title: Shape of a wave front in a heterogenous medium.
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, alpha = H, where alpha is the roughness exponent of the wave front in the medium, and H 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, alpha = 0 (logarithmic growth) at short times, followed by a crossover to the classical value, alpha = 1/2, at long times.
authors.affiliation: Institute for Advanced Studies in Basic Sciences, Gava Zang, Zanjan 45195-1159, Iran.
authors.forename: S Mehdi Vaez
authors.initials: SM
authors.lastname: Allaei
authors.forename: Muhammad
authors.initials: M
authors.lastname: Sahimi