"The source problem" - Transient waves propagating from internal sources in non-stationary media

Direct scattering of propagating transient waves originating from internal sources in non-stationary, inhomogeneous, dispersive, stratified media, is investigated. The starting point is a general, inhomogeneous, linear, first order, 2 × 2 system of equations. Particular solutions are obtained, as integrals of fundamental waves from point sources distributed throughout the medium. First, resolvent kernels are used to construct time dependent fundamental wave functions at the location of the point source. Wave propagators, closely related to the Green functions, at all times advance these time dependent waves into the surrounding medium. The propagator equations and the propagation of propagator kernel discontinuities along the characteristics of these equations are essential in the distributional proof, which is outlined. As an illustration, three special problems are studied; the inhomogeneous, second order wave equation, and source problems in homogeneous and time invariant media