弹性波模拟中局部透射边界的反射特征及参数优化  

Reflection characteristics and parameter optimization of a local transmitting boundary for the modeling of elastic waves

作　　者：邢浩洁 李小军[2] 刘爱文[1] 李鸿晶[3] 周正华 陈苏[1] XING Haojie;LI Xiaojun;LIU Aiwen;LI Hongjing;ZHOU Zhenghua;CHEN Su(Institute of Geophysics,China Earthquake Administration,Beijing 100081,China;College of Architecture and Civil Engineering,Beijing University of Technology,Beijing 100124,China;College of Civil Engineering,Nanjing Tech University,Nanjing 211816,China;School of Transportation Engineering,Nanjing Tech University,Nanjing 211816,China)

机构地区：[1]中国地震局地球物理研究所,北京100081 [2]北京工业大学建筑工程学院,北京100124 [3]南京工业大学土木工程学院,南京211816 [4]南京工业大学交通运输工程学院,南京211816

出　　处：《振动与冲击》2022年第12期301-312,共12页Journal of Vibration and Shock

基　　金：国家自然科学基金(U1839202,U2039208,51778588)。

摘　　要：研究一种新型局部透射边界对弹性波的反射特征,以提高模拟复杂波动问题时的边界精度。此时存在P-P、P-S和S-P、S-S两组(4种)反射,反射系数基于P波和S波势函数定义。将势函数表示的波场转化为u和w分量形式,再代入边界公式,推导出反射系数R_(pp),R_(ps),R_(sp),R_(ss)的表达式。理论分析与数值试验相结合,得出如下研究结果:新型边界的多种计算波速配置能够很好地实现对P,S两种物理波速波动能量的同步吸收;弹性介质自身特性给反射系数带来了附加零反射角度,这对边界精度有利;S-P反射有时会出现异常大值,这会严重破坏边界精度,不过,当大部分(如1/1,2/2,2/3,3/4,3/5,…)人工波速参数被严格设定为S波波速时就不会出现这个问题。In order to improve the boundary accuracy in the simulation of complex wave problems,the reflection characteristics of a new local transmitting boundary on elastic waves were thoroughly studied.In this case there are two groups(or 4 kinds)of reflection modes namely P-P,P-S,S-P,and S-S,respectively.Reflection coefficients are defined on the basis of the potential functions of P and S waves.After transforming the wave field expressions of potential functions into that of u and w components and substituting the results into the boundary formulas,the expressions of reflection coefficients R_(pp),R_(ps),R_(sp),and R_(ss) were derived.Combining theoretical analyses with numerical experiments,the following results were obtained:benefitted from the multiple computational wave velocities contained in the new boundary,a good simultaneous absorption of P and S waves with quite different velocities can be achieved.The property of elastic medium itself generates additional zero-reflection angles in reflection coefficients,which is advantageous to the boundary accuracy.Sometimes the S-P reflection may suffer from abnormal large amplitude,which is unacceptable in practical simulations.Fortunately,this can be avoided when most of(means 1/1,2/2,2/3,3/4,3/5,…)the artificial wave velocities are strictly set to be the S-wave velocity.

关 键 词：弹性波模拟 局部透射边界 反射系数 P波和S波的同步吸收 附加零反射角度 S-P大反射 

分 类 号：P315[天文地球—地震学] P631[天文地球—固体地球物理学]