应用非一致性网格和高阶有限元的井地电磁三维各向异性正演算法  

Three-dimensional anisotropic forward modeling algorithm for borehole-to-surface electromagnetic method using non-conforming meshes and high-order finite element

作　　者：秦策 付文亮 王绪本[2] 米晓利 杨云见 赵宁 QIN Ce;FU Wenliang;WANG Xuben;MI Xiaoli;YANG Yunjian;ZHAO Ning(School of Physics and Electronic Information Engineering,Henan Polytechnic University,Jiaozuo,Henan 454003,China;College of Geophysics,Chengdu University of Technology,Chengdu,Sichuan 610059,China;GME&Geochemical Surveys Management,BGP Inc.,CNPC,Zhuozhou,Hebei 072751,China)

机构地区：[1]河南理工大学物理与电子信息学院,河南焦作454003 [2]成都理工大学地球物理学院,四川成都610059 [3]东方地球物理公司综合物化探经理部,河北涿州072751

出　　处：《石油地球物理勘探》2024年第6期1410-1419,共10页Oil Geophysical Prospecting

基　　金：河南省自然科学基金项目“大地电磁法三维hp型自适应有限元正演及自适应网格反演方法研究”(242300420223)和“基于自适应多尺度有限元法的三维井中可控源电磁正反演研究”(242300421364);河南省高校基本科研业务费专项资金项目“随钻瞬变电磁超前探测多尺度成像研究”(NSFRF230428);河南理工大学科技创新团队项目“瞬变电磁场超前探测数值模拟与智能成像”(XJ2021000701)联合资助。

摘　　要：地下介质通常表现为电各向异性,增加了井地电磁法响应的复杂性。因此,针对各向异性介质模型进行正演模拟并总结规律,对于正确解释电磁勘探的观测数据至关重要。目前,对复杂三维地质模型进行精确建模是正演中的难点之一。本文使用一种基于八叉树网格的高精度建模方法,通过将六面体单元划分为八个较小的单元来局部细化网格,能够使用较少数量单元的同时保证建模的精度,从而降低计算成本。此外,为提高数值解的精度,在计算时使用高阶形函数。结合八叉树网格和高阶形函数实现了井地电磁法三维各向异性正演方法。通过对比各向异性层状模型的数值解与解析解,验证了算法的正确性。使用八叉树网格实现复杂各向异性油气模型精确建模,将异常体设置不同的水平和垂直电阻率,计算结果表明垂直电阻率对响应的影响大于水平电阻率。研究成果对实际的野外施工具有一定的指导作用,为进一步进行各向异性介质的三维反演打下基础。Electrical anisotropy typically exhibited by subsurface media increases the complexity of borehole‐tosurface electromagnetic(BSEM)responses.Therefore,forward modeling for anisotropic media models and summarizing their characteristics are crucial for accurately interpreting EM exploration data.Currently,precise modeling for complex three‐dimensional geological structures is one of the challenges in forward modeling.We employ a high‐precision modeling method based on octree grids.By subdividing hexahedral elements into eight smaller elements to locally refine the grids,this method ensures the accuracy of modeling with fewer cells,thereby reducing computational costs.Additionally,to improve the accuracy of numerical solutions,we use higher‐order shape functions during calculations.The three‐dimensional anisotropic forward modeling method for borehole‐to‐surface EM surveys is achieved by a combination of octree grids and higher‐order shape functions.The comparison of numerical solutions with analytical solutions of anisotropic layered models validates the correctness of the algorithm.We utilize octree grids to achieve precise modeling of complex anisotropic oil and gas models and set different horizontal and vertical resistivities for anomalous bodies.The results indicate that vertical resistivity has a greater influence on the response than horizontal resistivity.These findings provide practical guidance for field applications and lay the groundwork for further three‐dimensional inversion of anisotropic media.

关 键 词：各向异性 八叉树 有限单元法 高阶形函数 

分 类 号：P631[天文地球—地质矿产勘探]