中文摘要：

大地震等诸多激励均能激发全球自由振荡现象,通常表现为驻波形式的全球整体振荡.现有的地震波数值模拟方法多为非保结构方法,无法压制长时程计算中的积累误差.本文采用优化的三阶辛格式谱元法,对地球自由振荡及全球尺度的地震波传播进行了长时程模拟.通过与传统的基于Newmark算法的谱元方法结果对比分析,明确验证了本文所得优化的三阶辛格式谱元法在模拟地球自由振荡等大规模长时程问题上的优越性和准确性.上述进展在方法论层面为今后探测、刻画全球尺度地球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.

英文摘要：

Free oscillations of the Earth are usually as standing waves of entire globe,which can be excited by many factors such as a great earthquake.The oscillation types of this physical phenomenon depend on Earth′s structure and physical parameters.Therefore,intrinsic characters of the Earth can be revealed by studying Earth′free oscillations.Numerical simulation is an effective way to research seismic waves travelling in different earth models.In essence,the numerical simulation of Earth′s free oscillations is a long-term tracing of variable coefficient wave equation.The majority of numerical methods for seismic wave simulation are non-structurepreserving methods,which cannot suppress the accumulative error in long-time computation,e.g.,finite difference methods,pseudo-spectral methods,and finite element methods.In comparison,the symplectical methods based on the Hamilton system possess fine structure-preserving ability which makes them be suitable for the physical problem acquiring good precision in long-time simulation.The spectral element method combines the generality of the finite element method with the accuracy of spectral techniques.This method expands the solution in trigonometric series,of which a chief advantage is that the resulting method is of very high order.It also chooses high-degree piecewise polynomial basis functions,also achieving a very high order of accuracy.Symplectical methods introduced into spectral element methods may be an accurate and effective choice.In this research,a three-order symplectical spectral element method is modified for long-time simulation of Earth′s free oscillations and seismic waves propagating in the global range.The event simulated is a great earthquake（Mw8.6）off the west coast of northern Sumatra on 11 April 2012.The PREM earth model is used for simulation.Our method and traditional spectrum element method using Newmark time scheme are chosen for simulation respectively with the same parameters and computation scales.The time step adopted by our method is