Three‐dimensional DC resistivity forward modelling using finite elements in comparison with finite‐difference solutions
Three‐dimensional DC resistivity forward modelling using finite elements in comparison with finite‐difference solutions
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DOI：
10.1046/j.1365-246x.2002.01819.x
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发表时间：
2002-12
影响因子：
2.8
通讯作者：
Yuguo Li;K. Spitzer
中科院分区：
文献类型：
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作者：
Yuguo Li;K. Spitzer
本文提出了一种直流电阻率模型的三维有限元法。奇异性被删除，制定的问题的二次电位，这大大提高了精度。使用共轭梯度法求解所得到的线性方程组。已证明了具有缩放矩阵的不完全Cholesky预条件子比对称逐次超松弛预条件子快。紧凑的存储方案充分利用了系统矩阵的稀疏性和对称性。有限元（FE）和以前开发的有限差分（FD）计划进行了详细比较。一般来说，两种方案显示出良好的一致性，本文提出的垂直堤模型的视电阻率的相对误差总体上小于0.5%。FD方案在电导率对比度附近产生较大的误差，而FE方案需要的存储量约为FD方案的3.4倍，并且相对于粗网格而言不太稳健。作为对正演模拟方案的改进，提出了一种改进的奇异性消除技术。将水平层状大地或垂直接触视为正常结构，其解即为原始电位。这种技术的效果证明了两个例子：一个立方体在两层地球和立方体附近的垂直接触。
SUMMARY A 3-D finite-element scheme for direct current resistivity modelling is presented. The singularity is removed by formulating the problem in terms of the secondary potential, which improves the accuracy considerably. The resulting system of linear equations is solved using the conjugate gradient method. The incomplete Cholesky preconditioner with a scaled matrix has been proved to be faster than the symmetric successive overrelaxation preconditioner. A compact storage scheme fully utilizes the sparsity and symmetry of the system matrix. The finite-element (FE) and a previously developed finite-difference (FD) scheme are compared in detail. Generally, both schemes show good agreement, the relative error in apparent resistivity for a vertical dike model presented in this paper is less than 0.5 per cent overall. The FD scheme produces larger errors near the conductivity contrast, whereas the FE scheme requires approximately 3.4 times as much storage as the FD scheme and is less robust with respect to coarse grids. As an improvement to the forward modelling scheme, a modified singularity removal technique is presented. A horizontally layered earth or a vertical contact is regarded as the normal structure, the solution of which is the primary potential. The effect of this technique is demonstrated by two examples: a cube in two-layered earth and a cube near a vertical contact.