| 位场DFT算法研究 |
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| 引用本文： | 柴玉璞.位场DFT算法研究[J].地球物理学报,1988,31(2):211-224. |
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| 作者姓名： | 柴玉璞 |
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| 作者单位： | 石油部物探局重磁电研究所 河北固城 |
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| 摘 要： | 本文推广了经典的抽样定理,并据此导出了函数有限离散傅里叶变换误差方程（简称DFT误差方程,下同）。该方程把有限离散傅里叶变换中固有的离散效应和有限效应表示为确切的数学形式。离散效应被表示为一个含整参变量（参变量取0,1,…,N-1）的复无穷级数;有限效应被表示为一个含整参变量（参变量取0,1,…,N-1）的复无穷级数的DFT。 基于DFT误差方程和位函数特点,作者提出了两种位场数值傅里叶变换新算法--移样法和等效源续尾叠样法。移样法可近百倍地提高位场数值傅里叶反变换的精度,等效源续尾叠样法可数十倍地提高正变换精度。两种算法都不需要增加资料长度和取样密度,因而基本不需要增加计算机时间和内存。文中给出了算例。
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| 关 键 词： | 位场DFT算法 偏移抽样定理 DFT误差方程 移样法 等效源续尾叠样法 |
| 收稿时间： | 1986-12-07 |
ALGORITHM INVESTIGATION OF DFT OF POTENTIAL FIELD |
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| CHAI YU-PU.ALGORITHM INVESTIGATION OF DFT OF POTENTIAL FIELD[J].Chinese Journal of Geophysics,1988,31(2):211-224. |
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| Authors: | CHAI YU-PU |
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| Institution: | G. M. E. Institute of Geophysical Exploration Bureau, Petroleum Ministry |
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| Abstract: | In this paper the classical sampling theoems are extended into a more general form and in terms of the extensions the error expression of numerical Fourier transform (or DFT deviation equation) is developed in which the discretization effect and finite length effect inherent in the numerical Fourier Transform are expressed mathematically. The discretization effect is expressed as an infinite complex series which contains an integral parameter taking values of 0, 1, ..., N - 1 and the finite length effect is expressed as the DFT of another infinite complex series which contains an integral parameter taking values of 0, 1, ..., N - 1.Based on the DFT deviation equation and in terms of the features of potential function, the author propose an Equivalent Source Tail Fold technique which can improve the precision of forward numerical Fourier transform of potential by several tens of times and a Shift Sampling technique which can improve the precision of inverse numerical Fourier transform of potential by almost hundred limes. Both ESTF and SS technique require no increase of sample density and data length, therefore no more computer time and memory are needed comparing with traditional method. Some calculation examples are given. |
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| Keywords: | DFT algorithm of potential field Shift sampling theorem DFT deviation equation Shift sampling technique Equivalent soure tail fold technique |
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