For elastic wave scattering problems in unbounded anisotropic media, the existence of backward waves makes classic truncation techniques fail completely. This paper is concerned with an exact truncation technique for terminating backward elastic waves. We derive a closed form of elastrodynamic Green's tensor based on the method of Fourier transform and design two fundamental principles to ensure its physical correctness. We present a rigorous theory to completely classify the propagation behavior of Green's tensor, thus proving a conjecture posed by B\'ecache, Fauqueux and Joly (J. Comp. Phys., 188, 2003) regarding a necessary and suffcient condition of the non-existence of backward waves. Using Green's tensor, we propose a new radiation condition to characterize anistropic scattered waves at infinity. This leads to an exact transparent boundary condition (TBC) to truncate the unbounded domain, regardless the existence of backward waves or not. We develop a fast algorithm to evaluate Green's tensor and a high-accuracy scheme to discretize the TBC. A number of experiments are carried out to validate the correctness and efficiency of the new TBC.

翻译：针对无界各向异性介质中的弹性波散射问题，后向波的存在导致经典截断技术完全失效。本文研究一种用于终止后向弹性波的精确截断技术。我们基于傅里叶变换方法推导了弹性动力学格林张量的闭合形式，并设计了两个基本原理确保其物理正确性。我们提出了一个严格理论来完整分类格林张量的传播行为，从而证明了Bécache、Fauqueux和Joly（J. Comp. Phys., 188, 2003）提出的关于后向波不存在充要条件的猜想。利用格林张量，我们提出一种新的辐射条件来刻画各向异性散射波在无穷远处的特性。由此导出一种精确透明边界条件（TBC），无论是否存在后向波均可截断无界区域。我们开发了快速算法计算格林张量以及高精度格式离散TBC。通过大量实验验证了新TBC的正确性与有效性。