Skip to main content
SpringerLink
Log in

A stable regularization method of downward continuation of potential field

  • Published:
Studia Geophysica et Geodaetica Aims and scope Submit manuscript

Abstract

Downward continuation is known as one of the crucial steps in interpreting gravity or magnetic data. As the continuation depth and the influence of noise increases, the results of downward continuation become unstable. Based on the computation of the Chebyshev-Padé approximation function obtained by the Tikhonov regularization, this paper proposes a new regularized method intended for the downward continuation of potential fields. The Chebyshev-Padé approximation function is applied to calculate the continuation factor. In this study, the cross-correlation method is adopted to calculate the cut-off wavenumber, while the regularized low-pass filter is designed to calculate the downward continuation of the potential field. In order to validate this method, numerical simulation is conducted. We calculate the root mean square error of the theoretical data on the target plane and the data of downward continuation, as obtained using the improved regularization operator method, the Chebyshev-Padé approximation function method, the regularized Chebyshev-Padé approximation function method, and the method proposed in this paper, based on which a comparison is conducted. According to the simulation and experimental results, the effects of the continuation depth can be reduced significantly by the proposed method. Besides, the method demonstrates strong resistance to noise.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abedi M., Gholami A. and Norouzi G.H., 2013. A stable downward continuation of airborne magnetic data: A case study for mineral prospectivity mapping in Central Iran. Comput. Geosci., 52, 269–280.

    Article  Google Scholar 

  • Chen S.C. and Xiao P F., 2007. Wavenumber domain generalized inverse algorithm for potential field downward continuation. Chinese J. Geophys.-Chinese Ed., 50, 1571–1579 (in Chinese).

    Article  Google Scholar 

  • Cooper G.R.J., 2019. The downward continuation of aeromagnetic data from magnetic source ensembles. Near Surf. Geophys., 17, 101–107.

    Article  Google Scholar 

  • Dmitriev V. and Dmitrieva I., 2012. Iterative method for analytical continuation of the gravity field. Comput. Math. Model., 23, 51–55.

    Article  Google Scholar 

  • Evjen H.M., 1936. The place of the vertical gradient in gravitational interpretations. Geophysics, 1, 127–136.

    Article  Google Scholar 

  • Fedi M. and Florio G., 2002. A stable downward continuation by using the ISVD method. Geophys. J. Int., 151, 146–156.

    Article  Google Scholar 

  • Gang Y. and Lin Z., 2018. An improved stable downward continuation of potential fields using a truncated Taylor series and regularized vertical derivatives method. J. Geophys. Eng., 15, 2001–2008.

    Article  Google Scholar 

  • Guo L.H, Meng X.H, Chen Z.X., Li S.L. and Zheng Y.M., 2013. Preferential filtering for gravity anomaly separation. Comput. Geosci., 51, 247–254.

    Article  Google Scholar 

  • Hansen R.O. and Miyazaki Y., 1984. Continuation of potential fields between arbitrary surfaces. Geophysics, 49, 787–795.

    Article  Google Scholar 

  • Hansen P.C., 1994. Regularization tools: A MatLab package for analysis and solution of discrete ill-posed problems. Numer. Algorithms, 6, 1–35.

    Article  Google Scholar 

  • Lawson C.L. and Hanson R.J., 1974. Solving Least Squares Problems. Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • Li Y. and Oldenburg D.W., 2010. Rapid construction of equivalent sources using wavelets. Geophysics., 75, L51–L59.

    Article  Google Scholar 

  • Li Y., Devriese S.G., Krahenbuhl R.A. and Davis K., 2013. Enhancement of magnetic data by stable downward continuation for UXO application. IEEE Trans. Geosci. Remote Sens., 51, 3605–3614.

    Article  Google Scholar 

  • Li H., Wang G. and Bai Y., 2009. Calculus. Higher Education Press, Beijing, China (in Chinese).

    Google Scholar 

  • Liu D.J., Hong T.Q., Jia Z.H., Li J.S., Lu S.M., Sun X.F. and Xu S.Z., 2009. Wave number domain iteration method for downward continuation of potential fields and its convergence. Chinese J. Geophys.-Chinese Ed., 52, 1599–1605 (in Chinese).

    Google Scholar 

  • Ma G., Liu C., Huang D. and Li L., 2013. A stable iterative downward continuation of potential field data. J. Appl. Geophys., 98, 205–211.

