基于伴随原理和非结构化网格的大地电磁三维并行反演

At present, most three-dimensional (3D) magnetotellurics (MT) inversion algorithms are designed on structured grids. However, these approaches can not efficiently and accurately deal with complicated MT models with arbitrary surface topographies. In addition, these approaches which based on structured grids need a large amount of computational cost and are normally limited on small-scale and impractical models. Therefore, we need an new exploration for new 3D MT inversion algorithms. In this proposal, we present a novel 3D MT inversion algorithm which is based on the state-of-art unstructured grids. This novel approach has a capability of dealing with complicated models with arbitrary surface topographies. In the forward modeling, the domain-decomposition based vector finite-element method with unstructured grids is adopted to efficiently and accurately solve the electromagnetic fields. In the inversion, we still adopt the unstructured gird as the inversion grid. The inversion grid is completely independent on the forward grid. A new Octree tree is adopted to fast establish a map between the inversion and forward grids so that the procedure of updating the model parameters can be swiftly accomplished. To accelerate the inversion convergence rate, the adjoint method is adopted to fast compute the gradient of the objection function. Then, a novel L-BFGS algorithm is adopted to fast and stably accomplish the inversion procedure. Finally, we plan to test the performances of our new 3D MT inversion method on well-known benchmark MT models and field MT cases. Summarily, our new 3D MT inversion algorithm has a capability of efficiently inverting 3D large-scale magnetotellurics data set so that conductivity distributions of substructures with better resolutions can be obtained.

目前大地电磁法三维反演都是基于结构化网格，不能精细模拟复杂地形和地质体边界，且因计算消耗极大，反演规模小，尚难在实际中推广应用，因此探索与发展新的大地电磁法大规模快速三维反演无疑具有重要的理论意义和实际价值。本申请书拟提出一种基于非结构化网格和伴随原理的三维大地电磁反演算法，来快速、精细反演复杂三维地下电性结构。正演算法采用基于区域分解和非结构化网格的并行矢量有限元法，从而既可精细地模拟带复杂地形及地质边界的三维地质结构，又可精确、快速地计算其大地电磁响应。反演中同样采用非结构化网格，但独立于正演网格，以八叉树实现正反演网格间的快速映射和相互查询；采用内存消耗最小化的基于伴随原理与目标函数梯度的L-BFGS最优化并行算法，使目标函数快速、稳定地收敛于极小值，从而实现大地电磁法复杂模型三维精细反演，通过国际标准模型测试后，初步应用于实际大地电磁数据反演和解释，为进一步推广应用奠定基础。

目前大地电磁反演大多使用结构化网格，无法有效处理起伏地形和复杂地质结构，难以获得可靠的反演结果。本项目基于非结构化网格，开发了一系列的带地形复杂大地电磁2D/3D正反演技术和方法，研究的主要内容为：①考虑位移电流的情况下，利用非结构化三角形网格、有限元算法、实现了大地电磁和射线大地电磁的高精度快速2D正演计算，采用自适应和局部加密的技术，实现了正演精度的大幅度提高。②考虑位移电流的情况下，利用非结构化四面体网格、矢量有限元算法、实现了大地电磁和射线大地电磁的快速3D正演计算，采用面向目标自适应策略，测试并获得了针对电导率各项异性介质的最优化的后验误差计算算子，从而实现了正演精度的自动提高。③利用非结构化四面体网格、矢量有限元算法、实现了带地形复杂可控源电磁的3D正演计算，具备了同时处理任意电偶源和磁偶源的能力，采用网格加密计算，实现了正演精度的大幅度提高。④基于非结构化的反演网格，采用伴随原理实现了灵敏度矩阵的快速计算，采用正反演网格独立的策略，实现了反演的精度的大幅度提高和计算的显著加速，从而实现了带地形复杂（射线）大地电磁2D问题的电导率反演。⑤采用非结构化正反演网格独立的策略、伴随原理、高斯牛顿和L-BFGS反演算法，实现了带地形复杂（射线）大地电磁2D问题的电导率和介电常数的双参数反演。⑥采用正反演网格独立的策略、伴随原理、高斯牛顿和L-BFGS反演算法，实现了带地形复杂大地电磁3D问题的电导率约束和联合反演。取得的重要研究成果为：①完成了研发带地形复杂大地电磁三维电导率反演算法和程序的预期任务，兼顾了二维情况，还研究了高频射线大地电磁、地下电导率各向异性、电导率和介电常数双参数反演等新内容。②项目已发表学术论文41篇，其中SCI论文35篇，EI论文2篇，获得授权专利6项，出版中文专著4本。③资助博士研究生6人，4人获得博士学位。资助硕士研究生6人，5人获得硕士学位。项目成果在理论上具有创新性，提高了大地电磁的资料处理及解释水平，对促进勘探电磁法正反演的快速发展具有重要的理论及实际意义。