离散复镜像法求取层状介质的格林函数

对分层地层进行井间电磁成像时，需要求取分层介质中的格林函数。利用频率域中电磁场的边界条件，求出频率域分层介质的格林函数，再利用傅里叶逆变换，将格林函数变换到空间域，得到以Sommerfeld积分形式表达的解。为了避免积分中的奇异性，利用离散复镜像法将积分核用复镜像的指数求和式表示，引入广义函数荣方法，可以在不提取积分核中表面波项的条件下，采用数值方法提取准静态项，给出复镜像点的数目、位置和强度，使得该方法在多层介质情况下对格林函数的计算更为有效。对一个7层介质中的垂直磁偶极子的矢量势和标量势进行了计算，离散复镜像法与Sommerfeld精确积分的结果吻合较好，说明离散复镜像法是比较准确的。

Calculation of spatial-domain Green''''s functions for multi-layered media by discrete complex image method

The Green's functions for multi-layered media are needed when crosshole electromagnetic imaging is applied to stratified media.According to the boundary conditions,the spectral domain Green's functions for multi-layered media were formed.Then the spatial domain Green's functions can be obtained by the inverse Fourier transformation,which are represented by the Sommerfeld integrals.In order to avoid the singularity in the integration,the integrand was expressed to be sum of complex exponential terms by using discrete complex image method(DCIM).With generalized pencil of function(GPOF) method introduced,the number,location and intensity of images were obtained without extracting the quasi-static and surface wave terms in the integrand,which makes DCIM more efficient for multi-layered media.As a numerical example,the vector and scalar potential for a vertical magnetic dipole immersed in seven layers media were calculated,and the results got by DCIM and precise integration show that the DCIM is very accurate.