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An approximate solution of the Dyson equation related to a stochasticHelmholtz equation, which describes the acoustic dynamics of athree-dimensional isotropic random medium with elastic tensor fluctuating inspace, is obtained in the framework of the Random Media Theory. Thewavevector-dependence of the self-energy is preserved, thus allowing adescription of the acoustic dynamics at wavelengths comparable with the size ofheterogeneity domains. This in turn permits to quantitatively describe themixing of longitudinal and transverse dynamics induced by the medium's elasticheterogeneity and occurring at such wavelengths. A functional analysis aimed toattest the mathematical coherence and to define the region of validity in thefrequency-wavevector plane of the proposed approximate solution is presented,with particular emphasis dedicated to the case of disorder characterized by anexponential decay of the covariance function.

The mixing of polarizations in the acoustic excitations of disordered media with local isotropy