1887
Volume 34, Issue 1-2
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

Gradients of magnetic and gravity data are used routinely to enhance 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 first and second order, higher orders being used less frequently due to noise problems. This paper discusses the benefits of a generalized approach using fractional gradients, demonstrating their usefulness as an aid to interpretation, both on theoretical models and on aeromagnetic data from the Free State province, South Africa. 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 deconvolution solutions.

Loading

Article metrics loading...

/content/journals/10.1071/EG03051
2003-03-01
2026-01-14
Loading full text...

Full text loading...

References

  1. Blakely, R. J., 1995, Potential Theory in Gravity and Magnetic Applications’: Cambridge University Press.
  2. Caputo, M., 1993, The splitting of seismic rays due to dispersion in the Earth’s interior: Rend. Fis. Acc. Lincei (series IX), 4, 279-286.
  3. Craig, J. D., and Brown, J. C., 1986, Inverse problems in astronomy: Adam Hilger Ltd.
  4. Gunn, P. J., 1975, Linear Transformations of Gravity and Magnetic Fields: Geophysical Prospecting, 23, 300-312.
  5. Gunn, P. J., Fitzgerald, D., Yassi, N., and Dart, P., 1997, New Algorithms for Visually Enhancing Airborne Geophysical Data: Exploration Geophysics, 28, 220-224.
  6. Heymans, N., and Bauwens, J. C., 1994, Fractal rheological models and fractional differential equations for viscoelastic behaviour: Rheol. Acta, 33, 210-219.
  7. Hood, P. J., 1963, Gradient measurements in aeromagnetic surveying: Geophysics, 30, 891-902.
  8. Horn, B. K.P., 1982, Hill shading and the reflectance map: Geo-Processing, 2, 65-146.
  9. Hsu, S-K., Sibuet, J-C., and Shyu, C-T., 1996, High-resolution detection of geologic boundaries from potential field anomalies: An enhanced analytic signal technique: Geophysics, 61, 373-386.
  10. Hsu, S-K., 2002, Imaging magnetic sources using Euler’s equation: Geophysical Prospecting, 50, 15-25.
  11. Koeller, R. C., 1984, Applications of fractional calculus to the theory of viscoelasticity: J. Appl. Mech., 51, 299-307.
  12. Lenormand, R., 1992, Use of fractional derivatives for fluid flow in heterogenous media: 3rd European conference on the mathematics of oil recovery, Delft.
  13. Mainardi, F., 1996, Applications of fractional calculus in mechanics: Proceedings of the 2nd International Workshop on Transforms and Special Functions, Varna, 309-334.
  14. Nabighian, M. N., 1972, The analytic signal of two-dimensional magnetic bodies with polygonal cross-section: its properties and use for automated anomaly interpretation: Geophysics, 37, 507.
  15. Nabighian, M. N., 1974, Additional comments on the analytic signal of two dimensional magnetic bodies with polygonal cross-section: Geophysics, 39, 85-92.
  16. Nabighian, M. N., 1984, Toward a three-dimensional automatic interpretation of potential field data via generalized Hilbert transforms: Fundamental relations: Geophysics, 49, 780.
  17. Oldham, K. B., and Spanier, J., 1974, The fractional calculus. Theory and applications of differentiation and integration to arbitrary order, Academic Press.
  18. Reid, A. B., Allsop, J. M., Granser, H., Millet, A. J., and Somerton, I. W., 1990, Magnetic interpretation in three dimensions using Euler deconvolution: Geophysics, 55, 80-91.
  19. Stavrev, P. Y., 1997, Euler deconvolution using differential similarity transformations of gravity or magnetic anomalies: Geophysical Prospecting, 45, 207-246.
  20. Stephenson, G., 1978, Mathematical methods for science students, Longman Press.
  21. Thomson, D. T., 1982, Euldph : A new technique for making computer assisted depth estimates from magnetic data: Geophysics, 47, 31-37.
/content/journals/10.1071/EG03051
Loading
  • Article Type: Research Article
Keyword(s): analytic signals; edge detection; Euler deconvolution; Gradients; pole reduction; sunshading

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error