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Xing H J，Liu A W，Li X J，Chen S，Fu L. 2022. Application of an optimized transmitting boundary with multiple artificial wave velocities in spectral-element simulation of seismic wave propagation. Acta Seismologica Sinica，44（1）：26−39. DOI: 10.11939/jass.20210090
Citation: Xing H J，Liu A W，Li X J，Chen S，Fu L. 2022. Application of an optimized transmitting boundary with multiple artificial wave velocities in spectral-element simulation of seismic wave propagation. Acta Seismologica Sinica，44（1）：26−39. DOI: 10.11939/jass.20210090
shu

Application of an optimized transmitting boundary with multiple artificial wave velocities in spectral-element simulation of seismic wave propagation

  • 1.

    Institute of Geophysics，China Earthquake Administration，Beijing 100081，China

  • 2.

    Faculty of Architecture，Civil and Transportation Engineering，Beijing University of Technology，Beijing 100124，China

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  • Received Date: May 29, 2021
  • Revised Date: August 29, 2021
  • Available Online: January 20, 2022
  • Published Date: March 17, 2022
    Graphical Abstract
    • Abstract
  • This paper applied an optimized transmitting boundary with multiple artificial velocities （denoted as caj-MTF） that is recently proposed by the authors to the high-accuracy spectral-element simulation of seismic wave propagation, and made a comparison study with several other classical artificial （or absorbing） boundary conditions including Liao’s multi-transmitting formula （MTF） boundary, perfectly matched layer （PML） boundary, viscous-spring boundary and the first-order Clayton-Engquist paraxial-approximation boundary. The results obtained from theoretical analysis and numerical tests are as follows: ① The formulation of ca j-MTF is very similar to that of MTF, so it has most of the advantages of the latter, i.e., very simple expressions, easy to be implemented, adjustable accuracy, minimal computation cost, and general applicability. ② Unlike the traditional MTF boundary that has only a single artificial wave velocity （i.e., computational wave velocity）, ca j-MTF has multiple artificial wave velocities. In the simulation of elastic waves, the computational wave velocity parameters of ca j-MTF can be set to be P- and S-wave velocities, respectively. On this situation, the consistency between computational and physical wave velocities makes a significant improvement in the boundary accuracy. ③ ca j-MTF boundary has an slightly lower accuracy than that of PML boundary, whereas it is significantly superior to MTF, viscous-spring boundary and the first-order paraxial-approximation boundary. ④ ca j-MTF is superior to PML as it has much simpler formulations and better versatility. This work provides a convenient and high-efficient artificial boundary （or absorbing boundary） for spectral-element simulation of seismic wave propagation.
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  • 陈少林,孙杰,柯小飞. 2020. 平面波输入下海水-海床-结构动力相互作用分析[J]. 力学学报,52(2):578–590. doi: 10.6052/0459-1879-19-354
    Chen S L,Sun J,Ke X F. 2020. Analysis of water-seabed-structure dynamic interaction excited by plane waves[J]. Chinese Journal of Theoretical and Applied Mechanics,52(2):578–590 (in Chinese).
    戴志军,李小军,侯春林. 2015. 谱元法与透射边界的配合使用及其稳定性研究[J]. 工程力学,32(11):40–50. doi: 10.6052/j.issn.1000-4750.2014.03.0196
