摘要
本文利用龙格库塔法求解球坐标系下微分方程组,基于自重、可压缩和连续分层地球模型研究地震引起的地球变形,优化相关算法.首先对传统的两次同向积分法进行调整,对微分方程的齐次部分进行两次相向积分,分别由地心向上积分至震源和由地表向下积分至震源.接着利用震源间断条件求解震源上方和震源下方通解的组合系数,得到微分方程组的解矢量.基于该积分方法可以避免高阶微分方程组求解中精度丢失的问题.接着与均质地球模型下微分方程组解析解的比较,发现自重效应对走滑震源低阶求解结果的影响较大,对垂直引张震源变形解y_(4)的影响超过100阶.最后比较了均质地球模型和层状地球模型下高阶求解结果,发现两者的比值趋于稳定,当均质地球模型参数设置为震源所在层参数时,并且变形深度和震源处于模型同一层,两种地球模型下高阶变形解的比值趋于1.基于该发现,结合均质地球模型下渐近解,可解决实际分层地球模型下震源附近地震变形发散的问题.
In this paper,we use Runge-Kutta method to solve the differential equations in the spherical coordinate system.Based on self-gravitation,compressibility and continuous layered Earth model,we study the Earth deformation caused by earthquake,and optimize related algorithms.Firstly,we adjust the integration path of traditional method,and operate two opposite integrals for the homogeneous parts of differential equations.Integrate from the center of the Earth to the source point and from the Earth surface to the source point,respectively.Then,use the source discontinuity condition to obtain the combination coefficients of the upper and lower general solutions,further obtain the solution vector of the differential equations.Based on this integration method,one can avoid the loss of accuracy when solving the high-degree differential equations.By comparing with the analytical solution of the differential equations under the homogeneous earth model,we found that self-gravitation has significant effect on low-degree deformation solution of the strike-slip source,and the effect on solution y_(4) of the vertical tensile source exceeds 100 degree.Finally,we compared high-degree deformation solution under the homogeneous Earth model and the layered Earth model,and found that the ratio of the two tends to be stable.When the parameters of the homogeneous Earth model are set to the parameters of the layer where the seismic source is located,and the deformation depth is on the same layer as the seismic source,the ratio of high-degree deformation solution under the two Earth models tends to 1.Based on this discovery,combined with the asymptotic solution under the homogeneous earth model,it will solve the problem of seismic deformation divergence near the source under the layered Earth model.
作者
刘泰
唐河
佘雅文
付广裕
孟国杰
LIU Tai;TANG He;SHE YaWen;FU GuangYu;MENG GuoJie(Institute of Earthquake Forecasting,China Earthquake Administration,Beijing 100036,China;Key Laboratory of Computational Geodynamics,University of Chinese Academy of Sciences,Beijing 100049,China;School of Geophysics and Information Technology,China University of Geosciences,Beijing 100083,China)
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2022年第4期1229-1239,共11页
Chinese Journal of Geophysics
基金
国家自然科学基金(42104086,41874024,41904092)
中国地震局地震预测研究所基本科研业务费专项(2021IEF0504,2020IEF0506)
中国科学院精密测量科学与技术创新研究院大地测量与地球动力学国家重点实验室开放基金资助项目(SKLGED2021-2-1,SKLGED2021-4-2)
国家重点研发计划课题(2018YFC1503704,2019YEE0108900)联合资助.
关键词
微分方程组
两次相向积分
自重
层状地球模型
Differential equations
Two opposite integrals
Self-gravitation
Layered Earth model
