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A Novel Downward Continuation Method Based on Continued Fraction in Wavenumber Domain and Its Application on Aeromagnetic Data in the Xuanhua-Huailai Area, China

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Abstract

Satellite and airborne gravity and magnetic data are gathered away from the earth's surface, and the resolution is usually insufficient to describe the geological structures in detail. Therefore, downward continuation is typically used to enhance small-scale sources and improve spatial resolution to interpret potential field data. To further improve the stability and accuracy of the downward continuation, we present a new strategy based on the continued fraction approximation in the wavenumber domain. We established our method based on the relationship of the Taylor series and the continued fraction in the wavenumber domain. According to the comparison of different terms of the continued fraction, we found that a reasonable number of terms needs to be calculated using the continued fraction. In this way, stable results that are insensitive to noise can be obtained with the new method. Compared with the typical Taylor series method in the wavenumber domain, the improved Taylor series method, and the Tikhonov regularized downward continuation method, our new method is less sensitive to noise. The results demonstrated that continued fraction can be used to replace the classical Taylor series expansion with reasonable terms to implement more accurate and stable downward continuation. Finally, the new method was applied to reduced-to-pole total fields of aeromagnetic anomalies from the Xuanhua-Huailai area, and the results showed its superiority compared with the other methods. With the new downward continuation method, the small-scale anomalies and the structure distributions are more obvious and better depicted. The results are in good agreement with geological depictions.

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Data Availability Statement

The data are unavailable to the public and have restricted access due to the regulations from the Chinese Geological Survey.

References

  • 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.

    Article  Google Scholar 

  • Blakely, R. J. (1995). Potential theory in gravity and magnetic applications (pp. 313–319). Cambridge Univ. Press.

    Book  Google Scholar 

  • Cuyt, A., & Verdonk, B. (1988). Multivariate reciprocal differences for branched Thiele continued fraction expansions. Journal of Computational and Applied Mathematics, 21, 145–160.

    Article  Google Scholar 

  • Fedi, M., & Florio, G. (2002). A stable downward continuation by using ISVD method. Geophysical Journal International., 151, 146–156.

    Article  Google Scholar 

  • Hansen, P. C. (1998). Rank-deficient and discrete ill-posed problems: Numerical aspects of linear inversion. SIAM.

  • Lee, J., & Kim, D. H. (2011). Simple high-order approximations for unsteady-state diffusion, adsorption and reaction in a catalyst: A unified method by a continued fraction for slab, cylinder and sphere geometries. Chemical Engineering Journal, 173, 644–650.

    Article  Google Scholar 

  • Li, H. Q., Zhang, S. S., Xie, M. Z., Ren, J. S., & Zhou, J. F. (2020). Tectonic system and its geothermal water controlling in Zhangjiakou area. Coal Geology of China, 32(5), 74–82. in Chinese with English abstract.

    Google Scholar 

  • Li, S. F., & Chen, D. D. (2015). Comparative study on computing effect of continued fraction approximation and polynomial approximation. Journal of Bengbu University, 4, 29–31. in Chinese with English abstract.

    Google Scholar 

  • Li, S. F., Tan, J. Q., Xie, C. J., & Li, L. (2008). An iterative formula with four order convergence for solving equations based on Thile’s continued fraction. Journal of University of Science and Technology of China, 38, 138–140. in Chinese with English abstract.

    Google Scholar 

  • Li, Y. G., Devriese, S., 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.

    Article  Google Scholar 

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

    Google Scholar 

  • Ma, G. Q., Liu, C., Huang, D. N., & Li, L. L. (2013). A stable iterative downward continuation of potential field data. Journal of Applied Geophysics, 98, 205–211.

    Article  Google Scholar 

  • Ma, K. P., Feng, W., & Pan, S. M. (2002). The advanced applications and classic examples. National Defence Industry Press.

    Google Scholar 

  • Mansi, A. H., Capponi, M., & Sampietro, D. (2018). Downward continuation of airborne gravity data by means of the change of boundary approach. Pure and Applied Geophysics, 175(3), 977–988.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Pašteka, R., Kušnirák, D., & Karcol, R. (2018). Matlab tool REGCONT2: Effective source depth estimation by means of Tikhonov’s regularized downwards continuation of potential fields. Contributions to Geophysics and Geodesy, 48, 231–254.

    Article  Google Scholar 

  • Pawlowski, R. S. (1995). Preferential continuation for potential-field anomaly enhancement. Geophysics, 60(2), 390–398.

    Article  Google Scholar 

  • Qi, B., Feng, C., Tan, C., et al. (2019). Application of comprehensive geophysical-drilling exploration to detect the buried North Boundary active Fault Belt of Yanqing-Fanshan Basin in Sangyuan town, Beijing-Zhangjiakou Area. Geology in China, 46(3), 468–481. in Chinese.

