Abstract
Wave propagation in a heterogeneous medium, characterized by a distribution of local elastic moduli, is studied. Both acoustic and elastic waves are considered, as are spatially random and power-law correlated distributions of the elastic moduli with nondecaying correlations. Three models—a continuum scalar model, and two discrete models—are utilized. Numerical simulations indicate the existence, at all times, of the relation, , where is the roughness exponent of the wave front in the medium, and is the Hurst exponent that characterizes the spatial correlations in the distribution of the local elastic moduli. Hence, a direct relation between the static morphology of an inhomogeneous correlated medium and its dynamical properties is established. In contrast, for a wave front in random media, (logarithmic growth) at short times, followed by a crossover to the classical value, , at long times.
- Received 24 July 2005
DOI:https://doi.org/10.1103/PhysRevLett.96.075507
©2006 American Physical Society