廖彬彬^1,2,,
徐建桥¹,
孙和平^1,2,
周江存¹
1. 中国科学院测量与地球物理研究所, 大地测量与地球动力学国家重点实验室, 武汉 430077
2. 中国科学院大学, 北京 100049

基金项目: 国家重点基础研究发展计划（973计划）（2014CB845902）、国家自然科学基金（41474062）资助


详细信息

作者简介: 廖彬彬, 男, 1992年生, 博士研究生, 主要研究震后形变的数值模拟.E-mail:lbb1040407093@sina.com

中图分类号: P312

收稿日期:2018-07-10
修回日期:2019-05-15
上线日期:2019-07-05

Spectral element method to load deformation in a SNREI Earth

LIAO BinBin^1,2,,
XU JianQiao¹,
SUN HePing^1,2,
ZHOU JiangCun¹
1. State Key Laboratory of Geodesy and Earth's Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China
2. University of Chinese Academy of Sciences, Beijing 100049, China


MSC: P312

--> Received Date: 10 July 2018
Revised Date: 15 May 2019
Available Online: 05 July 2019


摘要
摘要:谱元法作为一种基于变分原理的数值方法，已经成为地球动力学数值模拟的重要手段.本文旨在对Martinec（2000）正演模拟表面负荷问题的谱-有限元方法进行改进.简单地介绍了谱元法计算负荷边值问题的相关理论，并推导了中性分层液体中的平衡方程以及其对应的弱形式解.在地球半径方向上，采取高阶样条函数作为负荷解的基函数，并利用高斯-勒让德方法进行数值积分.均质地球模型数值试验表明，相较于Martinec的方法，本文方法可以有效地加快数值解的收敛速度.最后，利用PREM模型计算了SNREI地球的负荷勒夫数.数值计算结果表明本文方法的收敛性和稳定性都非常好.本文方法获得的负荷勒夫数与采用传统龙格-库塔积分方法获得的结果相对误差在0.01%的量级.
关键词: 谱元法/
弱解/
中性分层流体/
SNREI地球/
负荷勒夫数

Abstract:As a numerical method based on variational principle, the spectral element method (SEM) has become an important means of numerical simulation of many geodynamic problems. This paper aims to improve the spectral-finite element method of Martinec (2000) to surface load forward problem. The related theoretical formulas of calculating the load deformation boundary value problem by spectral element method are briefly introduced, and the equilibrium equation in the neural stratified liquid and the corresponding weak form solution are derived. In the direction of the Earth's radius, the high-order spline functions are used as bases, and the numerical integration is performed by using the Gauss-Legendre method. The results of homogeneous earth model show that the proposed method can effectively speed up the convergence of numerical solutions compared with Martinec's method. Finally, the load Love numbers of the PREM model is calculated, which also show that this new method has good stability and convergence. The relative error between the results by our method and by traditional Runge-Kutta method is less than 0.01%.
Key words:Spectral element method/
Weak solution/
Neutrally stratified fluid/
SNREI earth/
Load Love numbers



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