摘要
采用格点型有限体积法,建立直流电测深2.5维正演模拟算法。首先,从点电源电位所满足的边值问题出发,导出格点型有限体积法控制方程的离散表达式,对边界条件近似处理后求解线性方程组即得离散电位数值解。其次,通过模拟计算均匀半空间模型和一维层状介质模型,与解析法计算结果对比,验证格点型有限体积正演算法的正确性和稳定性。分别采用本文建立的直流电测深2.5维正演模拟算法、Res2dmod开源软件构建的有限差分算法对典型二维地电模型进行正演模拟,得到2种算法的视电阻率拟断面图。研究结果表明:直流电测深2.5维正演模拟算法在一维求解域内的计算结果与解析解之间的相对误差小于2%,满足数值计算精度要求;该算法能定性判断异常体电阻率与围岩电阻率相对大小和异常体的空间展布,与经过验证的成熟软件Res2dmod相比较,电阻率数值解的绝对误差不超过3.4Ω·m,证明该算法能正确分析直流电测深2.5维异常响应规律,可为实测数据的定性解释提供指导。
A vertex-centered finite volume algorithm was developed for 2.5D direct current numerical modeling.Firstly,from the boundary value problem of variable coefficient Helmholtz equation for electric potential generated by the point source,the discrete expressions of governing equation were derived from vertex-centered finite volume scheme.The numerical solutions of discrete electric potential were calculated after the approximate treatment on the boundary conditions.Secondly,through the simulation of homogeneous half-space model and one-dimensional model,and compared with the analytical results,the correctness and stability of the vertexcentered finite volume forward algorithm were verified.Finally,the 2.5D direct current numerical modeling established in this paper and the finite difference algorithm constructed by Res2dmod open source software were used to simulate the typical two-dimensional ground electric model,and the apparent resistivity quasi-crosssectional views of the two algorithms were obtained.The results show that the relative error between the calculation results and the analytical results in the one-dimensional solution domain of the algorithm is less than 2%,which meets the requirements of numerical calculation accuracy.The algorithm established in this paper can qualitatively determine the relative value of the resistivity of the anomaly and the resistivity of the surrounding rock and the spatial distribution of the anomaly,and the absolute error of the numerical solution does not exceed 3.4Ω×m compared with the verified mature software Res2dmod.,which proves the lattice-point finite volume algorithm adopted in this paper can correctly analyze the 2.5D anomaly response law of DC bathymetry,and can provide guidance for the qualitative interpretation of the measured data.
作者
欧阳黎明
赵煊煊
童孝忠
谢维
李欢
OUYANG Liming;ZHAO Xuanxuan;TONG Xiaozhong;XIE Wei;LI Huan(School of Geosciences and Info-Physics,Central South University,Changsha 410083,China;Geological Survey Institute of Hunan Province,Changsha 410129,China;Coal Geological Geophysical Exploration Surveying&Mapping Institute of Shanxi Province,Jinzhong 030600,China)
出处
《中南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2023年第7期2758-2767,共10页
Journal of Central South University:Science and Technology
基金
湖南省自然科学基金资助项目(2022JJ30706,2023JJ30411)。
关键词
直流电测深
正演模拟
有限体积法
格点型
2.5维
direct current sounding
forward modeling
finite-volume method
vertex-centered scheme
2.5D
