1887
Volume 24, Issue 1
  • ISSN: 1569-4445
  • E-ISSN: 1873-0604

Abstract

Abstract

Downward continuation of potential field is a useful tool in the processing and interpretation of magnetic and gravity data, but its direct calculation in space or spectral domain is unstable even in the presence of a small level of the noise and consequently restricts its practical application. This paper introduces a new method that combines upward continuation, vertical gradient via smoothing filters (Tikhonov regularization or Gaussian filters) and an iterative method into a single scheme to improve the stability and accuracy of the downward continuation. The optimal interval of iteration numbers for our developed approach is estimated by analysing the correlation coefficient curve between consecutive iterations. Applications to synthetic and real magnetic data show that this method can yield a more stable downward continuation of potential field data.

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2026-01-24
2026-02-11
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References

  1. Abedi, M., Gholami, A. & Norouzi, G.H. (2013) A stable downward continuation of airborne magnetic data: a case study for mineral prospectivity mapping in Central Iran. Computers & Geosciences, 52, 269–280. Available from: https://doi.org/10.1016/j.cageo.2012.11.006
    [Google Scholar]
  2. Abedi, M., Gholami, A. & Norouzi, G.H. (2014) A new stable downward continuation of airborne magnetic data based on wavelet deconvolution. Near Surface Geophysics, 12, 751–762. Available from: https://doi.org/10.3997/1873‐0604.2014027
    [Google Scholar]
  3. Azadi, M., Abedi, M. & Norouzi, G.H. (2021) Stable downward continuation of airborne potential field geophysical data: an investigation of stabilizer family. Journal of Mining and Environment (JME), 12(2), 547–567. Available from: https://doi.org/10.22044/jme.2021.10740.2040
    [Google Scholar]
  4. Baniamerian, J., Liu, S. & Abbas, M.A. (2018) Stable computation of the vertical gradient of potential field data based on incorporating the smoothing filters. Pure and Applied Geophysics, 175, 2785–2806. Available from: https://doi.org/10.1007/s00024‐018‐1857‐2
    [Google Scholar]
  5. Benhadj Tahar, Y. & Berguig, M.C. (2024) Stable iterative downward continuation of potential field based on Runge‐Kutta method. Journal of Applied Geophysics, 220, 105278. Available from: https://doi.org/10.1016/j.jappgeo.2023.105278<./bib>
    [Google Scholar]
  6. Blakely, R.J. (1996) Potential theory in gravity and magnetic applications. Cambridge: Cambridge University Press.
    [Google Scholar]
  7. Clarke, G.K. (1969) Optimum second‐derivative and downward‐continuation filters. Geophysics, 34(3), 424–437. Available from: https://doi.org/10.1190/1.1440020
    [Google Scholar]
  8. Cooper, G. (2004) The stable downward continuation of potential field data. Exploration Geophysics, 35, 260–265. Available from: https://doi.org/10.1071/EG04260
    [Google Scholar]
  9. Cooper, G. (2019) The downward continuation of aeromagnetic data from magnetic source ensembles. Near Surface Geophysics, 17, 101–107. Available from: https://doi.org/10.1002/nsg.12035
    [Google Scholar]
  10. Cordell, L. & Grauch, V.J.S. (1985) Mapping basement magnetization zones from aeromagnetic data in the San Juan Basin, New Mexico. In: Hinze, W.J. (Ed.) The utility of regional gravity and magnetic anomaly maps. Houston, TX: SEG, pp. 181–197.
    [Google Scholar]
  11. Dampney, C.N.G. (1969) The equivalent source technique. Geophysics, 34, 39–53. Available from: https://doi.org/10.1190/1.1439996
    [Google Scholar]
