积分法三维电阻率成像

二维或是三维电阻率反演成像研究,最关键的环节是在反演系数矩阵即敏感矩阵(或雅可比矩阵)的求取上.本文从微分方程的积分解出发,推导了表达式极为简单的三维雅可比系数矩阵,构造了成像方程.根据反演方程系数的稀疏特征,采用改进的降维高斯赛德尔迭代法来求解该反演方程,并通过内外迭代的结合,对大型稀疏欠定方程能很快收敛,得到可靠的解答.合成数据模型结果及实际资料的成像结果表明积分法不但实现起来极容易,成像结果的精度也相当高.

3-D RESISTIVITY TOMOGRAPHY BY INTEGRAL METHOD

The key point of 2 D or 3 D resistivity tomography imaging is to get elements of sentivity matrix or Jacobi matrix. In this paper, based on integrated solution of differential equation, we derived simple and analytical expression of elements of sentivity matrix and formed imaging equations. According to sparse feature of the matrix, we use Gauss Sadel resolution method to solve such equations and use inner and outer iteration and multi curent poles techniques to improve the quality of image of resistivity structures. The model and field data results indicate that the method presented here is easy and the result resolution is high.