| 重、磁场三维傅里叶变换的若干问题 |
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| 引用本文： | 熊光楚.重、磁场三维傅里叶变换的若干问题[J].地球物理学报,1984,27(1):103-109. |
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| 作者姓名： | 熊光楚 |
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| 摘 要： | 本文利用极限变换的概念,推导了质点的重力位及偶极子的磁位的三维傅里叶变换。在这个基础上,推导了任意形状物体的重、磁场的三维傅里叶变换的一般表达式。根据这些式子,讨论了文1]中由三维谱求二维谱存在的问题,即对三维谱而言,不存在u2+v2+w2=0。
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| 关 键 词： | 傅里叶变换 任意形状物体 磁位 重力位 若干问题 三维谱 二维傅里叶变换 二维谱 均匀磁化 坐标原点 |
| 收稿时间： | 1982-07-19 |
SOME PROBLEMS ABOUT THE 3-D FOURIER TRANSFORMS OF THE GRAVITY AND MAGNETIC FIELDS |
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| XIONG GUANG-CHU.SOME PROBLEMS ABOUT THE 3-D FOURIER TRANSFORMS OF THE GRAVITY AND MAGNETIC FIELDS[J].Chinese Journal of Geophysics,1984,27(1):103-109. |
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| Authors: | XIONG GUANG-CHU |
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| Abstract: | In this paper, we have deduced the analytic expressions of the 3-D Fourier transforms of the gravity potential of a point mass and that of the magnetic potential of a magnetic di-pole （all situated at the origin of the coordinates）, by use of the idea of transform in the limit, i.e.V（u,v,w）=-4πf/（u2+v2+w2）U（u,v,w）=4πi（mxu+myv+mzw）/（u2+v2+w2）where V （u, v, w） and U （u, v, w） are respectively the Fourier transform of the gravity potential f/r and magnetic potential m·r/r3; r=（x2+y2+z2）1/2, （x, y, z） are the coordinates of a point in the space, u, v and w are the circular frequency relative to, y and z axies respectively; f is the constant of universal attraction; mx, my and mz are projections of magneticmoment m on x, y and z-axies respectively; i=-1.On the base of the two formulas mentioned above, we have obtained the general expressions of the 3-D Fouier transforms of the gravity and magnetic fields of 3-D bodies,At the end of the paper, we discussed the method of using 3-D Fourier transforms to derive the 2-D Fourier transforms of the gravity and magnetic field and an example is given to show how to use the method. |
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