Downward Continuation of Potential Field Data Based on Chebyshev–Padé Approximation Function

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.