复杂固-液介质的速度应力方程三角形单元间断伽辽金地震波模拟算法  

A discontinuous Galerkin seismic wave simulation algorithm for complex fluid-solid media based on triangular cell and velocity stress equation

作　　者：曹文忠 张伟 CAO WenZhong;ZHANG Wei(Institute of Geophysics,China Earthquake Administration,Beijing 100081,China;Department of Earth and Space Sciences,Southern University of Science and Technology,Shenzhen Guangdong 518055,China)

机构地区：[1]中国地震局地球物理研究所,北京100081 [2]南方科技大学地球与空间科学系,广东深圳518055

出　　处：《地球物理学报》2024年第2期684-695,共12页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(U1901602);中国地震局地球物理研究所基本科研业务费专项(DQJB22K45);上海市财政科技专项(2020J001-5);深圳市科技计划(KQTD20170810111725321);广东省重大人才工程引进类(2019QN01G801)资助.

摘　　要：间断伽辽金法可用于存在复杂边界条件的模型,同时具有高阶精度和易于并行计算的优点,因此近年来在地震波传播模拟研究中得到了快速发展.数值通量是间断伽辽金法的关键组成部分之一.相比于其他通量,基于Rankine-Hugoniot跳跃条件的通量(RH-condition通量)在固体和液体介质边界具有更宽的稳定性,可以使用更大的时间步长,尤其是液体和固体之间的波阻抗差异较大时.它已被用于基于四边形网格和速度-应变方程的间断伽辽金地震波固液介质模拟.本文为了模拟陆地自然水体等存在复杂固-液界面形状的地震波传播,并在未来与其他数值方法耦合,发展了基于三角形网格的RH-condition通量间断伽辽金方法,使用一阶速度-压力声波和一阶速度-应力弹性波方程模拟复杂固-液介质中地震波的传播.通过水平层状和sin型起伏固-液模型,验证了该方法模拟结果的准确性.通过数值模拟展示了所提出的间断伽辽金法在不同网格大小和阶数下的准确性和效率.最后通过一个复杂模型的例子表明存在复杂固-液界面时该方法可以准确施加固-液边界条件.The discontinuous Galerkin method(DG)can be used with models of complex geometry boundaries,and also has the advantages of higher-order accuracy and easy parallel computation,thus has been developed rapidly for seismic wave propagation simulation in recent years.Numerical flux is one of the key components of DG.Compared with other fluxes,Rankine-Hugoniot(RH)condition flux has better stability regions at the interface between solid and fluid media and can use a larger time step,especially when the wave impedance contrast between the solid and fluid is large.It has been used to simulate seismic wave propagation in fluid-solid media using the quadrilateral mesh and the velocity-strain equations.In this study,for simulating seismic wave propagation for natural reservoirs on land with complex shape of the fluid-solid interface and for coupling with other numerical methods in the future,the discontinuous Galerkin method based on RH-condition flux and triangular mesh is developed for seismic wave simulation in complex fluid-solid media using the velocity-stress equations for both acoustic and elastic media.The accuracy of the simulation is verified by the horizontal layered and sin-type fluid-solid models.The numerical simulations show the accuracy and efficiency of the proposed DG with different mesh sizes and orders.Finally,an example of the complex model is given to show that the method can accurately apply the fluid-solid boundary conditions in the presence of complex fluid-solid interfaces.

关 键 词：间断伽辽金 地震波模拟 固-液介质 数值通量 

分 类 号：P631[天文地球—地质矿产勘探] P315[天文地球—地质学]