The source-box wave propagation hybrid methods: general formulation and implementation

Originated by Alterman and Karal (AK) in 1968 as a domain-coupling technical algorithm, the generalized hybrid approach of wave injection is described by binding two subvolumes treated per partes by arbitrary wave-propagation methods. The generalized AK two-step procedure combines the source and path effects computed by one arbitrary method and local site effects computed by another (arbitrary) method using the first method's wavefield as input. The advantage of the approach arises from the fact that the connection between the methods keeps the formal wave-injection boundary perfectly permeable for the wavefield scattered by local structure and can be applied to a variety of hybrid formulations. This hybrid approach leads to more effective modelling of combined source, path and site effects (e.g. by multiple second-step computations with varying structure, using single first step input), thereby reducing computer memory and time requirements. The main innovation of the paper is the generalization of the boundary condition acting between two complementary subvolumes of AK hybrid wavepropagation methods.