地球自由振荡衰减模式的保结构模拟方法研究

尽管理论上地球自由振荡数值方法可处理莫霍面起伏、核幔边界起伏、地球内部横向非均匀性等重要问题，但现有时间域驻波数值模拟技术多基于非保结构计算，其长时程计算的积累误差难以避免，很难精确处理地球自由振荡模拟这一长时程追踪问题。近年来虽有相应的保结构方法问世，但仅适用于保守动力学系统；用其处理地球自由振荡这类具有衰减特性的非保守动力学问题，实难大幅提高精度及可靠性。本项目拟将保结构计算拓展至非保守动力学系统，通过对球体粘弹性波动方程离散化的稳定性、时间与空间离散的保结构格式等问题的研究，发展适用于衰减模式下地球自由振荡高精度模拟的、更为广义的保结构数值计算方法，大幅度降低长时程模拟的积累误差，为相关地球自由振荡过程的研究、深入理解地球自由振荡观测资料的细节、全球多尺度地球内部结构研究及地球内部非均匀性全貌刻画质量的提高奠定基础。

In this research, the structure-preserving modeling will be extended into the problem of non-conservative dynamical system and a high-precision and structure-preserving method for high-precision modeling of Earth’s free oscillations with attenuation will be presented. This method will be suitable for high-precision and long-time numerical simulations, which is required for high-precision modeling of Earth’s free oscillations with attenuation. It can be expected that the approach presented will be suitable for treating questions on the overall perspective of the Earth’s inner heterogeneity, such as fluctuations of the core-mantle boundary, the crust-mantle boundary and the Mohorovicic discontinuity. If this project is successful, it will be an important impact to all the geophysical studies which is related to Earth’s free oscillations.