The Application Of Fractional Calculus To Potential Field Data

G.R.J. Cooper; D.R. Cowan

doi:10.1071/ASEG2003ab028

ISSN: 2202-0586
E-ISSN:

oa The Application Of Fractional Calculus To Potential Field Data
Authors G.R.J. Cooper^a and D.R. Cowan^b
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^a School of Geosciences University of the Witwatersrand Johannesburg,, South Africa, [email protected] ^b Cowan Geodata 12 Edna Road, Dalkeith, Perth, [email protected]
Publisher: Australian Society of Exploration Geophysicists
Source: ASEG Extended Abstracts, Volume 2003, Issue ASEG2003 - 16th Geophysical Conference, Aug 2003, p. 1 - 5
DOI: https://doi.org/10.1071/ASEG2003ab028
- Published online: 01 Aug 2003

Abstract

Gradients of magnetic and gravity data are used routinely to sharpen the edges of anomalies, or as input to interpretation techniques such as analytic signal analysis or Euler deconvolution. The most commonly used gradients are of 1^st and 2ⁿ order, higher orders being used less frequently due to noise problems. This paper discusses the benefits of a generalised approach using fractional gradients, demonstrating their usefulness as an aid to interpretation. Fractional horizontal gradients are suggested as a means of avoiding the instability problems present when magnetic data from low latitudes is reduced to the pole. They also allow the use of an improved sunshading algorithm that is less affected by noise than the standard method. Fractional vertical gradients may be used to generate both enhanced analytic signal data and enhanced Euler decon volution solutions.

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2003-08-01

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References

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Mainardi F. 1996. Applications of fractional calculus in mechanics. Proceedings of the 2nd International Workshop on Transforms and Special Functions, Varna, 309-334.
Oldham K.B., and Spanier J. 1974. The fractional calculus. Theory and applications of differentiation and integration to arbitrary order. Academic Press.
Reid AB., Allsop J.M., Granser H., Millet AJ., and Somerton I.W. 1990. Magnetic interpretation in three dimensions using Euler deconvolution. Geophysics 55, 80-91.

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Article Type: Research Article

Keyword(s): Euler deconvolution; Gradients; pole reduction; sunshading

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