起伏地表条件下三维直流电场拟解析近似方法

为了研究起伏地表条件下三维直流电场问题,基于全空间的拟解析近似理论,推导出起伏地表条件下三维直流电场的拟解析近似理论公式。将起伏地表条件下地下存在异常体时所产生的异常电场分为两部分,其中一部分为地下三维异常体所产生的体异常电场,通过对异常体的体积分求得;另一部分为由起伏地表所产生的面异常电场,可以利用对起伏地表地空界面的面积分求得。利用拟解析理论,对两部分异常分别推导体电反射函数和面电反射函数,得到起伏地表下电场积分方程的拟解析近似公式。该理论公式为解决起伏地表问题提供了一种思路,丰富了拟解析理论的应用,为直接进行正反演模拟、消除起伏地表对电法勘探的影响打下了基础。

THE QUASI-ANALYTICAL METHOD FOR THE THREE-DIMENSIONAL D.C. ELECTRICAL FIELD MODELING ON UNDULATE TOPOGRAPHY

The quasi-analytical method is a means for solving integration equations.To study the three-dimensional D.C.electrical field under surface topography,this paper puts forward the formula of the quasi-analytical theory for the three-dimensional D.C.electrical field under the surface topography based on the quasi-analytical theory for the whole space.The authors divide the anomalous electric field at the surface into two parts,one is the body anomalous electric field caused by the anomalous body,which can be solved by the body integral,whereas the other is the surface anomalous electric field resulting from the interface between the earth and the air,which can be calculated by the surface integral.The authors inferred the body electrical reflectivity tensor and the surface electrical reflectivity tensor separately.The quasi-analytical theory was used to deduce the formula of the quasi-analytical theory under the surface topography.This formula can give us a train of thought for solving the surface topography problem.It can enrich the quasi-analytical theory and promote the forward and inverse modeling of the D.C.electrical field,thus laying a foundation for eliminating the effect of the surface topography.