### Abstract

A contour transformation method is applied to the computation of the Sommerfeld integral associated with a vertical electric dipole above Earth. In this method the slowly varying part of the transformed Sommerfeld integrand is approximated by a few exponential terms using Prony's method. The resulting integrals are then carried out analytically, thereby, yielding incomplete Lipschitz-Hankel integrals. Therefore numerical integration of the Sommerfeld integral is unnecessary since the incomplete Lipschitz-Hankel integrals are computed using efficient Bessel series expansions. This method is compared with a direct numerical integration of the Sommerfeld integral and a contour deformation technique which also utilizes Prony's method. The results demonstrate that the contour transformation method enables the accurate and efficient computation of the Sommerfeld integral for all source and observation locations (i.e., near zone, far zone and even grazing). This technique can also be applied to problems involving multiple layers.

Original language | English (US) |
---|---|

Pages (from-to) | 309-317 |

Number of pages | 9 |

Journal | Radio Science |

Volume | 28 |

Issue number | 3 |

State | Published - May 1993 |

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### ASJC Scopus subject areas

- Computer Networks and Communications
- Atmospheric Science
- Computers in Earth Sciences
- Geochemistry and Petrology
- Geophysics
- Instrumentation

### Cite this

*Radio Science*,

*28*(3), 309-317.

**Application of the contour transformation method to a vertical electric dipole over Earth.** / Dvorak, Steven L; Mechaik, Mehdi M.

Research output: Contribution to journal › Article

*Radio Science*, vol. 28, no. 3, pp. 309-317.

}

TY - JOUR

T1 - Application of the contour transformation method to a vertical electric dipole over Earth

AU - Dvorak, Steven L

AU - Mechaik, Mehdi M.

PY - 1993/5

Y1 - 1993/5

N2 - A contour transformation method is applied to the computation of the Sommerfeld integral associated with a vertical electric dipole above Earth. In this method the slowly varying part of the transformed Sommerfeld integrand is approximated by a few exponential terms using Prony's method. The resulting integrals are then carried out analytically, thereby, yielding incomplete Lipschitz-Hankel integrals. Therefore numerical integration of the Sommerfeld integral is unnecessary since the incomplete Lipschitz-Hankel integrals are computed using efficient Bessel series expansions. This method is compared with a direct numerical integration of the Sommerfeld integral and a contour deformation technique which also utilizes Prony's method. The results demonstrate that the contour transformation method enables the accurate and efficient computation of the Sommerfeld integral for all source and observation locations (i.e., near zone, far zone and even grazing). This technique can also be applied to problems involving multiple layers.

AB - A contour transformation method is applied to the computation of the Sommerfeld integral associated with a vertical electric dipole above Earth. In this method the slowly varying part of the transformed Sommerfeld integrand is approximated by a few exponential terms using Prony's method. The resulting integrals are then carried out analytically, thereby, yielding incomplete Lipschitz-Hankel integrals. Therefore numerical integration of the Sommerfeld integral is unnecessary since the incomplete Lipschitz-Hankel integrals are computed using efficient Bessel series expansions. This method is compared with a direct numerical integration of the Sommerfeld integral and a contour deformation technique which also utilizes Prony's method. The results demonstrate that the contour transformation method enables the accurate and efficient computation of the Sommerfeld integral for all source and observation locations (i.e., near zone, far zone and even grazing). This technique can also be applied to problems involving multiple layers.

UR - http://www.scopus.com/inward/record.url?scp=0027593275&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027593275&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0027593275

VL - 28

SP - 309

EP - 317

JO - Radio Science

JF - Radio Science

SN - 0048-6604

IS - 3

ER -