均匀大地交变电偶极子电磁响应直接计算式

Direct calculation of the response of an electric dipole on a homogeneous earth

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.

To compute an AC electric dipole＇s response on a homogeneous earth,the paper uses rigorous mathematical methods deducing the S.A.Schelkunoff vector potential partial derivatives and its divergence＇s ones based on the vector potential and its divergence＇s expressions from the book named＂The Principle of Electromagnetic Sounding＂written by Piao Huarong,through which the fields computation expressions are gained not including Hankel transforms.The expressions,however,still are made up Bessel functions.For convenience of calculation,the Matlab programming platform is chosen to program,in which the Bessel functions supplied by Matlab are called.And then the paper has computed fields components of eight different depth on the conditions known of source parameters and fields positions through the fields direct computation expressions. The computation results are displayed in form of sheets at last.Through summarizing,the paper concludes three points as the following：Firstly,the computation method supplied by the paper can compute any point＇s fields except the source one,which has solved the problem of the fields＇ computation from the source right below that the digital filter does not deal with.Secondly,the consume of calculation time is less than 1 millisecond using the paper＇s method, which declares it has compute rapidly. Lastly,because of strict mathematical deduction, the fields＇ computation expressions＇ results can be used directly by the forward and the inversion on 3D anomalous body.As a result,the fields＇ computational method from the papers has certain application prospects.