Arbitrarily wide-angle wave equations for complex media

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.