  Marchenko methods are based on integral representations which express Green's
functions for virtual sources and/or receivers in the subsurface in terms of
the reflection response at the surface. An underlying assumption is that inside
the medium the wave field can be decomposed into downgoing and upgoing waves
and that evanescent waves can be neglected. We present a new derivation of
Green's function representations which circumvents these assumptions, both for
the acoustic and the elastodynamic situation. These representations form the
basis for research into new Marchenko methods which have the potential to
handle refracted and evanescent waves and to more accurately image steeply
dipping reflectors.
