论文详情
传统的异常电位法将总电位分为背景场(一次场)电位和异常场(二次场)电位,背景场电位通常是简单模型背景场电位方程的解析解,但起伏地表条件下背景场电位方程无解析解。针对这一问题,利用改进的异常电位法,定义了适用于起伏地表条件的自然边界条件。将该方法引入井中激电的正演模拟,对二维线源场进行井中激电井地正演模拟,并采用加权余量法推导了新形成的边界条件,求解对应的有限单元积分方程。将直接解法求解器引入正演模拟,求解最终的线性方程组得到总电位,证明了起伏地表条件下有限单元法正演模拟的精度和效率。将几个典型的起伏地表模型试算结果与采用传统的总电位法得到的结果进行了比较,验证了该方法的正确性与有效性。
The conventional singularity removal approach is a commonly used secondary potential approach that divides the total potential into its background field (primary field) and the singularity field (secondary potential) components.While the primary field can be expressed as an analytical solution of simple models,such as uniform half-space or layered-earth models,it is unavailable under undulating terrain conditions.An improved secondary potential approach proposed by Penz is therefore adopted in direct current method,where a new natural boundary condition is defined for applications in undulating topography.Here this secondary potential approach is adopted for the forward modeling of the induced polarization in borehole.Forward modeling of the borehole-ground induced polarization method for a two-dimensional line source is studied.The new boundary value is deduced via the weighted residual method,and the corresponding finite element integral equation is obtained.The direct solution solver is introduced to solve the final system of linear equations,which improves the accuracy and efficiency of the forward modeling under the undulating topography.Tests on several typical models under undulating topography demonstrate its validity and superiority over traditional total potential methods.
国家自然科学基金项目(41604093,51541408)共同资助。