Propagation of acoustic waves as a probe for distinguishing heterogeneous media with short-range and long-range correlations

The propagation of acoustic waves in strongly heterogeneous media is studied using direct numerical simulations. Two types of heterogeneous media are considered. In one type, the spatial distribution of the local elastic constants contain long-range correlations with a power law, nondecaying correlation function. The correlation length is, therefore, as large as the linear size of the system. In the second type of heterogeneous media the correlation length is decreased, up to the linear size of the blocks in the computational grid and, therefore, the distribution of the elastic constants is uncorrelated or white noise, but with the same mean and variance as that of the correlated media. We find that there are fundamental differences between wave propagation in the two types of heterogeneous media. In particular, the evolution of four distinct characteristics of the waves, namely, the amplitude of the coherent wavefront (CWF), its width, the spectral densities and the scalogram (wavelet transformation of the waves' amplitudes at different scales and times), and the dispersion relations are completely different for uncorrelated and correlated media. Such differences point to wave propagation experiments that can detect important characteristics of the heterogeneities that a medium may contain, and help distinguish correlated disordered media from uncorrelated ones