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为了能计算出交变电偶极子在均匀大地中的电磁响应,本文在朴化荣编著的《电磁测深法原理》一书中的谢昆诺夫矢量位的表达式和矢量位散度的表达式基础上,用数学手段严格推导出矢量位的偏导数和矢量位散度的偏导数,从而得到不含汉克尔变换的场计算式;由于场计算式中含有贝赛尔函数,为计算方便,选用Matlab编程并调用其提供的贝赛尔函数,然后用场直接计算式求解了在源参数和场点参数已知情况下的8个不同深度处的场分量并以表格的形式给出了电磁分量与总场的计算值.通过总结得出3点结论:(1)本文方法可计算除源点外任一点场,解决了数字滤波法无法计算源点正下方场的问题;(2)本文方法计算场的时间小于1毫秒,计算速度快;(3)本文场计算式有严格的数学推导,其计算结果可以被三维异常体的正反演直接使用.因此,本文的场计算方法具有一定的应用前景.
In order to calculate the electromagnetic response of the alternating electric dipole in a uniform earth, the expressions of the Shechenoloff vector bits and the expression of vectorial divergence in the article “Principles of Electromagnetic Sounding” written by Parkh Young-wing On the basis of mathematical formulas, the partial derivatives of vector and the partial derivatives of vectorial divergence are strictly deduced, so that the field calculation without Hankel transform is obtained. Since the field calculation contains Bessel function, It is convenient to use MATLAB to program and call the Bessel functions provided by it. Then the field components at eight different depths, which are known under the condition of source parameter and field point parameter, are solved by the field direct calculation formula and given in tabular form (1) The method of this paper can compute any point field except the source point and solve the problem that the digital filter method can not calculate the field just below the source point. (2) The method in this paper calculates the field time less than 1 millisecond, and the calculation speed is fast. (3) The calculation formulas in this paper have rigorous mathematical derivation, and the calculation results can be directly used by the forward and inverse of the three-dimensional anomaly. Therefore, Before a certain application view.