CAJ | 학술논문

无限域中的波动方程数值模拟往往需要稳定有效的吸收边界来消除人为边界截断所引起的虚假反射.本文首先写出了全匹配层(PML)内SH波的波动方程推导结果,并给出了方程的Crank-Nicolson计算格式与其中窄间导数2阶,6阶,10阶精度的有限差分算法以及伪谱法算法.然后设计了均匀各向同性介质模型和分层溶洞模型并引入图像处理中的信噪比(SNR)概念来定量研究边界吸收效果同PML宽度、不同精度算法的关系.数值结果表明当匹配层宽度比较薄时可以用低精度的有限差格式来获得比较好的吸收效果,当匹配层比较宽时,采用高精度的算法可以获得很好的吸收效果.最后对"反射系数"进行了讨论,指出"反射系数"的不足和文中用SNR来定量衡量吸收边界
무한역중적파동방정수치모의왕왕수요은정유효적흡수변계래소제인위변계절단소인기적허가반사.본문수선사출료전필배층(PML)내SH파적파동방정추도결과,병급출료방정적Crank-Nicolson계산격식여기중착간도수2계,6계,10계정도적유한차분산법이급위보법산법.연후설계료균균각향동성개질모형화분층용동모형병인입도상처리중적신조비(SNR)개념래정량연구변계흡수효과동PML관도、불동정도산법적관계.수치결과표명당필배층관도비교박시가이용저정도적유한차격식래획득비교호적흡수효과,당필배층비교관시,채용고정도적산법가이획득흔호적흡수효과.최후대"반사계수"진행료토론,지출"반사계수"적불족화문중용SNR래정량형량흡수변계
When modeling wave propagation in infinite space,it is necessary to have stable absorbing boundaries to effectively eliminate spurious reflections from the truncation boundaries.The SH wave equations for Perfectly Matched Layers (PML) are deduced and their Crank-Nicolson scheme are presented in this paper.We use the second-,sixth-,and tenth-order finite difference and pseudo-spectral algorithms to compute the spatial derivatives.Two numerical models,a homogeneous isotropic medium and a multi-layer model with a cave,are designed to investigate how the absorbing boundary width and the algorithms determine PML effects.Numerical results show that,for PML,the Iow-order finite difference algorithms have fairly good absorbing effects when the absorbing boundary is thin,whereas,high-order algorithms always have good absorption when the boundary is thick.Finally,we discuss the reflection coefficient and point out its shortcomings,which is why we use the SNR to quantitatively scale the PML effects.