to the three‐saddle‐point analysis where the behavior of the wave can be approximated by parabolic cylinder functions. We show that in such a case our result agrees better with the experiment than GOA. The uniform asymptotic approximation of the waves extends the domain of validity of the image source representation, which is extremely useful when the layer is thick.",
author = "Chew, {W. C.} and Kong, {J. A.}",
year = "1982",
month = "1",
day = "1",
doi = "10.1029/RS017i003p00509",
language = "English (US)",
volume = "17",
pages = "509--513",
journal = "Radio Science",
issn = "0048-6604",
publisher = "American Geophysical Union",
number = "3",

}

TY - JOUR

T1 - Asymptotic approximation of waves due to a dipole on a two‐layer medium

AU - Chew, W. C.

AU - Kong, J. A.

PY - 1982/1/1

Y1 - 1982/1/1

N2 - The TM wave due to a horizontal magnetic dipole is first expanded in terms of a series of integrals, each of which is interpreted as due to an image source. Each of the image source integrals possesses a branch point and a high‐order pole which can be close to the saddle point. To facilitate uniform asymptotic approximation, the branch point is first removed by a transformation, which results in an integral with a high‐order pole near three saddle points. The uniform asymptotic approximation of such an integral is obtained through the use of the generalized Weber's function. The result agrees with numerical integration much better than the geometrical optics approximations (GOA). For the case of TE waves, the pole is far away, and our analysis reduces to the three‐saddle‐point analysis where the behavior of the wave can be approximated by parabolic cylinder functions. We show that in such a case our result agrees better with the experiment than GOA. The uniform asymptotic approximation of the waves extends the domain of validity of the image source representation, which is extremely useful when the layer is thick.

AB - The TM wave due to a horizontal magnetic dipole is first expanded in terms of a series of integrals, each of which is interpreted as due to an image source. Each of the image source integrals possesses a branch point and a high‐order pole which can be close to the saddle point. To facilitate uniform asymptotic approximation, the branch point is first removed by a transformation, which results in an integral with a high‐order pole near three saddle points. The uniform asymptotic approximation of such an integral is obtained through the use of the generalized Weber's function. The result agrees with numerical integration much better than the geometrical optics approximations (GOA). For the case of TE waves, the pole is far away, and our analysis reduces to the three‐saddle‐point analysis where the behavior of the wave can be approximated by parabolic cylinder functions. We show that in such a case our result agrees better with the experiment than GOA. The uniform asymptotic approximation of the waves extends the domain of validity of the image source representation, which is extremely useful when the layer is thick.

UR - http://www.scopus.com/inward/record.url?scp=0020127179&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0020127179&partnerID=8YFLogxK

U2 - 10.1029/RS017i003p00509

DO - 10.1029/RS017i003p00509

M3 - Article

AN - SCOPUS:0020127179

VL - 17

SP - 509

EP - 513

JO - Radio Science

JF - Radio Science

SN - 0048-6604

IS - 3

ER -