全球尺度地震波传播的保结构算法研究

项目名称： 全球尺度地震波传播的保结构算法研究

项目编号： No.41204041

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 地球物理学和空间物理学

项目作者： 汪文帅

作者单位： 宁夏大学

项目金额： 25万元

中文摘要： 地震波数值模拟是地震勘探和地震学研究的重要部分。尽管现有的如有限差分、有限元等技术基本能满足小尺度问题的模拟需要,然而对于大尺度,尤其是全球尺度地震波传播的计算而言,由于涉及到长时程追踪,且前述方法大多是非高精度保结构方法,长时程计算时不可避免地产生高积累误差,导致数值频散严重,很难精确处理全球尺度地震波传播这一长时程追踪问题。因此,发展针对于全球尺度地震波传播数值模拟的高精度保结构算法成为关键。本项目针对球坐标下非均匀介质中弹性波方程拟构造谱元法结合新推的力梯度辛算法的离散方法,通过对其保结构性、精度及效率等问题的研究,发展适用于全球尺度地震波传播的高精度保结构数值模拟方法,使长时程模拟时的积累误差大幅降低,数值频散得以压制；并用间断算子处理地球内部的非均匀层间断面,显著提高模拟精度。保结构新方法的推出,将为高精度处理类似全球尺度三维非均匀介质中地震波传播的长时程计算问题提供新的途径。

中文关键词： 地震波传播；保结构算法；谱元法；地球自由振荡；

英文摘要： Numerical simulation of seismic waves constitues an important part for seismological research and seismic exploration.There are many methods, such as finite difference method, finite element mthod, can deal with simulation of small-scale or regional seismic wave propagation effectively. But for large-scale, especially for global simulation of seismic waves propagtion, no effective method is avaliable to deal with the problem of invetable accumulated errors and numerical dispersion that encounted in the present non-high precision structure-preserving methods because of the issue of long-time computation, casuing much difficulty in tracing global-scale seismic wave propagation. Therefore, it is very critical to develop a reliable algorithms of high-precision global-scale numerical simulation of seismic wave propagation to address the said issue. In this research project, the issue of tracing long-time simulation of elastic wave propagation in spherical coordinates will be addressed effectively via a constructed structure-preserving algorithm of combining spectral element method with new force-gradient symplectic method. And the problems like the stability,precision and time-space structure-preserving properties in the spherical coordinates will be well studied. Also, a kind of dicontinuous opteror is employed to

英文关键词： seismic wave propagation；structure-preserving algorithm；spectral element method；Earth free oscillations；