Cubic-spline-interpolation-based FFT and its application in forward modeling of gravity and magnetic fields
ZHOU Yinming1,2, DAI Shikun1,3, LI Kun1,3, HE Zhan-xiang4, HU Xiaoying2, WANG Jinhai5
1. School of Geosciences and Info-physciences, Central South University, Changsha, Hunan 410083, China; 2. GME & Geochemical Surveys of BGP, CNPC, Zhuozhou, Hebei 072751, China; 3. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education, Changsha, Hunan 410083, China; 4. SUSTech Academy for Advanced Interdisciplinary Studies, Shenzhen, Guangdong 518055, China; 5. The 3rd Geological Prospecting Institute of Qinghai Province, Xining, Qinghai 810029, China
Abstract:Discrete Fourier transform (DFT) plays an important role in signal processing,spectral analysis and numerical solution to partial differential equation (PDE). In the process of discretization,conventional FFT causes spectrum confusion and boundary effects. FFT based on Gauss integral weakens truncation effects,but reduces calculation efficiency. A Fourier transform method based on cubic-spline interpolation is proposed. First it discretizes Fourier transform integral into multiple units,and uses cubic spline interpolation to represent the function change in every unit,and finally adds the integrals of all units and gets the results of Fourier transform. This method makes full use of the high-order continuity and sampling flexibility of spline interpolation integration,and analytic calculation of unit integral.It provides a new idea for efficient and precise Fourier transform. Using the Gauss function designed,we compared 1D and 2D forward and inverse transforms with analytical solutions.It is verified that the theory of the method is correct,and its calculation accuracy is high. A continuum model is designed,then we applied fast Fourier transform based on cubic-spline interpolation to 3D numerical simulation of gravity and magnetic fields. The results show that the method can reduce the influence of truncation effect,and has high calculation accuracy and efficiency. Also,this has been proved by real data.
周印明, 戴世坤, 李昆, 何展翔, 胡晓颖, 王金海. 基于样条插值的FFT及其在重磁场正演中的应用[J]. 石油地球物理勘探, 2020, 55(4): 915-922,930.
ZHOU Yinming, DAI Shikun, LI Kun, HE Zhan-xiang, HU Xiaoying, WANG Jinhai. Cubic-spline-interpolation-based FFT and its application in forward modeling of gravity and magnetic fields. Oil Geophysical Prospecting, 2020, 55(4): 915-922,930.
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