2017/05/31 by Maria Grazia Izzo, Giancarlo Ruocco, Stefano Cazzato
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Acoustic Wave Phenomena Research #Condensed matter physics #Isotropy #Materials science #Mixing (physics) #Optics #Physics #Quantum mechanics #Seismic Imaging and Inversion Techniques #Seismic Waves and Analysis #cond-mat.dis-nn
paper · pdf · doi:10.3389/fphy.2018.00108
18 pages, 8 figures, 4 supplementary notes. Revisited version for Frontiers in Physics
openalex publication_date 2018/10/09 · arxiv created 2018/10/21 · arxiv updated 2018/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
An approximate solution of the Dyson equation related to a stochastic Helmholtz equation, which describes the acoustic dynamics of a three-dimensional isotropic random medium with elastic tensor fluctuating in space, is obtained in the framework of the Random Media Theory. The wavevector-dependence of the self-energy is preserved, thus allowing a description of the acoustic dynamics at wavelengths comparable with the size of heterogeneity domains. This in turn permits to quantitatively describe the mixing of longitudinal and transverse dynamics induced by the medium's elastic heterogeneity and occurring at such wavelengths. A functional analysis aimed to attest the mathematical coherence and to define the region of validity in the frequency-wavector plane of the proposed approximate solution is presented, with particular emphasis dedicated to the case of disorder characterized by an exponential decay of the covariance function.