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Arbitrarily wide-angle wave equations for complex media

机译：复杂介质的任意广角波动方程

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摘要

By combining various ideas related to one-way wave equations (OWWEs), half-space stiffness relation, special finite-element discretization, and complex coordinate stretching, a systematic procedure is developed for deriving a series of highly accurate space-domain versions of OWWEs. The resulting procedure is applicable to complex media where the governing equation (full wave equation) is a second order differential system, making the procedure applicable for general heterogeneous, anisotropic, porous, viscoelastic media. Owing to their high accuracy in representing waves propagating in an arbitrarily wide range of angles, the resulting equations are named Arbitrarily Wide-angle Wave Equations (AWWEs). In order to illustrate the proposed procedure, AWWEs are derived for one-way propagation in acoustic as well as elastic media. While acoustic AWWEs can be considered as modified versions of well-known space-domain OWWEs based on rational approximations of the square root operator, the elastic AWWEs are significantly different from the existing elastic OWWEs. Unlike the existing elastic OWWEs, elastic AWWEs are displacement-based and are applicable to general anisotropic media. Furthermore, AWWEs are simple in their form, and appear amenable to easy numerical implementation.
机译：通过结合与单向波动方程（OWWE），半空间刚度关系，特殊的有限元离散化和复杂的坐标拉伸有关的各种思想，开发了一种系统的程序来导出一系列高精度的OWWE空间域版本。所得过程适用于控制方程（全波方程）为二阶微分系统的复杂介质，因此该过程适用于一般的非均质，各向异性，多孔，粘弹性介质。由于其在表示在任意大角度范围内传播的波的准确性很高，因此将得出的方程式称为任意广角波方程（AWWE）。为了说明所提出的程序，导出了AWWE，以便在声学和弹性介质中进行单向传播。虽然基于平方根算子的有理逼近，声学AWWE可以被认为是众所周知的空域OWWE的修改版本，但弹性AWWE与现有的弹性OWWE明显不同。与现有的弹性OWWE不同，弹性AWWE是基于位移的，适用于一般的各向异性介质。此外，AWWE的形式很简单，并且似乎易于数字实现。

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