基于Lorenz规范的空间-波数域大地电磁三维正演

Forward modeling of three-dimensional magnetotelluric based on Lorenz gauge in space-wavenumber domain

大地电磁勘探方法由于其成本低、施工简单、探测深度广等优点,广泛应用于矿产资源普查、油气勘探和深部构造研究等领域.如何提高大规模三维大地电磁数值模拟的精度和效率一直是研究热点.本文基于空间-波数域方法,实现了基于Lorenz规范的空间-波数域三维大地电磁数值模拟.基于二次场计算原理,引入Lorenz规范,将Maxwell方程组转化为关于二次场矢量位的亥姆霍兹方程;利用水平方向二维傅里叶变换,将空间域三维偏微分方程转换为多个波数下相互独立的常微分方程,方程采用二次插值有限单元法计算,得到定带宽线性方程组,方程计算量小、并行性好,采用追赶法求解,提高了算法效率;引入压缩算子,用迭代法逐次逼近真实解.充分利用了空间-波数域方法数值精度高、内存需求少、效率高的特点.设计棱柱体模型验证了算法的正确性、分析了算法的收敛性,说明算法对不同频率、不同电导率对比度模型均具有很好的适应性.利用Dublin(DTM1)模型进行三维大地电磁数值模拟,结果表明:在满足精度要求的前提下,空间-波数域算法比空间域算法占用内存少、耗时短;相比基于Coulomb规范的空间-波数域算法,基于Lorenz规范的空间-波数域方法耗时更短、占用内存更少,效率提高至少3倍以上,体现了新方法的优势.

The magnetotelluric method(MT)is widely used for the geophysical exploration of mineral resource exploration,oil-gas exploration,and study of deep structure because of its advantages of low cost,simple construction,and large detecting depth.How to improve the accuracy and efficiency of the 3D MT forward modeling in large scale is focus of study.Based on the space-wavenumber domain method,we study the 3D MT forward modeling in the space wavenumber domain based on the Lorenz gauge.We adopt secondary field method,by introducing the Lorenz gauge,the Maxwell equations can be converted into Helmholtz equations of the vector potential.With the help of the horizontal 2D Fourier transform,the 3D partial differential equation can be transformed into independent ordinary differential equations of several different wavenumbers.The equations are solved by the finite element method of quadratic interpolation,the linear equations are constant bandwidth,low-calculation and highly parallel,we further improve the efficiency of the algorithm by using a chasing method.The compact operator is applied to iterative computing method to approach the real solution.It makes full use of the advantages of the space-wavenumber domain method,like high numerical accuracy,low memory requirement,and high efficiency.We design a prism model to verify the accuracy and discuss the convergence of algorithm,we can conclude that the proposed method is suitable for different frequencies and large conductivity contrast anomalies.The results of Dublin(DTM1)model for 3D MT modeling show that compared with the existing spatial domain algorithms,based on fulfilling requirement for precision,the space-wavenumber domain methods spend less time and require less memory.The space-wavenumber domain algorithm of the Lorenz gauge is more efficient than that of the Coulomb gauge,increased by at least 3 times,which reflects the advantages of the new space-wavenumber domain method.