二维井间电磁场的正反演计算

提出了一种改进的逐次逼近解法 ,并用该方法对轴对称二维井间电磁场进行了正反演计算。与逐次逼近解法相比 ,该方法收敛性强 ,应用范围广 ,可适用于高电导率对比地层。与直接求解积分方程相比 ,由于不必进行直接的大型复矩阵求逆运算 ,该方法计算速度快 ,所需内存少。反演中采用了Born迭代算法 ,将成像区域集中于一定范围内。考虑到信息量和计算机内存的限制 ,采用双重面元分割法 ,将反演区域分割为一定数目的大面元 ,每个大面元被分割为几个小面元。属于同一大面元的不同小面元具有不同的磁矢势 ,但具有相同的电导率 ,从而减少了反演过程中未知量的数目。根据第一次成像结果确定出更准确的成像范围 ,并进行第二次成像。数值计算结果表明 ,改进的逐次逼近解法是计算二维井间电磁场的一种有效方法 ,将该方法用于反演过程能够得到较高分辨率的二维井间电导率图像。

Forward modelling and inversion of 2-D cross-hole electromagnetic fields

A modified successive approximation method (MSAM) was presented. The problems of forward and inverse of cylindrically symmetric 2 D cross hole electromagnetic fields were solved by using this method. It converges more powerfully than the former successive approximation method. It can be applied to the structures with the strong conductivity anomalies. It also has the higher speed and less memory requirements than the direct solving method for integral equations. The Born iteration algorithm based on MSAM was applied to the inversion. The imaging region was concentrated only to a particular range. Considering the limitation of information and computer memory, the double cell decomposition scheme was applied during the imaging process. The scheme decomposes the imaging region into a certain number of the big cells, and then it decomposes each big cell into several small cells. In the scheme, the different small cells in the same big cell have the different magnetic vector potentials and the same conductivity. So the number of unknown quantities can be greatly reduced. After the first inversion is completed, the second imaging process can be carried out. The numerical results indicate that MSAM is an efficient method for giving the high resolution 2 D cross hole conductivity images.