Calculation of gravity due to a vertical cylinder using a spherical harmonic series and numerical integration

Sung-Ho Na; Hyoungrea Rim; Young-Hong Shin; Mutaek Lim; Yeong-Sue Park

doi:10.1071/EG14123

ISSN: 0812-3985
E-ISSN: 1834-7533

Calculation of gravity due to a vertical cylinder using a spherical harmonic series and numerical integration
Authors Sung-Ho Na^a,c, Hyoungrea Rim^b,c,d, Young-Hong Shin^b, Mutaek Lim^b and Yeong-Sue Park^b,c
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^a Space Geodetic Observation Center, NGII, Sejong 339-821, Korea. ^b Korea Institute of Geoscience and Mineral Resources, Daejeon 305-350, Korea. ^c Geophysical Exploration, Korea University of Science and Technology, Daejeon 305-350, Korea. ^d Corresponding author. Email: [email protected]
Publisher: Australian Society of Exploration Geophysicists
Source: Exploration Geophysics, Volume 46, Issue 4, Dec 2015, p. 381 - 386
DOI: https://doi.org/10.1071/EG14123
- Received: 12 Dec 2014
- Accepted: 12 Dec 2014
- Published online: 01 Dec 2015

Abstract

[

We developed a spherical harmonic series that represents the gravitational potential and its gravity field due to a buried right vertical cylinder. This series can be used at far- and intermediate-regions, and is fast and accurate, using only a few terms. We compared the values of the fields acquired by this new spherical harmonic series, with ones computed by direct numerical integrations, using a fine-mesh structure for a vertical cylinder. Results of the calculations are shown and performances of the two different methods are compared. Faithfulness of the spherical harmonic series is tested with an inversion example.

In this paper, the spherical harmonic series of the gravitational potential and its gravity field due to a right vertical cylinder was developed. This series can be used at far and intermediate regions, and it is fast and accurate, using only a few terms.

]

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References

Dwight, H. B., 1961, Tables of integrals and other mathematical data: The Macmillan Company.
Gradshteyn, I. S., and Ryzhik, I. M., 1980, Table of integrals, series, and products: Academic Press.
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Morse, P. M., and Feshbach, H., 1953, Methods of theoretical physics - part II: McGraw-Hill Book Company, Inc.
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Calculation of gravity due to a vertical cylinder using a spherical harmonic series and numerical integration

Exploration Geophysics 46, 381 (2015); https://doi.org/10.1071/EG14123

/content/journals/10.1071/EG14123

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Article Type: Research Article

Keyword(s): gravity; gravity potential; numerical integration; spherical harmonics; vertical cylinder

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Calculation of gravity due to a vertical cylinder using a spherical harmonic series and numerical integration

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