自然电位测井是石油勘探中探测地层物理参数的重要手段.自然电位满足交界面具有跳跃间断的椭圆边界值问题.本文提出一种基于笛卡尔网格的间断捕捉方法,求解该椭圆交界面问题.理论分析证明了方法的二阶收敛性,数值例子进一步说明了方法的有效性.“,”Spontaneous potential(SP)log is an important technique to detect parameters of the formation in petroleum exploitation.The spontaneous potential satisfies an elliptic boundary problem with jump conditions on interfaces.A jump condition capturing method based on Cartesian grid is proposed and applied to solve such elliptic interface problems.Second-order convergence of the method is indicated