    Dai Z J,Li X J,Hou C L. 2015. A combination usage of transmitting formula and spectral element method and the study of its stability[J]. Engineering Mechanics,32(11):40–50 (in Chinese).
    杜修力,赵密,王进廷. 2006. 近场波动模拟的人工应力边界条件[J]. 力学学报,38(1):49–56. doi: 10.3321/j.issn:0459-1879.2006.01.007
    Du X L,Zhao M,Wang J T. 2006. A stress artificial boundary in FEA for near-field wave problem[J]. Chinese Journal of Theoretical and Applied Mechanics,38(1):49–56 (in Chinese).
    景立平. 2004. 多次透射公式实用形式稳定性分析[J]. 地震工程与工程振动,24(4):20–24. doi: 10.3969/j.issn.1000-1301.2004.04.004
    Jing L P. 2004. Stability analysis of practical formula for multi-transmitting boundary[J]. Earthquake Engineering and Engineering Vibration,24(4):20–24 (in Chinese).
    李宁,谢礼立,翟长海. 2007. 基于混合有限元格式的完美匹配层与多次透射公式人工边界比较研究[J]. 地震学报,29(6):643–653. doi: 10.3321/j.issn:0253-3782.2007.06.009
    Li N,Xie L L,Zhai C H. 2007. Comparison of perfectly matched layer and multi-transmitting formula artificial boundary conditions based on hybrid finite element formulation[J]. Acta Seismologica Sinica,29(6):643–653 (in Chinese).
    李小军,廖振鹏. 1996. 时域局部透射边界的计算飘移失稳[J]. 力学学报,28(5):627–632. doi: 10.3321/j.issn:0459-1879.1996.05.016
    Li X J,Liao Z P. 1996. The drift instability of local transmitting boundary in time domain[J]. Acta Mechanica Sinica,28(5):627–632 (in Chinese).
    李小军,廖振鹏,关慧敏. 1995. 粘弹性场地地形对地震动影响分析的显式有限元-有限差分方法[J]. 地震学报,17(3):362–369.
    Li X J,Liao Z P,Guan H M. 1995. An explicit finite element-finite difference method for the analysis of the influence of viscous-elastic site topography on seismic wave motion[J]. Acta Seismologica Sinica,17(3):362–369 (in Chinese).
    廖振鹏. 2002. 工程波动理论导论[M]. 第二版. 北京: 科学出版社: 156–181.
    Liao Z P. 2002. Introduction to Wave Motion Theories in Engineering[M]. 2nd ed. Beijing: Science Press: 156–181 （in Chinese）.
    廖振鹏,李小军. 1995. 推广的多次透射边界:标量波情形[J]. 力学学报,27(1):69–78.
    Liao Z P,Li X J. 1995. Generalized multi-transmitting boundary:Scalar wave case[J]. Acta Mechanica Sinica,27(1):69–78 (in Chinese).
    廖振鹏,黄孔亮,杨柏坡,袁一凡. 1984. 暂态波透射边界[J]. 中国科学:A辑,(6):556–564.
    Liao Z P,Huang K L,Yang B P,Yuan Y F. 1984. A transmitting boundary for transient wave analyses[J]. Science in China:Series A,27(10):1063–1076.
    廖振鹏,周正华,张艳红. 2002. 波动数值模拟中透射边界的稳定实现[J]. 地球物理学报,45(4):533–545. doi: 10.3321/j.issn:0001-5733.2002.04.011
    Liao Z P,Zhou Z H,Zhang Y H. 2002. Stable implementation of transmitting boundary in numerical simulation of wave motion[J]. Chinese Journal of Geophysics,45(4):533–545 (in Chinese).
    刘晶波,李彬. 2005. 三维黏弹性静-动力统一人工边界[J]. 中国科学:E辑,35(9):966–980.
    Liu J B,Li B. 2005. A unified viscous-spring artificial boundary for 3-D static and dynamic applications[J]. Science in China:Series E,48(5):570–584. doi: 10.1360/04ye0362
    谢志南,章旭斌. 2017. 弱形式时域完美匹配层[J]. 地球物理学报,60(10):3823–3831. doi: 10.6038/cjg20171012
    Xie Z N,Zhang X B. 2017. Weak-form time-domain perfectly matched layer[J]. Chinese Journal of Geophysics,60(10):3823–3831 (in Chinese).
    邢浩洁,李鸿晶. 2017a. 透射边界条件在波动谱元模拟中的实现:一维波动[J]. 力学学报,49(2):367–379.
    Xing H J,Li H J. 2017a. Implementation of multi-transmitting boundary condition for wave motion simulation by spectral element method:One dimension case[J]. Chinese Journal of Theoretical and Applied Mechanics,49(2):367–379 (in Chinese).
    邢浩洁,李鸿晶. 2017b. 透射边界条件在波动谱元模拟中的实现:二维波动[J]. 力学学报,49(4):894–906.
    Xing H J,Li H J. 2017b. Implementation of multi-transmitting boundary condition for wave motion simulation by spectral element method:Two dimension case[J]. Chinese Journal of Theoretical and Applied Mechanics,49(4):894–906 (in Chinese).
