基于二维数据的加权非线性共轭梯度三维反演

The 3D Inversion with Non-linear Conjugate Gradient Based on 2D DC Resistivity Data

针对当前电阻率数据的解释仍以二维反演为主,而地下为三维结构的情况,研究起伏地形条件下三维源二维采集方式获取的多条测线测深数据的三维反演问题。正演算法采用三棱柱剖分的有限单元法,可以模拟起伏地形下的复杂模型;在求解大型线性方程组时采用了不完全乔利斯基分解回代技术,大大提高了三维多点电源的正演计算速度;在计算偏导数矩阵过程中,依据互换原理,只需有效组合正演时每个点电源所对应的节点电位便可得到偏导数矩阵,节约大量计算时间。其次三维反演算法采用加权正则化共轭梯度法,抑制了严重病态的非线性问题。模型计算结果表明:加权非线性共轭梯度反演算法既保证了反演稳定收敛,又能适合起伏地形反演,达到了满意的效果。

In view of the current resistivity data interpretation, the 2D inversion is still taken as the main point, but actually the 3D structure is used more underground. This paper presents a research on the 3D inversion for the multiple line sounding data over rugged terrain area. Triangular-prism mesh finite element method is employed in forward algorithm, which can be used to simulate the complex models with the topography. In solving large linear equations, incomplete Cholesky decomposition and back substitution technique are used, which can significantly improve the speed of 3D multi-source modeling. According to the interchangeable principle, the partial derivative matrix could be acquired by combining the potential of forward simulation, which saves large amount of time. The weighted regu non- arized conjugate gradient is applied to 3D inversion, which solves the severely ill-posed inear problem. The model calculation results show that this method could both guarantee the stable inversion convergence and be suitable for rugged topography inversion to reach satisfactory results.