  12. Evjen, H.M. (1936) The place of the vertical gradient in gravitational interpretations. Geophysics, 1, 127–136. Available from: https://doi.org/10.1190/1.1437067
    [Google Scholar]
  13. Fedi, M. & Florio, G. (2002) A stable downward continuation by using the ISVD method. Geophysical Journal International, 151(1), 146–156. Available from: https://doi.org/10.1046/j.1365‐246X.2002.01767.x
    [Google Scholar]
  14. Hansen, P.C. (1998) Rank‐deficient and discrete Ill‐posed problems: numerical aspects of linear inversion. Philadelphia: SIAM.
    [Google Scholar]
  15. Hansen, P.C. (1994) Regularization tools ‘A Matlab package for analysis and solution of discrete ill‐posed problems’. Numerical Algorithms, 6, 1–35.
    [Google Scholar]
  16. Hansen, R.O. & Miyazak, Y. (1984) Continuation of potential fields between arbitrary surfaces. Geophysics, 49, 787–795. Available from: https://doi.org/10.1190/1.1441707
    [Google Scholar]
  17. Huang, Y., Lv, Z. & Wu, L. (2020) One‐step compensation downward continuation method free of iteration in wave number domain. Acta Geodaetica et Geophysica, 55, 163–181. Available from: https://doi.org/10.1007/s40328‐020‐00285‐6
    [Google Scholar]
  18. Huestis, S.P. & Parker, R.L. (1979) Upward and downward continuation as inverse problems. Geophysical Journal of the Royal Astronomical Society, 57, 171–188. Available from: https://doi.org/10.1111/j.1365‐246X.1979.tb03779.x
    [Google Scholar]
  19. Li, D., Guo, Z., Du, J. & Chen, C. (2021) Stable downward continuation of the total‐field magnetic anomaly derived by using equivalent sources. Journal of Applied Geophysics, 193, 104429. Available from: https://doi.org/10.1016/j.jappgeo.2021.104429
    [Google Scholar]
  20. Li, H., Chen, S., Li, Y., Zhang, B., Zhao, M. & Han, J. (2023) Stable downward continuation of the gravity potential field implemented using deep learning. Frontiers in Earth Science, 10, 1065252. Available from: https://doi.org/10.3389/feart.2022.1065252
    [Google Scholar]
  21. Li, Y.G., Devriese, S.G., Krahenbuhl, R.A. & Davis, K. (2013) Enhancement of magnetic data by stable downward continuation for UXO application. IEEE Transactions on Geoscience and Remote Sensing, 51, 3605–3614. Available from: https://doi.org/10.1190/1.3255125
    [Google Scholar]
  22. Li, Y. & Oldenburg, D.W. (2010) Rapid construction of equivalent sources using wavelets. Geophysics, 75(3), L51–L59. Available from: https://doi.org/10.1190/1.3378764
    [Google Scholar]
  23. Ma, G., Liu, C., Huang, D. & Li, L. (2013) A stable iterative downward continuation of potential field data. Journal of Applied Geophysics, 98, 205–211. Available from: https://doi.org/10.1016/j.jappgeo.2013.08.018
    [Google Scholar]
  24. Ma, T., Wu, Y., Hu, X. & Wu, M. (2014) One‐step downward continuation of potential fields in a wave number domain. Journal of Geophysics and Engineering, 11(2), 025002. Available from: https://doi.org/10.1088/1742‐2132/11/2/025002
    [Google Scholar]
  25. Pašteka, R., Richter, F.P., Karcol, R., Brazda, K. & Hajach, M. (2009) Regularized derivatives of potential fields and their role in semi‐automated interpretation methods. Geophysical Prospecting, 57, 507–516. Available from: https://doi.org/10.1111/j.1365‐2478.2008.00780.x
    [Google Scholar]
  26. Pašteka, R., Karcol, R., Kušnirák, D. & Mojzeš, A. (2012) REGCONT: a matlab based program for stable downward continuation of geophysical potential fields using Tikhonov regularization. Computers & Geosciences, 49, 278–289. Available from: https://doi.org/10.1016/j.cageo.2012.06.010
    [Google Scholar]
  27. Pawlowski, R.S. (1995) Preferential continuation for potential‐field anomaly enhancement. Geophysics, 60(2), 390–398. Available from: https://doi.org/10.1190/1.1443775
