基于GLC多项式谱元法的大地电磁场二维正演模拟  

Two-dimensional forward modeling of magnetotelluric field based on GLC polynomial spectral element method

作　　者：钟志豪 李予国[1,2] ZHONG Zhihao;LI Yuguo(College of Marine Geosciences,Ocean University of China,Qingdao,Shandong 266100,China;Key Lab of Submarine Geosciences and Prospecting Techniques,Ministry of Education,Ocean University of China,Qingdao,Shandong 266100,China)

机构地区：[1]中国海洋大学地球科学学院,山东青岛266100 [2]中国海洋大学“海底科学与探测技术”教育部重点实验室,山东青岛266100

出　　处：《石油地球物理勘探》2024年第6期1395-1409,共15页Oil Geophysical Prospecting

基　　金：国家自然科学基金项目“西太平洋地球系统多圈层相互作用重大研究计划项目”(91958210)资助。

摘　　要：为了提高大地电磁场数值模拟的精度和效率,提出基于Gauss-Lobatto-Chebyshev(GLC)基函数谱元法的大地电磁场正演模拟方法。该方法首先从麦克斯韦方程组出发,推导了二维大地电磁场边值问题;然后基于Galerkin加权余量法将微分形式的边值问题转换成积分弱形式;最后采用GLC正交多项式插值基函数对全局问题进行离散化,利用Pardiso求解器求解大型稀疏线性方程组得到大地电磁场,实现了二维大地电磁场数值模拟。为了提高数值模拟效率,文中算法采用变密度规则网格剖分技术,即在电性复杂区域使用细网格,在电性均匀区域使用粗网格,采用OpenMP编程模式实现了多个频点的并行计算,以此达到缩短计算时间的目的。通过一维层状介质模型数值模拟结果验证了文中算法的正确性和精度,相比于Gauss-Lobatto-Legendre(GLL)多项式谱元法的数值模拟结果,GLC多项式谱元法的模拟结果精度更高。针对国际标准模型COMMEMI 2D-1和带地形模型,进行了基于GLC多项式谱元法、有限差分法和基于三角网格有限元法的正演模拟,三者数值结果对比表明,GLC多项式谱元法计算精度更高、网格依赖性更低。The two dimensional forward modeling of magnetotelluric(MT)fields based on the Gauss‑Lobatto‑Chebyshev(GLC)basis function spectral element method is put forward to improve the accuracy and efficiency of the numerical simulation of magnetotelluric fields.Under the guidance of this method,we derive the 2D MT boundary value problem and then transform it into the integral weak form through Galerkin weighted residual method.At last,we discretize the global problem using GLC interpolation basis functions and obtain MT fields after solving the large‑scale sparse linear equations system using the Pardiso solver,successfully numerically simulating it.To improve the computational efficiency of the numerical simulation,we adopt a variable density regular grid generation technique.This technique,by using finer grids in electrically complex areas and coarser grids in electrically homogeneous areas,can reduce computational time.In addition,parallel processing of multiple frequencies is achieved using OpenMP programming.Numerical simulation results of a one‑dimensional layered media model validate the correctness and accuracy of the proposed algorithm,showing a higher accuracy of the GLC polynomial spectral element method compared with GLL.Forward modeling based on the GLC polynomial spectral element method,finite difference method,and triangular mesh finite element method is conducted for the COMMEMI 2D‑1 model and the terrain model,and the comparison results show that the GLC method has a higher accuracy and less grid dependence.

关 键 词：大地电磁法 数值模拟 CHEBYSHEV多项式 并行计算 直接求解器 

分 类 号：P631[天文地球—地质矿产勘探]