横向非均匀地球模型的自由振荡保结构模拟研究

Earth free oscillation, usually as a continuous oscillation of entire globe following the way of standing wave, can be excited by many sources, e.g., a great earthquake or volcanic eruption. Real oscillation types are mostly affected by structures and physical parameters of the Earth. Therefore, Earth’s intrinsic characters can be reflected directly by studying on Earth free oscillation. .With the development of numerical methods, especially, with the rapid development of massive parallel processing, numerical simulation is proved to be an effective way to solve the problem of Earth free oscillation. In essence, the numerical simulation is a long-time tracing of variable coefficient wave equation, which demands huge computation cost..In most simulation, one dimension Earth models are used to decline the solving difficulties. On account of the great difference between those simple models and realistic Earth, the simulation results cannot be satisfied..Numerical methods can be divided into two types, symplectical method and non- symplectical method, by the energy conservation criterion. At the moment, the majority of numerical methods for seismic wave simulation are non-structure-preserving methods, which cannot suppress the accumulative error in long-time computation, e.g., finite difference method, pseudo-spectral method and finite element method. In comparison, the symplectical methods based on Hamilton system possess fine structure-preserving ability. These methods can be fit for physical problems that acquiring high precision in long-time simulation. .The spectral element method is adopted commonly in simulation of Earth free oscillation, because it combines the flexibility of the finite element method with the high accuracy and rapid convergence of spectral techniques. These advantages make spectral element method be used in massive parallel processing conveniently. However, the Newmark time scheme adopted by traditional spectral element method is a second-order momentum-preserving method, the accuracy of which cannot be assured after long computation. Incorporating the symplectical method into spectral element method may be an accurate and effective choice. .Aiming to these disadvantages, in this program, two major research will be progressed. Firstly, a new Earth model S362M is developed to realize the lateral heterogeneous model, by incorporating the structures and parameters of mantle plumes into a radial inhomogeneous Earth model S362ANI. Secondly, an optimized three-order symplectical spectral element method is developed, considering the optimum symplectic coefficients. .This improvement can be a new and valid alternative numerical method for investigation on heterogeneity (especially, the lateral heterogeneity) in global scale.

地球的自由振荡是地球的本征振荡，受地球的结构及物性参数的影响。通过研究自由振荡问题，可以直观探析地球的内部结构及组成，并克服常规行波探测对观测点数量和分布要求高的限制。随着数值算法的发展，特别是大规模并行计算的飞速发展，弹性波方程数值模拟逐渐成为较便捷且行之有效的驻波探测（全球自由振荡求解）新方法。传统的全球尺度数值模拟为简化求解的难度，采用的地球模型多为一维理论地球模型或径向非均匀的准三维地球模型。另外，为降低模拟占用的庞大的计算资源，现有的模拟多采用谱元法进行空间离散，采用二阶数值算法进行时间离散。针对现有研究的不足，本项目拟构建横向非均匀地球模型，并进一步优化三阶保结构算法。课题将依托大规模并行计算平台，进行大尺度地震波传播模拟。本项目的研究进展将在理论和方法层面上为探测、刻画全球尺度地球非均匀（特别是横向非均匀）结构的驻波数值方法奠定了部分基础，并为相关研究领域提供了新的选择。

地球的自由振荡是地球的本征振荡，受地球的结构及物性参数的影响。通过研究自由振荡问题，可以直观探析地球的内部结构及组成，并克服常规行波探测对观测点数量和分布要求高的限制。此外，该问题的研究结果将有助于类地星球的构造探测，因为深空探测的观测条件和观测数量受很大的限制。随着数值算法的发展，特别是大规模并行计算的飞速发展，弹性波方程数值模拟逐渐成为较便捷且行之有效的驻波探测（全球自由振荡求解）新方法。传统的全球尺度数值模拟为简化求解的难度，采用的地球模型多为一维理论地球模型或径向非均匀的准三维地球模型。同时，为降低模拟占用的庞大的计算资源，现有的模拟多采用谱元法进行空间离散，采用二阶数值算法进行时间离散。已有的研究表明，采用简化模型及传统谱元算法进行自由振荡问题的长时程追踪，其结果的稳定性和可靠性很难满足要求。针对现有研究的不足，本项目取得了两项成果：一、参考相关学科方向关于地幔柱等深部构造的最新理论，构建了可供数值模拟使用的横向非均匀地球模型；二、参考关于辛算法最新的研究，进一步优化了项目主持人之前研究所得的三阶保结构算法。课题依托了大规模并行计算平台，进行了多组大尺度地震波传播的数值实验。本项目的研究进展将在理论和方法层面上为探测、刻画全球尺度地球非均匀（特别是横向非均匀）结构的驻波数值方法奠定基础，并为相关研究领域（如：深地构造探测、深空类地星球的结构探测等）提供新的选择。同时，本项目构建的保结构算法亦可应用于资源探测和工程物探等领域的正演研究。