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本文对2.5维直流电阻率正演进行了研究.通过傅立叶变换,推导了点电源2.5维直流电阻率的边值问题和变分问题.使用有限单元法对变分问题进行了求解,从模拟精度和计算效率两方面考虑,采用了对矩形单元再进行三角形剖分的网格剖分方法,从而降低了线性方程组的阶数,减少了计算量.在大型线性方程组的求解中,采用了紧缩矩阵存储的方式,并采用了不完全LU分解的稳定双共轭梯度算法,提高了运算速度.推导了异常场电位的偏微分方程,并给出了基于异常场算法的思路,采用异常场算法的正演模拟降低了点电源附近电位函数的奇异性,提高了正演精度.通过理论模型的计算和比较,验证了正演算法的正确性.
In this paper, the forward modeling of 2.5-D DC resistivity is studied.The boundary value problems and variational problems of 2.5-D DC resistivity of point source are deduced by Fourier transform.The variational problems are solved by finite element method, Considering both the computational efficiency and the mesh triangulation of rectangular elements, the gridding method of triangulation is used to reduce the order of linear equations and reduce the computational cost.In the solution of large linear equations, The storage method of compact matrix is reduced and a stable bi-conjugate gradient algorithm with incomplete LU decomposition is adopted to improve the computing speed.The partial differential equation of the abnormal field potential is deduced and the idea based on the anomalous field algorithm is given.Using anomalous field The forward simulation of the algorithm reduces the singularity of the potential function near the point power and improves the forward precision, and the correctness of the forward algorithm is verified through the theoretical model comparison and comparison.