Abstract
To further improve the stability and accuracy of the downward continuation, we presented a new strategy based on the Chebyshev–Padé approximation in the frequency domain. First, we compared the errors between the function exp(x) and its different approximation functions, including Taylor series, Chebyshev approximation, Padé approximation, and Chebyshev–Padé approximation. Meanwhile, the filter characteristic curves of the different functions in the frequency domain are calculated. It turned out that the Chebyshev–Padé approximation is the most precise function. Similar to the Taylor series expansion, different downward continuation methods were established based on these approximation functions in the frequency domain. We compared the accuracy of these downward continuation methods using model tests with and without noise. The results showed that the downward continuation based on Chebyshev–Padé approximation was insensitive to the noise and can obtain a more precise result. To further compare these methods and prove the superiority of Chebyshev–Padé approximation, the iteration methods of downward continuation were proposed. We can obtain an accurate result within less iterations using Chebyshev–Padé approximation. To further suppress the noise effect, we improved the iteration methods using upward continuation. Once again, the model tests showed that the Chebyshev–Padé approximation is a preferred method to implement downward continuation. Finally, the method was applied on a field gravity data and showed its superiority. It demonstrated that we can use the Chebyshev–Padé approximation to replace the classical Taylor series expansion to implement more precise and stable downward continuation.
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Acknowledgements
The authors would like to thank Prof. Roman Pasteka and one anonymous reviewer for their valuable and constructive comments and suggestions that improved this work. This research was partly supported by the Fundamental Research Funds for the Central Universities (Grant nos. lzujbky-2017-75 and lzujbky-2016-22), Hubei Subsurface Multi-scale Imaging Key Laboratory (China University of Geosciences) (SMIL-2017-09) and basic scientific research business special fund project of Second Institute of Oceanography, State Oceanic Administration (14275-10). Funding was provided by State Key Laboratory of Marine Geology, Tongji University (Grant no. MGK1610). Ministry of science and technology major special instrument: “The sea - air gravimeter development” (2011YQ12004505).
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Zhou, W., Li, J. & Yuan, Y. Downward Continuation of Potential Field Data Based on Chebyshev–Padé Approximation Function. Pure Appl. Geophys. 175, 275–286 (2018). https://doi.org/10.1007/s00024-017-1680-1
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DOI: https://doi.org/10.1007/s00024-017-1680-1