    Google Scholar 

  • Ren, J., Jiang, C., & Zhang, Z. (1980). China’s tectonic structure and its evolution. Beijing: Scientific Press. in Chinese.

    Google Scholar 

  • Tran, K. V., & Nguyen, T. N. (2020). A novel method for computing the vertical gradients of the potential field: Application to downward continuation. Geophysical Journal International, 202, 1316–1329.

    Google Scholar 

  • Wang, Y. G., Zhang, F. X., Wang, Z. W., Meng, L. S., & Zhang, J. (2011). Taylor series iteration for downward continuation of potential fields. Oil Geophysical Prospecting, 46(4), 657–662. in Chinese with English abstract.

    Google Scholar 

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

    Article  Google Scholar 

  • Yao, C. L., Li, H. W., Zheng, Y. M., Meng, X. H., & Zhang, Y. W. (2012). Research on iteration method using in potential field transformations. Chinese Journal of Geophysics, 55, 2062–2078.

    Article  Google Scholar 

  • Zeng, X. N., Li, X. H., Liu, D. Z., & Han, S. Q. (2011). Regularization analysis of integral iteration method and the choice of its optimal step-length. Chinese Journal of Geophysics, 54, 2943–2950.

    Google Scholar 

  • Zeng, X. N., Li, X. H., Su, J., Liu, D. Z., & Zou, H. X. (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. N., Liu, D. Z., Li, X. H., Chen, D. X., & Niu, C. (2014). An improved regularized downward continuation of potential field data. Journal of Applied Geophysics, 106, 114–118.

    Article  Google Scholar 

  • Zhang, C., Huang, D. N., Zhang, K., Pu, Y. T., & Yu, P. (2016). Magnetic interface forward and inversion method based on padé approximation. Applied Geophysics, 13(4), 712–720.

    Article  Google Scholar 

  • Zhang, C., Lü, Q., Yan, J. Y., & Qi, G. (2018). Numerical solutions of the mean-value theorem: New methods for downward continuation of potential fields. Geophysical Research Letters, 45, 3461–3470.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Zhang, D., Liu, Z., & Lu, H. (2013a). Hebei Geothermal. Beijing: Geological Publishing House. in Chinese.

    Google Scholar 

  • Zhang, H. L., Ravat, D., & Hu, X. Y. (2013b). 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. N., Li, J. Y., & Yuan, Y. (2018). Downward continuation of potential field data based on Chebyshev-Padé approximation function. Pure and Applied Geophysics, 175, 275–286.

    Article  Google Scholar 

Download references

Acknowledgements

This research was partly supported by the National Natural Science Foundation of China (42004068, 41904122), the Second Tibetan Plateau Scientific Expedition and Research Program (Grant No. 2019QZKK0704), China Geological Survey’s project (DD20189642, DD20190012 and DD 20190129), the Science and Technology Plan of Gansu Province (20JR5RA251), and the Special Project for Basic Scientific Research Service (JYYWF20180101 and JKY202007).

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Authors and Affiliations

  1. School of Earth Sciences, Key Laboratory of Mineral Resources in Western China (Gansu Province), Lanzhou University, Lanzhou, 730000, Gansu, China

    Wenna Zhou

  2. China Deep Exploration Center (SinoProbe Center), Chinese Academy of Geological Sciences, Beijing, 100037, China

    Chong Zhang & Dailei Zhang

  3. Chengdu Center, China Geological Survey, Chengdu, 610081, Sichuan Province, China

    Chong Zhang

  4. Geothermal and Hot Dry Rock Exploration and Development Technology Innovation Center of the Ministry of Natural Resources, Shijiazhuang, 050061, Hebei, China

    Dailei Zhang

Authors
  1. Wenna Zhou
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  2. Chong Zhang
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  3. Dailei Zhang
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Contributions

WZ: Methodology, software, formal analysis, visualization, writing—original draft, review and editing, funding acquisition, supervision. CZ: formal analysis, visualization, writing—original draft, review & editing, funding acquisition. DZ: methodology, review & editing, validation, writing—review & editing, funding acquisition.

Corresponding authors

Correspondence to Wenna Zhou or Chong Zhang.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Zhou, W., Zhang, C. & Zhang, D. A Novel Downward Continuation Method Based on Continued Fraction in Wavenumber Domain and Its Application on Aeromagnetic Data in the Xuanhua-Huailai Area, China. Pure Appl. Geophys. 179, 777–793 (2022). https://doi.org/10.1007/s00024-021-02937-2

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