论文部分内容阅读
文章推导出地球表面位场的付里叶变换与感应场源分布之间的关系式。当拉普拉斯变换中的变量P等于波数时,位场的付里叶变换是场源分布频谱的拉普拉斯变换。上述关系式可以用来确定与数据相吻合的所有可能的场源分布。这个解是非均匀问题的特殊解和均匀问题的一般解(也就是,对于这种解,位场在表面上为零)的叠加。可以将场源分布展开成一个已知函数的集合,展开系数由解一个线性方程组来确定,可以采用一些物理上的约束条件来限制展开系数的变化范围。给出了两个实例来说明这种方法的效果:转换一条综合重力剖面和一条热流剖面来确定与数据相吻合的密度或热源分布。
The article deduces the relationship between the Fourier transform of the Earth’s surface field and the distribution of the induced field source. When the variable P in the Laplace transform is equal to the wavenumber, the Fourier transform of the field is the Laplace transform of the field source distribution spectrum. The above relationship can be used to determine all possible field source distributions that match the data. This solution is a superposition of the special solution to the non-uniform problem and the general solution to the uniform problem (that is, the surface field is zero on the surface for this solution). The distribution of field sources can be expanded into a set of known functions. The expansion coefficients are determined by solving a linear system of equations. Some physical constraints can be used to limit the range of expansion coefficients. Two examples are given to illustrate the effect of this method: Conversion of a composite gravity profile and a heat flux profile to determine the density or heat source distribution consistent with the data.