1887
Volume 48 Number 3
  • E-ISSN: 1365-2478

Abstract

Existing techniques for computing the gravitational field due to a homogeneous polyhedron all transform the required volume integral, expressing the field due to a volume distribution of mass, into a surface integral, expressing the potential due to a surface mass distribution over the boundary of the source body. An alternative representation is also possible and results in a surface integral expressing the potential due to a variable‐strength double layer located on the polyhedral source boundary. Manipulation of this integral ultimately allows the gravitational field component in an arbitrary direction to be expressed as a weighted sum of the potentials due to two basic source distributions. These are a uniform‐strength double layer located on all faces and a uniform‐strength line source located along all edges. The derivatives of the gravitational field components can also be expressed in a similar form as can the magnetic field components due to a homogeneous magnetic polyhedron. It follows that the present approach can be used to generate a universal program capable of modelling all the commonly used potential field responses due to 3D bodies of arbitrary shape.

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2001-12-24
2024-04-18
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References

  1. BarnettC.T.1976. Theoretical modeling of the magnetic and gravitational fields of an arbitrary shaped three‐dimensional body. Geophysics41, 13531364.
    [Google Scholar]
  2. BrandL.1957. Vector Analysis. John Wiley & Sons, Inc.
  3. FurnessP.1994. A physical approach to computing magnetic fields. Geophysical Prospecting42, 405416.
    [Google Scholar]
  4. GötzeH.J. & LahmeyerB.1988. Application of three‐dimensional interactive modeling in gravity and magnetics. Geophysics53, 10961108.
    [Google Scholar]
  5. GuptasarmaD. & SinghB.1999. New scheme for computing the magnetic field resulting from a uniformly magnetized arbitrary polyhedron. Geophysics64, 7074.
    [Google Scholar]
  6. HolsteinH. & KetteridgeB.1996. Gravimetric analysis of uniform polyhedra. Geophysics61, 357364.
    [Google Scholar]
  7. IvanM.1994. Upward continuation of potential fields from a polyhedral surface. Geophysical Prospecting42, 391404.
    [Google Scholar]
  8. LiX. & ChouteauM.1998. Three‐dimensional gravity modeling in all space. Surveys in Geophysics19, 339368.
    [Google Scholar]
  9. MacMillanW.D.1958. The Theory of the Potential. Dover Publications, Inc.
  10. MaxwellJ.C.1954. A Treatise on Electricity and Magnetism. Dover Publications, Inc.
  11. OkabeM.1979. Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies. Geophysics44, 730741.
    [Google Scholar]
  12. PaulM.K.1974. The gravity effect of a homogeneous polyhedron for three‐dimensional interpretation. Pure and Applied Geophysics112, 553561.
    [Google Scholar]
  13. PohánkaV.1988. Optimum expression for computation of the gravity field of a homogeneous polyhedral body. Geophysical Prospecting36, 733751.
    [Google Scholar]
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  • Article Type: Research Article

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