Abstract
Waves from a point source in a homogeneous medium will propagate spherically. This can be described by the Sommerfeld radiation condition. However, it is hard to use simple formula to describe radiation condition for wave propagation in a stratified medium. A generalized Sommerfeld radiation was proposed by Xu in 1990, applying contour integral and asymptotic approximation. The study in this area becomes more active recently. Papers in 2008 and 2009 from different aspects presented rigorous analysis for results similar to Xu's condition. On the other hand, Chandler-Wolde, Bo Zhang and their coworkers introduced the upward propagating radiation condition.In this paper we introduce an upward propagating radiation condition for waves in essentially stratified medium with unbounded inhomogeneity or unbounded rough boundary.The upward propagating radiation conditions can be used to formulate direct and inverse scattering problems in nonlocal perturbed medium.
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