三维井间电磁场的正反演计算

FORWARD MODELLING AND INVERSION OF 3-D CROSS-HOLE ELECTROMAGNETIC FIELDS

提出了一种计算体积分方程的方法———改进型局域非线性迭代 (MLNI) ,并用其对三维井间电磁场进行正反演计算 .该方法将井间大尺度散射体分为近场和远场区域两部分 ,它们的位置和尺寸均随场点位置的变化而改变 .采用局域非线性近似计算近场区域的影响 ,将远场区域的影响作为外部激励源 ,采用迭代方法计算 .该方法具有计算速度快、所需内存量少、收敛性好的优点 .在反演中采用基于MLNI的非线性反演方法 ,利用这种方法可以将成像区域集中于一定范围内而不是整个三维空间 .该反演方法由于考虑到了雅可比矩阵元素的非线性项 ,因而与传统的Born迭代反演方法相比更为精确和稳定 .考虑到信息量和计算机内存的限制 ,第 1次成像采用双重体元分割法进行较粗略的成像 ,然后缩小成像范围进行第 2次较精确的成像 .数值计算结果表明 ,MLNI是一种有效的计算井间大尺度异常体散射场的方法 。

The method of modified local nonlinear iteration (MLNI) for volume integral equations is introduced and used to calculate forward and inverse problems of 3 D cross hole electromagnetic fields. The large scale scatters are divided into two kinds, the near region scatters and the far region scatters, whose locations and sizes are determined by the position of the field point. The influence of near region scatters is computed by the method of local nonlinear approximation, while that of the far region scatters is treated as external exciting source and is calculated reiteratively. The method has the advantages, such as faster calculating speed, less computer memory requirements and more efficient convergency. The nonlinear inversion algorithm based on MLNI is applied to inversion problems which can concentrate the imaging region to a particular range instead of whole 3 D domain. Since the algorithm considers the effect of the nonlinear term in each element of the Jacobi matrix, it is more accurate and stable in comparison with the convenitional iterative Born inversion method. The double cell decomposition method is applied during the first rough imaging process considering the limitation of the information and computer memory, then the imaging range is reduced and the second more accurate imaging process can be carried out. Numerical results indicate that MLNI is an efficient method to compute the scattering fields of large scale scatters and that the application of the method to inversion can give high resolution 3 D cross hole conductivity images.