Skip to main content

Volume 57 Supplement 8

Special Issue: Applications and Interpretation of Modern Magnetic Surveys

Can we estimate total magnetization directions from aeromagnetic data using Helbig’s integrals?


An algorithm that implements Helbig’s (1963) integrals for estimating the vector components (mx, my, mz) of the magnetic dipole moment from the first order moments of the vector magnetic field components (ΔX, ΔY, ΔZ) is tested on real and synthetic data. After a grid of total field aeromagnetic data is converted to vector component grids using Fourier filtering, Helbig’s infinite integrals are evaluated as finite integrals in small moving windows using a quadrature algorithm based on the 2-D trapezoidal rule. Prior to integration, best-fit planar surfaces must be removed from the component data within the data windows in order to make the results independent of the coordinate system origin. Two different approaches are described for interpreting the results of the integration. In the “direct” method, results from pairs of different window sizes are compared to identify grid nodes where the angular difference between solutions is small. These solutions provide valid estimates of total magnetization directions for compact sources such as spheres or dipoles, but not for horizontally elongated or 2-D sources. In the “indirect” method, which is more forgiving of source geometry, results of the quadrature analysis are scanned for solutions that are parallel to a specified total magnetization direction.


  1. Bhattacharyya, B. K., A method for computing the total magnetization vector and the dimensions of a rectangular block-shaped body from magnetic anomalies, Geophysics, 31, 74–96, 1966.

    Article  Google Scholar 

  2. Blakely, R. J., Potential Theory in Gravity and Magnetic Applications, Cambridge University Press, Cambridge, 441 pp., 1995.

    Book  Google Scholar 

  3. Emilia, D. A. and R. L. Massey, Magnetization estimation for nonuniformly magnetized seamounts, Geophysics, 39, 223–321, 1974.

    Article  Google Scholar 

  4. Helbig, K., Some integrals of magnetic anomalies and their relation to the parameters of the disturbing body, Zeitschrift für Geophysik, 29(2), 83–96, 1963.

    Google Scholar 

  5. Lourenco, J. S. and H. F. Morrison, Vector magnetic anomalies derived from measurements of a single component of the field, Geophysics, 38(2), 359–368, 1973.

    Article  Google Scholar 

  6. Macmillian, S., S. Maus, T. Bondar, A. Chambodut, V. Golovkov, R. Holme, B. Langlais, V. Lesur, F. Lowes, H. Lühr, W. Mai, M. Mandea, N. Olsen, M. Rother, T. Sabaka, A. Thomson, and I. Wardinski, Ninth generation International Geomagnetic Reference Field released, EOS, Transactions, American Geophysical Union, 84(46), 503, 18 November 2003.

    Article  Google Scholar 

  7. McCracken, D. D. and W. S. Dorn, Numerical Methods and Fortran Programming, John Wiley and Sons, Inc., New York, 457 pp., 1964.

    Google Scholar 

  8. Mederios, W. E. and J. B. C. Silva, Simultaneous estimation of total magnetization direction and 3-D spatial orientation, Geophysics, 60(5), 1365–1377, 1995.

    Article  Google Scholar 

  9. Parker, R. L., L. Shure, and J. A. Hildebrand, The application of inverse theory to seamount magnetism, Rev. Geophys., 25, 17–40, 1987.

    Article  Google Scholar 

  10. Rajagopalan, S., P. Schmidt, and D. Clark, Rock magnetism and geophysical interpretation of the Black Hill Norite, South Australia, Exploration Geophysics, 24, 209–212, 1993.

    Article  Google Scholar 

  11. Rao, B. S. R., T. K. S. Prakasa Rao, and A. S. Krishna Murthy, A note on magnetized spheres, Geophys. Prosp., 25, 746–757, 1977.

    Article  Google Scholar 

  12. Schmidt, P. W. and D. A. Clark, Directions of magnetization and vector anomalies derived from total field surveys, Preview, 70, 30–32, 1997.

    Google Scholar 

  13. Schmidt, P. W. and D. A. Clark, The calculation of magnetic components and moments from TMI: A case history from the Tuckers igneous complex, Queensland, Exploration Geophysics, 29, 609–614, 1998.

    Article  Google Scholar 

  14. Schnetzler, C. C. and P. T. Taylor, Evaluation of an observational method for estimation of remanent magnetization, Geophysics, 49, 282–290, 1984.

    Article  Google Scholar 

  15. U.S. Geological Survey and Sander Geophysics, Ltd., Digital data from the Isleta-Kirtland aeromagnetic survey, collected south of Albuquerque, New Mexico, U.S. Geological Survey Open-File Report 98-341 (CD-ROM), 1998.

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Jeffrey D. Phillips.

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Phillips, J.D. Can we estimate total magnetization directions from aeromagnetic data using Helbig’s integrals?. Earth Planet Sp 57, 681–689 (2005).

Download citation

Key words

  • Aeromagnetic
  • magnetization
  • interpretation