大地电磁测深三维正反演并行自适应算法及其实现技术研究

Deep Exploration in China is the main part of the 13th Five-Year Science & Technology Blueprint of National Land & Resources. Magnetotellurics (MT) is an electromagnetic geophysical method for inferring the earth's subsurface electrical conductivity. MT has become one of the most important tools in deep Earth research. But the three-dimensional MT inversion for real large-scale problems are suffering from the huge computational cost and efficiency of the algorithms. Research on the algorithms for three-dimensional large-scale MT inversion becomes more and more valuable in theory and application. In the project, the parallel adaptive algorithms are developed for the three-dimensional MT forward simulation and inversion, which are based on the unstructured mesh and can deal with complicated MT models with arbitrary surface topographies. The project will also focus on the efficient implementations of these algorithms towards on the heterogeneous many-core computer. A new parallel adaptive extended immersed finite element method and an efficient parallel precondition technique will be designed for MT forward simulation. For MT inversion, a parallel adaptive inversion algorithm based on the sensitive analysis will be developed. In the inversion algorithm, meshes for inversion are different from the mesh for forward simulation. The parallel algorithm for field interpolation between two grids will introduced. The multi-level idea will be used in the designing of parallel local mesh refinement & partition algorithms and dynamic load balancing method, which make the inversion on heterogeneous many-core computer more efficient. Finally, the performances of the new algorithms for MT forward simulation and inversion will be tested on well-known benchmark MT models and the real field MT cases in the Middle-Lower Yangtze River Valley metallogenic belt.

十三五期间，我国将全面实施深地探测战略。大地电磁测深法是研究地质结构的一种重要的地球物理勘探方法。现有大地电磁反演算法由于计算量大，难以适用于实际数据的大规模反演解释。探索与发展新的大地电磁测深大规模三维反演算法具有重要的理论意义和实际价值。本项目拟提出适用于复杂介质反演计算的基于非结构网格的电磁场正反演并行自适应数值算法，并开展面向异构众核体系结构的算法高效实现技术研究。围绕大地电磁测深问题，研究并行自适应浸入有限元方法，提出求解高阶棱单元离散问题的高效预条件子和基于涡流问题敏感矩阵的并行自适应大地电磁测深反演算法。设计多层自适应并行加密、网格并行剖分、非结构网格间场插值及动态负载均衡算法，支持异构协同计算。最后，针对长江中下游成矿带三维勘探数据开展示范应用研究。

大地电磁测深法是研究地质结构的一种重要的地球物理勘探方法。三维大地电磁正反演计算面临计算量大、地形复杂的挑战。项目围绕向地球深部进军和软件自主可控的国家战略需求，开展大地电磁测深三维正反演并行算法研究及软件研制工作。提出了高效的正演模拟方法，特别是解决了高阶非拟合网格类有限元离散方法（浸入有限元方法，扩展有限元方法、界面罚有限元方法）实现中关键的高阶界面积分问题，另外提出了基于区域分解思想的复杂度为O(NlogN)并行波源转移预条件方法。在自适应反演计算方法方面，理论证明了电磁涡流问题的不适定性，提出了一个基于伴随方法和非线性共轭梯度方法的反演算法，进而提出了自适应反演算法。在并行实现方面，扩展了并行自适应有限元软件开发平台PHG的功能，实现了对浸入有限元方法以及非拟合网格有限元方法的并行实现的支持，基于PHG研制了电磁涡流计算软件包。在国产超级计算机神威太湖之光上完成了数百万核的实际地形计算。相关算法及软件研究成果有望应用于实际地球物理勘探中。