地面频率电磁法三维正反演研究及统一平台建设

Three-dimensional modeling and inversion of ground frequency-domain electromagnetic (FDEM) methods become the key issue in detailed and quantitative interpretation of large-scale electromagnetic data. Due to the singularity of the electromagnetic sources, the speed and accuracy of the forward modeling, the applicability and computing efficiency of the inversion, three-dimensional inversion have very limited application in practical exploration. To solve these problems, we propose to adopt the finite-volume (FV) method to solve the coupling equations in Lorenz gauge. The complicated topography or interface are simulated by hexahedral grids and coordinate transformation. The discretization technology for arbitrary transmitting sources are introduced to represent different kinds of electromagnetic sources. By using the aggregation multigrid solver, domain decomposition technique and parallel computation together, we can significantly improve the speed of forward calculation, thus carry out fast three-dimensional modeling for different kinds of FDEM methods. Meanwhile, a general formula for the Jacob matrix for various types of electromagnetic data is established, which serve as the kernel in the parallel computation of the sensitivity or gradient of the object function. To implement the three-dimensional parallel inversion for electromagnetic data effected by topography, the “global” optimization algorithm – truncated Newton method and other gradient based inversion methods (Nonlinear conjugate gradient, Gauss-Newton, L-BFGS) will be utilized to minimize the object function. We extremely expect to build and implement a unified platform for FDEM modeling and inversion, with which different electromagnetic sources and data can be easily solved. This research will improve the technology and level of detailed processing and interpretation for FDEM data definitely.

地面频率域电磁法三维正反演成为大规模电磁数据精细化和定量解释的关键。然而受多类型场源、复杂起伏地形、正演模拟的速度和精度以及三维反演的适用性等问题的困扰，三维反演仍难于在实际勘探中获得广泛应用。为此，本项目拟采用有限体积法求解Lorenz规范条件下耦合势对称方程，利用坐标变换技术模拟起伏地形或地电界面，使用场源等效技术离散不同类型场源，引入聚集多重网格、区域分解以及并行求解技术提升正演计算速度，实现任意场源的地面频率域电磁法三维快速正演。另外，建立不同数据集的雅克比矩阵的统一表达式，采用一种“全局”优化算法—截断高斯牛顿法及多种经典反演方法(非线性共轭梯度、高斯牛顿法、L-BFGS等)实现带地形的地面频率域电磁法三维并行反演。本项目期望以此建立地面频率域电磁三维正反演统一平台，实现不同类型场源、不同数据类型的地面频率电磁三维正演模拟和反演解释，提高我国地面频率域电磁勘探三维精细化解释水平。

本项目针对频率域电磁三维正反演快速计算和实用化问题，采用有限体积法求解Lorenz规范条件下耦合势对称方程实现了任意场源频率域电磁法三维正演，并引入聚集多重网格求解技术实现大规模问题的线性代数方程组高精度快速求解；提出一种“全局”优化算法—截断牛顿法和多种经典反演方法实现了地面频率域电磁法三维反演，建立了地面频率域电磁三维正反演平台，为提高地面电磁勘探的三维精细化解释提供技术支撑。主要研究内容和成果如下：.(1)实现了不同类型场源和不同数据类型的地面频率域电磁三维正演。采用有限体积法离散Lorenz规范条件的磁矢势和标势耦合对称方程，并将不同类型场源分解成一系列短导线电性源组合，成功实现任意场源下频率域三维电磁正演模拟。通过典型地电模型模拟验证了本文开发的算法能够实现不同类型场源和各种不同应用范围频率域三维电磁正演模拟，同时具有避免一次场计算和计算精度较高等优点。.(2)引入聚集多重网格算法（AGMG）实现频率域电磁法三维正演过程中大型稀疏线性代数方程组求解，极大地提升了三维正演的计算速度和效率，为解决困扰大规模电磁法三维正反演的计算效率问题提供技术支撑。.(3)提出“全局”优化的截断牛顿法实现了频率域电磁法三维反演，有效解决传统反演算法收敛速度慢、对初始模型依赖程度高以及容易陷入局部最小值等问题，为频率域电磁法三维反演提供一种新的途径。.(4)实现了多种（STD、NLCG、L-BFGS、GNCG、TRN）反演算法的频率域电磁法三维反演，并以大地电磁法为例，通过典型地电模型试验综合评价各种算法的优缺点，为频率域电磁法三维反演的方法选择和实用化提供技术参考。.(5)建立了频率电磁法三维正反演统一框架和平台，实现了不同场源和不同观测数据集的地面频率域电磁法三维正反演及基于MPI的并行加速，为频率域电磁法的“精细化”和“透明化”三维解释打下坚实的基础。