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Using the Martin-Siggia-Rose method, we study propagation of acoustic wavesin strongly heterogeneous media which are characterized by a broad distributionof the elastic constants. Gaussian-white distributed elastic constants, as wellas those with long-range correlations with non-decaying power-law correlationfunctions, are considered. The study is motivated in part by a recent discoverythat the elastic moduli of rock at large length scales may be characterized bylong-range power-law correlation functions. Depending on the disorder, therenormalization group (RG) flows exhibit a transition to localized regime in{\it any} dimension. We have numerically checked the RG results using thetransfer-matrix method and direct numerical simulations for one- andtwo-dimensional systems, respectively.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Let

Localization of Elastic Waves in Heterogeneous Media with Off-Diagonal Disorder and Long-Range Correlations