谱元法模拟地震波传播地震点源处理方法  

The Approximation Approaches for Seismic Point Sources with Spectral Element Method When Simulating Seismic Wavefields

作　　者：李孟洋 刘少林 杨顶辉[3] 李小凡 LI Mengyang;LIU Shaolin;YANG Dinghui;LI Xiaofan(College of Earth and Planetary Sciences,University of Chinese Academy of Sciences,Beijing 100049,China;National Institute of Natural Hazards,Ministry of Emergency Management of China,Beijing 100085,China;Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China;Institute of Geophysics and Geomatics,China University of Geosciences,Wuhan 430074,Hubei,China)

机构地区：[1]中国科学院大学地球与行星科学学院,北京100049 [2]应急管理部国家自然灾害防治研究院,北京100085 [3]清华大学数学科学系,北京100084 [4]中国地质大学地球物理与空间信息学院,武汉430074

出　　处：《地震研究》2025年第3期401-412,共12页Journal of Seismological Research

基　　金：国家自然科学基金(42174111);北京市自然科学基金(8222033);上海佘山地球物理国家野外科学观测研究站开放基金项目(SSOP202203).

摘　　要：在利用谱元法求解地震波运动方程时需要对方程进行离散,然而由于震源项常包含δ函数,该函数是奇异函数,通过数值近似具有一定难度,因此需要采用特殊方式处理震源项。引入δ函数的2类离散形式,以谱元法求解地震波运动方程为例,详细给出了震源项离散形式。为了验证这种震源处理方法的有效性,开展了多组数值模拟实验。首先在规则网格下,模拟了δ函数离散形式处理单极震源和矩张量震源的情况;其次在非规则网格下,模拟了δ函数离散形式处理地震点源情况。数值实验表明,在谱元法模拟地震波传播时,利用δ函数离散形式近似地震点源项,可得到高精度数值模拟结果。When solving the seismic wave equation with the spectral element method,it is necessary to discretize the equation.However,due to the presence of the δ function in the source term,which is a singular function,achieving accurate numerical approximation poses certain challenges.Therefore,special techniques are required to handle the source term.Two types of discrete forms of delta function are introduced in this paper.Using the spectral element method for numerical solution of seismic wave propagation,the discretized form of the source term is presented in detail.To validate the effectiveness of this source treatment approach,several numerical experiments were conducted.Firstly,the discrete form of the δ function was simulated for handling single-force and moment tensor sources on regular grid models.Secondly,the discrete form of the δ function was simulated for handling seismic point sources on an irregular grid model.The numerical experiments demonstrate that when simulating seismic wave propagation with the spectral element method,approximating the point source term with the discrete form of delta function can help to obtain high-precision results from numerical simulation.

关 键 词：谱元法 地震波运动方程 数值模拟 Δ函数 

分 类 号：P315.3[天文地球—地震学]