    Article  Google Scholar 

  • Ma T., Wu Y., Hu X. and Wu M., 2014. One-step downward continuation of potential fields in a wavenumber domain. J. Geophys. Eng., 11, 025002.

    Article  Google Scholar 

  • Oliveira Jr. V.C., Barbosa V.C. and Uieda L., 2013. Polynomial equivalent layer. Geophysics., 78, G1–G13.

    Article  Google Scholar 

  • Pawlowski R.S., 1995. Preferential continuation for potential-field anomaly enhancement. Geophysics, 60, 390–398.

    Article  Google Scholar 

  • Pasteka R., Karcol R., Kušnirák D. and Mojzeš A., 2012. REGCONT: A MATLAB based program for stable downward continuation of geophysical potential fields using Tikhonov regularization. Comput. Geosci., 49, 278–289.

    Article  Google Scholar 

  • Ravat D., Pignatelli A., Nicolosi I. and Chiappini M., 2007. A study of spectral methods of estimating the depth to the bottom of magnetic sources from near-surface magnetic anomaly data. Geophys. J. Int., 169, 421–434.

    Article  Google Scholar 

  • Spector A. and Grant F.S., 1970. Statistical models for interpreting aeromagnetic data. Geophysics, 35, 293–302.

    Article  Google Scholar 

  • Tikhonov A.N., Glasko V.B., Litvinenko O.K. and Melikhov V.R., 1968. Analytic continuation of a potential in the direction of disturbing masses by the regularization method. Izv.-Phys. Solid. Earth, 12, 738–747.

    Google Scholar 

  • Xu S.Z., 2006. The integral-iteration method for continuation of potential fields. Chinese J. Geophys.-Chinese Ed., 49, 1054–1060 (in Chinese).

    Article  Google Scholar 

  • Xu S.Z., Yang J.Y., Yang C.F., Xiao P.F., Chen S.C. and Guo Z.H., 2007. The iteration method for downward continuation of a potential field from a horizontal plane. Geophys. Prospect., 55, 883–889.

    Article  Google Scholar 

  • Zeng X., Li X., Su J., Liu D. and Zou H., 2013. An adaptive iterative method for downward continuation of potential-field data from a horizontal plane. Geophysics., 78, J43–J52.

    Article  Google Scholar 

  • Zeng X., Liu D., Li X., Chen D. and Niu C., 2014. An improved regularized downward continuation of potential field data. J. Appl. Geophys., 106, 114–118.

    Article  Google Scholar 

  • Zeng X., Li X., Jia W. and Liu D., 2015. A new regularization method for calculating the vertical derivatives of the potential field. Chinese J. Geophys.-Chinese Ed., 58, 1400–1410 (in Chinese).

    Google Scholar 

  • Zhang H., Chen L.W., Ren Z.X., Wu M.P., Luo S.T. and Xu S.Z., 2009. Analysis on convergence of iteration method for potential fields downward continuation and research on robust downward continuation method. Chinese J. Geophys.-Chinese Ed., 52, 511–518 (in Chinese).

    Article  Google Scholar 

  • Zhang H., Ravat D. and Hu X., 2013. An improved and stable downward continuation of potential field data: The truncated Taylor series iterative downward continuation method. Geophysics, 78, J75–J86.

    Article  Google Scholar 

  • Zhou W., Li J. and Yuan Y., 2018. Downward continuation of potential field data based on Chebyshev-Padé approximation function. Pure Appl. Geophys., 175, 275–286.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 51305454).

Author information

Authors and Affiliations

  1. The Seventh Department of Army Engineering University, No.97, Hepingxilu Road, Shi Jia-Zhuang, He Bei Province, China

    Jinpeng Li, Yingtang Zhang, Hongbo Fan & Zhining Li

  2. Luoyang Electronic Equipment Test Center of China, Luoyang, 471003, China

    Fucheng Sun

Authors
  1. Jinpeng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yingtang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongbo Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhining Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Fucheng Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongbo Fan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, J., Zhang, Y., Fan, H. et al. A stable regularization method of downward continuation of potential field. Stud Geophys Geod 64, 391–406 (2020). https://doi.org/10.1007/s11200-019-0760-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11200-019-0760-3

Keywords

Search

Navigation