王新宇,王程,毛玉蓉,等. 基于混合网格有限元的直流电阻率法三维正演研究[J]. 煤田地质与勘探,2022,50(5):136−143. DOI: 10.12363/issn.1001-1986.21.06.0338
引用本文: 王新宇,王程,毛玉蓉,等. 基于混合网格有限元的直流电阻率法三维正演研究[J]. 煤田地质与勘探,2022,50(5):136−143. DOI: 10.12363/issn.1001-1986.21.06.0338
WANG Xinyu,WANG Cheng,MAO Yurong,et al. 3D forward modeling of DC resistivity method based on finite element with mixed grid[J]. Coal Geology & Exploration,2022,50(5):136−143. DOI: 10.12363/issn.1001-1986.21.06.0338
Citation: WANG Xinyu,WANG Cheng,MAO Yurong,et al. 3D forward modeling of DC resistivity method based on finite element with mixed grid[J]. Coal Geology & Exploration,2022,50(5):136−143. DOI: 10.12363/issn.1001-1986.21.06.0338

基于混合网格有限元的直流电阻率法三维正演研究

3D forward modeling of DC resistivity method based on finite element with mixed grid

  • 摘要: 直流电阻率法因效率高、成本低等特点广泛应用于有色金属、煤田等矿产资源勘探和地质调查行业。但在井–地、地–井电阻率法勘探过程中,钻孔因素(井液电阻率和钻孔孔径)对不同探测模式下视电阻率响应的影响尚未明确,是否影响视电阻率资料的解释是值得探讨的一个问题。因此,提出采用混合网格有限元法实现直流电阻率三维正演。给出异常电位法满足的边值问题及有限元变分问题,应用三棱柱和四面体混合网格实现对计算区域的快速离散,并建立2种网格的线性插值基函数和单元系数矩阵;采用SSOR–PCG迭代算法求解异常电位满足的大型线性方程组,得到各观测点的响应。在保证计算精度的前提下,应用混合网格有效地离散钻孔地电模型,探讨钻孔因素对井–地、地–井观测方式视电阻率数据的影响特征。对于井–地观测方式:钻孔附近视电阻率受钻孔因素影响最大,严重影响视电阻率资料的合理解释,但随着测点收发距的增加,视电阻率响应逐渐趋于围岩电阻率;而且随着发射源深度的增加,钻孔对地表视电阻率响应的影响也逐渐减小。对于地–井观测方式:钻孔因素对浅部数据影响较大,对深部数据影响小,相比于井液电阻率,视电阻率响应更易受钻孔孔径的影响。直流电阻率法混合网格有限元三维正演算法的提出,对实际井–地、地–井电阻率法勘探具有理论指导意义,可结合钻孔信息进行正演模拟分析,选择合适的收发距,有效压制钻孔因素对实测资料的影响。

     

    Abstract: The DC resistivity method is widely used in the mineral resources exploration and geological survey industries because of its high efficiency and low cost, such as non-ferrous metals and coal fields. However, in the process of borehole–to–surface and surface–to–borehole resistivity method exploration, the influence of borehole factors (borehole fluid resistivity and borehole diameter) on the apparent resistivity response in different exploration modes is unclear, and whether it will affect the interpretation of apparent resistivity data is an issue worth exploring. Therefore, we proposed a mixed grid finite element method to realize the 3D forward modeling of DC resistivity. Then we gave the boundary value problem and the finite element variational problem satisfied by the abnormal electric potential method, applied the trigonal and tetrahedral grid to achieve a fast discretization of the computational region, and established the linear interpolation basis function and the element matrix of the two kinds of the grids. Finally, we used the SSOR–PCG iterative algorithm to solve the large-scale linear equations satisfied by the secondary potential and obtained the response of every observation point. On the premise of ensuring the calculation accuracy, we applied the mixed grid to discrete the borehole geoelectric model and explored the characteristics of the influence of borehole factors on the apparent resistivity data of the borehole-to-surface and surface-to-borehole observation methods. For the borehole-to-surface observation method: the apparent resistivity near the borehole is most influenced by the borehole factor, which seriously affects the reasonable interpretation of the apparent resistivity data. However, with the increase of the transmit-receive distance of the observation point, the apparent resistivity response gradually inclines to the resistivity of the surrounding rock. And with the depth of the emission source increases, the influence of borehole on the apparent resistivity response of the surface is also gradually reduced. For surface-to-borehole observation method: the borehole factor has a greater influence on shallow data and less influence on deep data, and the apparent resistivity response is more susceptible to the influence of borehole diameter than borehole fluid resistivity. The 3D forward modeling of mixed grid finite element method of DC resistivity method will provide theoretical guidance for practical borehole-to-surface and surface-to-borehole resistivity exploration, geophysical workers can combine the borehole information with the 3D forward modeling and select the appropriate transmit-receive distance to effectively suppress the influence of borehole on the observed data.

     

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