  Classical acoustic wave-field representations consist of volume and boundary
integrals, of which the integrands contain specific combinations of Green's
functions, source distributions and wave fields. Using a unified matrix-vector
wave equation for different wave phenomena, these representations can be
reformulated in terms of Green's matrices, source vectors and wave-field
vectors. The matrix-vector formalism also allows the formulation of
representations in which propagator matrices replace the Green's matrices.
These propagator matrices, in turn, can be expressed in terms of Marchenko-type
focusing functions. An advantage of the representations with propagator
matrices and focusing functions is that the boundary integrals in these
representations are limited to a single open boundary. This makes these
representations a suitable basis for developing advanced inverse scattering,
imaging and monitoring methods for wave fields acquired on a single boundary.
