任意各向异性介质三维非结构谱元法直流电阻率正演模拟研究

各向异性是地电异常解释中不可忽视的因素，广泛存在于裂隙或层理发育的地质环境中.本文针对任意各向异性条件下直流电阻率法三维正演问题进行研究，结合非结构谱元法建立模拟算法，充分利用谱方法的指数收敛性以及非结构有限元对地形和复杂异常体刻画能力，提高计算精度和效率.通过灵活的四面体网格剖分和高阶谱插值，实现了复杂介质任意各向异性模型电阻率响应的高精度数值模拟.我们首先通过层状各向异性模型验证本文非结构谱元法的计算精度，进而我们以半空间中立方体模型为例分析各向异性对电阻率响应的影响特征，并通过计算针对不同各向异性参数的视电阻率极性图，探究地下介质各向异性特征识别方法.最后，我们针对典型的山脊模型计算和分析存在地形效应条件下各向异性电流场分布及视电阻率特征.模型计算结果表明基于四面体网格的谱元法模拟带有复杂地形和异常体的任意各向异性模型具有很高的计算精度.本文的研究成果将在推进电阻率方法用于解决裂隙及层理等环境和工程地质问题中发挥积极作用.

DC resistivity forward modelling for arbitrarily anisotropic media using the unstructured spectral element method

Anisotropy widely exists in the geological environment with well-developed fractures or bedding, which is a key factor that cannot be ignored when interpreting DC resistivity data. In this paper, we study three-dimensional forward modelling of the DC resistivity method for arbitrarily anisotropic media, and establish a simulation algorithm based on the unstructured spectral element method. This method makes full use of exponential convergence of the spectral method and the ability of the unstructured finite-element to delineate terrain and complex underground structures, so that the modelling accuracy and efficiency can be improved simultaneously. Via flexible tetrahedral meshing and high-order spectral interpolation, a high-precision numerical simulation of resistivity response for arbitrarily anisotropic media can be achieved. To do so, we first verify the accuracy of the unstructured spectral element method on a layered anisotropic model, and then take the model of a cube buried in a half space as an example to analyze the influence of anisotropy on resistivity response. We compare the polar plots of apparent resistivity for different anisotropy parameters to explore the means of identifying the anisotropy of underground media. Finally, we calculate and analyze the distribution of the current and apparent resistivity affected by the topography in a typical anisotropic ridge model. Calculation results show that the spectral element method based on tetrahedral grids has high calculation accuracy for simulating arbitrary anisotropic models with complex terrain and abnormal bodies. Research results of this paper would contribute to the advancement of the DC resistivity method applied to the solution of the environmental and engineering problems.