    邢浩洁,李小军,刘爱文,李鸿晶,周正华,陈苏. 2021. 波动数值模拟中的外推型人工边界条件[J]. 力学学报,53(5):1480–1495. doi: 10.6052/0459-1879-20-408
    Xing H J,Li X J,Liu A W,Li H J,Zhou Z H,Chen S. 2021. Extrapolation-type artificial boundary conditions in the numerical simulation of wave motion[J]. Chinese Journal of Theoretical and Applied Mechanics,53(5):1480–1495 (in Chinese).
    于彦彦,丁海平,刘启方. 2017. 透射边界与谱元法的结合及对波动模拟精度的改进[J]. 振动与冲击,36(2):13–22.
    Yu Y Y,Ding H P,Liu Q F. 2017. Integration of transmitting boundary and spectral-element method and improvement on the accuracy of wave motion simulation[J]. Journal of Vibration and Shock,36(2):13–22 (in Chinese).
    章旭斌,廖振鹏,谢志南. 2015. 透射边界高频耦合失稳机理及稳定实现:SH波动[J]. 地球物理学报,58(10):3639–3648. doi: 10.6038/cjg20151017
    Zhang X B,Liao Z P,Xie Z N. 2015. Mechanism of high frequency coupling instability and stable implementation for transmitting boundary:SH wave motion[J]. Chinese Journal of Geophysics,58(10):3639–3648 (in Chinese).
    Clayton R,Engquist B. 1977. Absorbing boundary conditions for acoustic and elastic wave equations[J]. Bull Seismol Soc Am,67(6):1529–1540. doi: 10.1785/BSSA0670061529
    Higdon R L. 1986. Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation[J]. Math Comput,47(176):437–459.
    Higdon R L. 1991. Absorbing boundary conditions for elastic waves[J]. Geophysics,56(2):231–241. doi: 10.1190/1.1443035
    Huang J J. 2018. An incrementation-adaptive multi-transmitting boundary for seismic fracture analysis of concrete gravity dams[J]. Soil Dyn Earthq Eng,110:145–158. doi: 10.1016/j.soildyn.2017.12.002
    Liao Z P. 1996. Extrapolation non-reflecting boundary conditions[J]. Wave Motion,24(2):117–138. doi: 10.1016/0165-2125(96)00010-8
    Liao Z P,Wong H L. 1984. A transmitting boundary for the numerical simulation of elastic wave propagation[J]. Int J Soil Dyn Earthq Eng,3(4):174–183.
    Liao Z P,Liu J B. 1992. Numerical instabilities of a local transmitting boundary[J]. Earthq Eng Struct Dyn,21(1):65–77. doi: 10.1002/eqe.4290210105
    Liu Y S,Teng J W,Lan H Q,Si X,Ma X Y. 2014. A comparative study of finite element and spectral element methods in seismic wavefield modeling[J]. Geophysics,79(2):T91–T104. doi: 10.1190/geo2013-0018.1
    Shi L,Wang P,Cai Y Q,Cao Z G. 2016. Multi-transmitting formula for finite element modeling of wave propagation in a saturated poroelastic medium[J]. Soil Dyn Earthq Eng,80:11–24. doi: 10.1016/j.soildyn.2015.09.021
    Xie Z N,Zhang X B. 2017. Analysis of high-frequency local coupling instability induced by multi-transmitting formula:P-SV wave simulation in a 2D waveguide[J]. Earthq Eng Eng Vib,16(1):1–10. doi: 10.1007/s11803-017-0364-2
    Xing H J,Li X J,Li H J,Liu A W. 2021a. Spectral-element formulation of multi-transmitting formula and its accuracy and stability in 1D and 2D seismic wave modeling[J]. Soil Dyn Earthq Eng,140:106218. doi: 10.1016/j.soildyn.2020.106218
    Xing H J,Li X J,Li H J,Xie Z N,Chen S L,Zhou Z H. 2021b. The theory and new unified formulas of displacement-type local absorbing boundary conditions[J]. Bull Seismol Soc Am,111(2):801–824. doi: 10.1785/0120200155
    Zeng C,Xia J H,Miller R D,Tsoflias G P. 2011. Application of the multiaxial perfectly matched layer (M-PML) to near-surface seismic modeling with Rayleigh waves[J]. Geophysics,76(3):T43–T52. doi: 10.1190/1.3560019
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