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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。
The most critical issue in resistivity imaging is the Jacobian partial derivative matrix. In this paper, we derive a new Jacobian partial derivative matrix of resistivity imaging from the integral solution of two-dimensional differential equations and form an imaging equation. The image of the resistivity distribution can be obtained by solving the imaging equation using the Gauss-Sedl iteration method combined with internal and external iteration. The numerical simulation results show that this method is effective and reliable. Especially, it is worth noting that the initial model of the integral method resistivity imaging method can be uniform model, reducing the dependence on the initial model. For the single high resistance body which is difficult to obtain good imaging results by other methods, the integral method also obtains better imaging results. Henan Shangqiu a field data show that the imaging results and the actual geological conditions are in good agreement.