heterogeneous acoustic media from uncorrelated waves

The Green’s function of acoustic or elastic wave propagation can, for loss-less
media, be retrieved by correlating the wave field that is excited by random
sources and is recorded at two locations. Here the generalization of this idea
to attenuating acoustic waves in an inhomogeneous medium is addressed, and
it is shown that the Green’s function can be retrieved from waves that are
excited throughout the volume by spatially uncorrelated injection sources with
a power spectrum that is proportional to the local dissipation rate. For a finite
volume, one needs both volume sources and sources at the bounding surface for
the extraction of the Green’s functions. For the special case of a homogeneous
attenuating medium defined over a finite volume, the phase and geometrical
spreading of the Green’s function is correctly retrieved when the volume sources
are ignored, but the attenuation is not.