中文摘要：

刘晶波和王艳提出了一种弹性水平成层半空间中平面P-SV波斜入射时平面内自由波场时域计算的一维化有限元方法,该方法采用黏性人工边界条件近似地模拟下部基岩半空间的辐射阻尼,可导致平面P-SV波以大角度入射时自由场计算精度降低。本文提出一种精确模拟基岩半空间辐射阻尼的人工边界条件。由于基岩半空间中外行波是传播方向已知的平面P波和SV波,利用弹性介质的应力—位移本构关系建立了人工边界处应力与速度的阻抗边界条件;采用该人工边界条件替代黏性边界条件,改进了P-SV波斜入射时成层半空间自由场的时域算法。数值试验表明,与采用黏性边界条件的自由场算法相比,改进方法具有更高的计算精度,其计算结果与理论解吻合更好。

英文摘要：

A 1D finite element method in time domain has been proposed by Liu and Wang for calculating the in-plane free wave field in elastic layered half space under the plane P and SV waves of oblique incidence（Engineering Mechanics,2007,24（7）： 16-22（in Chinese） and Acta Mechanica Sinica,2007,23： 673-680）.The viscous artificial boundary condition is used in this method to approximately model the radiation damping of underlying bedrock half space.This leads to the 1D finite element method with low accuracy.An artificial boundary condition is proposed in this paper,which can exactly model the radiation damping of bedrock half space.Due to that the outgoing waves in bedrock are the plane P and SV waves with known propagation directions,using the constitutive relation between stress and displacement in elastic media,the impedance boundary condition between stress and velocity on artificial boundary is developed.The 1D finite element method is further improved by using the new artificial boundary condition to replace the viscous boundary condition.Numerical examples indicate that the improved 1D finite element method has the higher accuracy than the original method,and the solution using the improved method is identical very well with the theoretical solution.