点源两层大地三维地电模型视电阻率边界元解

本文用两层均匀大地人工点源作用下的空间电位分布作为基本解，导出了下伏基岩中陷含三维地质体情况下，关于电位的边界积分方程组，用边界单元法解积分方程求得地表电位，从而求得了一定装置下的视电阻率。本文方法的独特优点是积分只须在异常体边界面上进行了测线可以沿任意方向。用联剖法计算了均匀半空间下含球形异常体的ρｓ曲线，所得结果与其他学者用解析方法所求得的结果一致。用中间梯度法计算下层基岩中含有一长方体，测线

APPARENT RESISTIVITY SOLUTION OF 3-D MODEL WITH BOUNDARY ELEMENT METHOD

In this paper,by using the electric potential distribution which is originated from the artificial point current sources in the earth model of two horizontal layers as basic solution,we deduced the boundary integral equations about electric potential with an inhomogeneous conductivity object in the earth.Then we got the electric potential distribution on the ground by solving the integral equations with boundary element method,further,we got the calculating results of apparent resistivity.That the integration is only done in the boundary planes and the direction of observational line is arbitrary are the specific advantages. Using united-section methed,we calculated the apparent resistivi-ty with an inhomogeneous spherical object in the model of homogeneous half space,the results con-formed to the analytical solutions got by other researchers. Using gradient-section method,we calcu-lated the apparent resistivity with a rectangular inhomogeneous object in the lower layer,the angle be-tween the direction of observational line and the trend of rectangular objct is 45°,the results con-formed to the experimental and theoretic analytical solutions got by other researchers. Finally,we discussed the applications of this method in the field of the precursors of ground resis-tivity and the electric prospecting.