    [Google Scholar]
  28. Peters, L.J. (1949) The direct approach to magnetic interpretation and its practical application. Geophysics, 14(3), 290–320. Available from: https://doi.org/10.1190/1.1437537
    [Google Scholar]
  29. Roy, K.K. (2008) Potential theory in applied geophysics. Berlin, Heidelberg: Springer‐Verlag.
    [Google Scholar]
  30. Rytov, R.A. (2025) Artificial neural network for downward continuation of anomalous magnetic fields. Russian Journal of Earth Sciences, 25, ES2024. Available from: https://doi.org/10.2205/2025ES000996
    [Google Scholar]
  31. Tai, Z., Zhang, F., Zhang, F. & Hao, M. (2016) Approximate iterative operator method for potential‐field downward continuation. Journal of Applied Geophysics, 128(2016), 31–40. Available from: https://doi.org/10.1016/j.jappgeo.2016.03.021
    [Google Scholar]
  32. Tikhonov, A.N., Glasko, V.B., Litvinenko, O.K. & Melikhov, V.R. (1968) Analytic continuation of a potential in the direction of disturbing masses by the regularization method. Izvestiya, Physics of the Solid Earth, 12, 738–747. [in Russian; English translation: 738–747].
    [Google Scholar]
  33. Trompat, H., Boschetti, F. & Hornby, P. (2003) Improved downward continuation of potential field data. Exploration Geophysics, 34, 249–256. Available from: https://doi.org/10.1071/EG03249
    [Google Scholar]
  34. Wang, J., Meng, X. & Zhou, Z. (2018) A constrained scheme for high precision downward continuation of potential field data. Pure and Applied Geophysics, 175, 3511–3523. Available from: https://doi.org/10.1007/s00024‐018‐1861‐6
    [Google Scholar]
  35. Wang, Z., Zhang, Q., Chen, D., Liu, Z., Pan, M., Hu, J., Chen, Z. et al. (2022) A new potential‐field downward continuation iteration method based on adaptive filtering. In: IEEE Transactions on Geoscience and Remote Sensing. New York City, IEEE. pp. 1–11.
  36. Xu, S.Z., Yang, J., Yang, C., Xiao, P., Chen, S. & Guo, Z. (2007) The iteration method for downward continuation of a potential field from a horizontal plane. Geophysical Prospecting, 55, 883–889. Available from: https://doi.org/10.1111/j.1365‐2478.2007.00634.x
    [Google Scholar]
  37. Zeng, X., Li, X., Su, J., Liu, D. & Zou, H. (2013) An adaptive iterative method for downward continuation of potential‐field data from a horizontal plane. Geophysics, 78, J43–J52. Available from: https://doi.org/10.1190/geo2012‐0404.1
    [Google Scholar]
  38. Zhang, C., Lü, Q., Yan, J. & Qi, G. (2018) Numerical solutions of the mean‐value theorem: new methods for downward continuation of potential fields. Geophysical Research Letters, 45, 3461–3470. Available from: https://doi.org/10.1002/2018GL076995
    [Google Scholar]
  39. Zhang, H., Ravat, D. & Hu, X. (2013) An improved and stable downward continuation of potential field data: the truncated Taylor series iterative downward continuation method. Geophysics, 78(5), J75–J86. Available from: https://doi.org/10.1190/geo2012‐0463.1
    [Google Scholar]
  40. Zhang, Y., Wong, Y.S. & Lin, Y. (2016) BTTB–RRCG method for downward continuation of potential field data. Journal of Applied Geophysics, 126, 74–86. Available from: https://doi.org/10.1016/j.jappgeo.2016.01.009
    [Google Scholar]
  41. Zhou, W.N., Li, J.Y. & Yuan, Y. (2017) Downward continuation of potential field data based on Chebyshev–Padé approximation function. Pure and Applied Geophysics, 175, 275–286. Available from: https://doi.org/10.1007/s00024‐017‐1680‐1
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Filtering; Inversion; Potential field

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