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Fast 3D forward modeling of the magnetic field and gradient tensor on an undulated surface

  • Kun Li
  • Long-Wei Chen
  • Qing-Rui Chen
  • Shi-Kun Dai
  • Qian-Jiang Zhang
  • Dong-Dong Zhao
  • Jia-Xuan Ling
Article
  • 35 Downloads

Abstract

Magnetic field gradient tensor technique provides abundant data for delicate inversion of subsurface magnetic susceptibility distribution. Large scale magnetic data inversion imaging requires high speed and accuracy for forward modeling. For arbitrarily distributed susceptibility data on an undulated surface, we propose a fast 3D forward modeling method in the wavenumber domain based on (1) the wavenumber-domain expression of the prism combination model and the Gauss–FFT algorithm and (2) cubic spline interpolation. We apply the proposed 3D forward modeling method to synthetic data and use weighting coefficients in the wavenumber domain to improve the modeling for multiple observation surfaces, and also demonstrate the accuracy and efficiency of the proposed method.

Keywords

Undulated surface magnetic field gradient tensor 3D forward modeling Gauss–FFT algorithm wavenumber domain 

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Notes

Acknowledgements

We thank Dr. Yungui Xu and Dr. Shunguo Wang for help with the English. The editors and reviewers are also thanked for comments and suggestions that improved the manuscript.

References

  1. Blakely, R. J., 1996, Potential theory in gravity and magnetic applications: Cambridge University Press.Google Scholar
  2. Burrows, B. L., and Colwell, D. J., 1990, The fourier transform of the unit step function: International Journal of Mathematical Education in Science and Technology, 21(4), 629–635.CrossRefGoogle Scholar
  3. Chen, Z. X., Meng, X. H., and Liu, G. F., 2012, The GPU-based parallel calculation of gravity and magnetic anomalies for 3D arbitrary bodies: Geophysical and Geochemical Exploration, 36(1), 117–121.Google Scholar
  4. Chai, Y. P., 1996, Shift sampling theory about Fourier transform computation: Science in China (Series E), 26(5), 450–456.Google Scholar
  5. Eppelbaum, L. V., 2011, Study of magnetic anomalies over archaeological targets in urban environments: Physics & Chemistry of the Earth, 36(16), 1318–1330.CrossRefGoogle Scholar
  6. Furness, P., 1994, A physical approach to computing magnetic fields: Geophysical Prospecting, 42(5), 405–416.CrossRefGoogle Scholar
  7. Kangaziyan, M., Oskooi, B., and Namaki, L., 2012, Investigation of Topographic Effect on Synthetic Magnetic Data: Istanbul 2012-International Geophysical Conference and Oil & Gas Exhibition., 1–4.CrossRefGoogle Scholar
  8. Li, S. L., and Li, Y. G., 2014, Inversion of magnetic anomaly on rugged observation surface in the presence of strong remanent magnetization: Geophysics, 79(2), J11–J19.Google Scholar
  9. Nabighian, M. N., Grauch, V. J. S., Hansen, R. O., et al., 2005, The historical development of the magnetic method in exploration: Geophysics, 70(6), 33–61.CrossRefGoogle Scholar
  10. Naidu, P. S., and Mathew, M. P., 1994, Correlation filtering: a terrain correction method for aeromagnetic maps with application: Journal of Applied Geophysics, 32(2–3), 269–277.CrossRefGoogle Scholar
  11. Prutkina, I., and Salehb, A., 2009, Gravity and magnetic data inversion for 3D topography of the Moho discontinuity in the northern Red Sea area: Egypt, J. Geodyn., 47(5), 237–245.CrossRefGoogle Scholar
  12. Pedersen, L. B., Bastani, M., and Kamm, J., 2015, Gravity gradient and magnetic terrain effects for airborne applications-A practical fast Fourier transform technique: Geophysics, 80(2), J19–J26.Google Scholar
  13. Ren, Z. Y., Tang, J. T., and Kalscheuer, T., et al., 2017, Fast 3D large-scale gravity and magnetic modeling using unstructured grids and an adaptive multilevel fast multipole method: Journal of Geophysical Research, 122(1), 79–109.Google Scholar
  14. Singh, S. K., 1978, Magnetic Anomaly due to a Vertical Right Circular Cylinder with Arbitrary Polarization: Geophysics, 43(1), 173–178.CrossRefGoogle Scholar
  15. Singh, B., and Guptasarma, D., 2001, New method for fast computation of gravity and magnetic anomalies from arbitrary polyhedra: Geophysics, 66(2), 521–526.CrossRefGoogle Scholar
  16. Tontini, F. C., 2005, Magnetic-anomaly Fourier spectrum of a 3D Gaussian source: The Leading Edge, 70(1), L1–L5.Google Scholar
  17. Tontini, F. C., Cocchi, L., and Carmisciano, C., 2009, Rapid 3-D forward model of potential fields with application to the Palinuro Seamount magnetic anomaly (southern Tyrrhenian Sea, Italy): Journal of Geophysical Research Solid Earth, 114(B2), 1205–1222.Google Scholar
  18. Ugalde, H., and Morris, B., 2008, An assessment of topographic effects on airborne and ground magnetic data: Leading Edge, 27(1), 76–79.CrossRefGoogle Scholar
  19. Wu, L. Y., and Tian, G., 2014, High-precision Fourier forward modeling of potential fields: Geophysics, 79(5), 59–68.CrossRefGoogle Scholar
  20. Wu, L. Y., 2016, Efficient modelling of gravity effects due to topographic masses using the Gauss FFT method: Geophysical Journal International, 205(1), 160–178.CrossRefGoogle Scholar
  21. Wu, L. Y., and Lin, Q., 2017, Improved Parker’s method for topographic models using Chebyshev series and low rank approximation: Geophysical Journal International, 209(2), 1296–1325.CrossRefGoogle Scholar
  22. Wu, X. Z., 1983, The computation of spectrum of potential field due to 3-D arbitrary bodies with physical parameters varying with depth: Chinese Journal of Geophysics, 26(2), 177–187.CrossRefGoogle Scholar
  23. Yao, C. L., Hao, T. Y., Guan, Z. N., et al., 2003, High-speed computation and efficient storage in 3-D gravity and magnetic inversion based on genetic algorithms: Chinese Journal of Geophysics, 46(2), 351–361.CrossRefGoogle Scholar

Copyright information

© Editorial Office of Applied Geophysics and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Kun Li
    • 1
    • 2
    • 3
  • Long-Wei Chen
    • 4
  • Qing-Rui Chen
    • 1
    • 2
    • 3
  • Shi-Kun Dai
    • 1
    • 2
    • 3
  • Qian-Jiang Zhang
    • 1
    • 2
    • 3
    • 4
  • Dong-Dong Zhao
    • 1
    • 2
    • 3
  • Jia-Xuan Ling
    • 1
    • 2
    • 3
  1. 1.Hunan Key Laboratory of Nonferrous Resources and Geological Hazards ExplorationChangshaChina
  2. 2.Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring of Ministry of EducationCentral South UniversityChangshaChina
  3. 3.School of Geosciences and Info-Physics of Central South UniversityChangshaChina
  4. 4.School of College of Earth Sciences of Guilin University of TechnologyGuilinChina

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