弹性波混合差分解法的透射边界条件

TRANSMISSION BOUNDARY CONDITION FOR MIXED VARIABLE FINITEDIFFERENCE METHOD

文中将基于离散应力、速度混合变量弹性波方程的各种数值解法统称为混合差分法，该文研究这类解法中人工边界的透射边界条件．基于波动沿边界法向传播的特征量分析，给出了横观各向同性介质中复杂形状边界的透射条件．该文是一种局部透射条件，所需计算量极小．文中将此方法与交错网格差分解法结合并应用于横观各向同性介质弹性波计算．数值算例及反射系数分析表明，该方法很好地消除了人工边界对来波的反射．

All kinds of numerical methods based on discretization of firstorder velocitystress hyperbolic system of elastic wave equations are named as mixed variable finitedifference methods in this paper, and the transmission boundary condition of artifical boundaries for the mixed variable finitedifference methods is studied here. The transmission condition of complex geometrical boundaries in transversely isotropic media is presented based on characteristic variables of wavefields propagating in the normal direction of the boundary. The boundary condition proposed in this paper is a local artificial boundary condition, with which the computation cost is very low. Elastic wave propagations in transversely isotropic media are modelled by staggered grid finitedifference method incorporated with the boundary conditin presented. Numerical results and analysis of reflection coefficients show that the reflections of incoming waves by artificial boundaries are efficiently reduced.