### 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 language | English (US) |
---|---|

Pages (from-to) | 509-513 |

Number of pages | 5 |

Journal | Radio Science |

Volume | 17 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1982 |

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### ASJC Scopus subject areas

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

### Cite this

*Radio Science*,

*17*(3), 509-513. https://doi.org/10.1029/RS017i003p00509

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

Research output: Contribution to journal › Article

*Radio Science*, vol. 17, no. 3, pp. 509-513. https://doi.org/10.1029/RS017i003p00509

}

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 -