Modeling of multi-scale media in discrete form

Small-scale heterogeneity, which cannot be resolved deterministically, has significant effects on wave propagation. In random media concepts, small-scale spatial fluctuations of the velocity are described by only a few statistical measures, e.g. mean value, spatial correlation function and correlation length. Although the statistical derivation is developed for the continuous case, all computations should be performed in the discrete medium because observational data are discrete and band-limited. This constraint results in inaccurate results in modeling and estimation. In addition, the interaction between the methods of the modeling and the medium properties gives another constraint. In this paper, a discrete random medium, approximated to multi-scale behavior, is modeled. The method is based on the superposition of a Gaussian medium with different scale of heterogeneity and derives a discrete multi-scale random medium which shows band-limited characteristics between the period of the model and the Nyquist period determined by the sampling interval.