  Using the Martin-Siggia-Rose method, we study propagation of acoustic waves
in strongly heterogeneous media which are characterized by a broad distribution
of the elastic constants. Gaussian-white distributed elastic constants, as well
as those with long-range correlations with non-decaying power-law correlation
functions, are considered. The study is motivated in part by a recent discovery
that the elastic moduli of rock at large length scales may be characterized by
long-range power-law correlation functions. Depending on the disorder, the
renormalization group (RG) flows exhibit a transition to localized regime in
{\it any} dimension. We have numerically checked the RG results using the
transfer-matrix method and direct numerical simulations for one- and
two-dimensional systems, respectively.
