This paper describes a method for the fast evaluation of the Sommerfeld integrals for modeling a vertical dipole antenna array in a borehole. When we analyze the antenna inside a medium modeled by multiple cylindrical layers with the Method of Moment (MoM), we need a Green's function including the scattered field from the cylindrical boundaries. We focus on the calculation of Green's functions under the condition that both the detector and the source are situated in the innermost layer, since the Green's functions are used to form the impedance matrix of the antenna. Considering bounds on the location of singularities on a complex wave number plane, a fast convergent integration path where pole tracking is unnecessary is considered for numerical integration. Furthermore, as an approximation of the Sommerfeld integral, we describe an asymptotic expansion of the integrals along the branch cuts. The pole contribution of TM01 and HE11 modes are considered in the asymptotic expansion. To obtain numerical results, we use a fast convergent integration path that always proves to be accurate and efficient. The asymptotic expansion works well under specific conditions. The Sommerfeld integral values calculated with the fast evaluation method is used to model the array antenna in a borehole with the MoM. We compare the MoM data with experimental data, and we show the validity of the fast evaluation method.
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Satoshi EBIHARA, Weng Cho CHEW, "Calculation of Sommerfeld Integrals for Modeling Vertical Dipole Array Antenna for Borehole Radar" in IEICE TRANSACTIONS on Electronics,
vol. E86-C, no. 10, pp. 2085-2096, October 2003, doi: .
Abstract: This paper describes a method for the fast evaluation of the Sommerfeld integrals for modeling a vertical dipole antenna array in a borehole. When we analyze the antenna inside a medium modeled by multiple cylindrical layers with the Method of Moment (MoM), we need a Green's function including the scattered field from the cylindrical boundaries. We focus on the calculation of Green's functions under the condition that both the detector and the source are situated in the innermost layer, since the Green's functions are used to form the impedance matrix of the antenna. Considering bounds on the location of singularities on a complex wave number plane, a fast convergent integration path where pole tracking is unnecessary is considered for numerical integration. Furthermore, as an approximation of the Sommerfeld integral, we describe an asymptotic expansion of the integrals along the branch cuts. The pole contribution of TM01 and HE11 modes are considered in the asymptotic expansion. To obtain numerical results, we use a fast convergent integration path that always proves to be accurate and efficient. The asymptotic expansion works well under specific conditions. The Sommerfeld integral values calculated with the fast evaluation method is used to model the array antenna in a borehole with the MoM. We compare the MoM data with experimental data, and we show the validity of the fast evaluation method.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e86-c_10_2085/_p
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@ARTICLE{e86-c_10_2085,
author={Satoshi EBIHARA, Weng Cho CHEW, },
journal={IEICE TRANSACTIONS on Electronics},
title={Calculation of Sommerfeld Integrals for Modeling Vertical Dipole Array Antenna for Borehole Radar},
year={2003},
volume={E86-C},
number={10},
pages={2085-2096},
abstract={This paper describes a method for the fast evaluation of the Sommerfeld integrals for modeling a vertical dipole antenna array in a borehole. When we analyze the antenna inside a medium modeled by multiple cylindrical layers with the Method of Moment (MoM), we need a Green's function including the scattered field from the cylindrical boundaries. We focus on the calculation of Green's functions under the condition that both the detector and the source are situated in the innermost layer, since the Green's functions are used to form the impedance matrix of the antenna. Considering bounds on the location of singularities on a complex wave number plane, a fast convergent integration path where pole tracking is unnecessary is considered for numerical integration. Furthermore, as an approximation of the Sommerfeld integral, we describe an asymptotic expansion of the integrals along the branch cuts. The pole contribution of TM01 and HE11 modes are considered in the asymptotic expansion. To obtain numerical results, we use a fast convergent integration path that always proves to be accurate and efficient. The asymptotic expansion works well under specific conditions. The Sommerfeld integral values calculated with the fast evaluation method is used to model the array antenna in a borehole with the MoM. We compare the MoM data with experimental data, and we show the validity of the fast evaluation method.},
keywords={},
doi={},
ISSN={},
month={October},}
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TY - JOUR
TI - Calculation of Sommerfeld Integrals for Modeling Vertical Dipole Array Antenna for Borehole Radar
T2 - IEICE TRANSACTIONS on Electronics
SP - 2085
EP - 2096
AU - Satoshi EBIHARA
AU - Weng Cho CHEW
PY - 2003
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E86-C
IS - 10
JA - IEICE TRANSACTIONS on Electronics
Y1 - October 2003
AB - This paper describes a method for the fast evaluation of the Sommerfeld integrals for modeling a vertical dipole antenna array in a borehole. When we analyze the antenna inside a medium modeled by multiple cylindrical layers with the Method of Moment (MoM), we need a Green's function including the scattered field from the cylindrical boundaries. We focus on the calculation of Green's functions under the condition that both the detector and the source are situated in the innermost layer, since the Green's functions are used to form the impedance matrix of the antenna. Considering bounds on the location of singularities on a complex wave number plane, a fast convergent integration path where pole tracking is unnecessary is considered for numerical integration. Furthermore, as an approximation of the Sommerfeld integral, we describe an asymptotic expansion of the integrals along the branch cuts. The pole contribution of TM01 and HE11 modes are considered in the asymptotic expansion. To obtain numerical results, we use a fast convergent integration path that always proves to be accurate and efficient. The asymptotic expansion works well under specific conditions. The Sommerfeld integral values calculated with the fast evaluation method is used to model the array antenna in a borehole with the MoM. We compare the MoM data with experimental data, and we show the validity of the fast evaluation method.
ER -