二维电阻率成像研究(英文)

2D Resistivity Tomography Study

电阻率成像中最关键的问题就是获得雅可比偏导数矩阵。本文从二维微分方程的积分解出发推导了一种新的电阻率成像的雅可比偏导数矩阵，同时形成了成像方程。用内外迭代相结合的高斯塞德儿迭代方法解成像方程可以得到电阻率的分布图像。数值模拟结果表明该方法是有效和可靠的，尤其值得注意的是积分法电阻率成像方法初始模型可以采用均匀模型，减小了对初始模型的依赖。对用其它方法难以获得好的成像结果的单一高阻体，积分法也得到了较好的成像结果。河南商丘某野外资料结果表明，成像结果和实际地质情况吻合较好。

One of the main problems in resistivity tomography is to get Frechet derivative matrix (sensitivity matrix). In this paper we use an integral solution of differential equation to derive a new Frechet derivative matrix for 2D media. Simultaneously the linear equation is formed, we call it 'tomography equation'. A resistivity image can be gotten through solving the tomography equation with Gaus-Seidel iteration method in which the inner and outer iteration and multistack technique are used at the same time. Synthetic data tests show that the method is reliable and effective, especially the initial model can be homogeneous, hence it reduces the dependency on the initial resistivity model. The image of a high resistivity body is also quite good, but it is very difficult to get good image of single high resistivity body with some other methods. A test on a field data set in ShangQiu of China is also given, it shows there is a high resistivity anomaly in the middle of the profile. The result coincides with field evidences.