MODELING OF MULTISCALE 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 on ly a few statistical measures, e.g. mean value, spatial correlation fu nction and correlation length. Although the statistical derivation is developed for the continuous case, all computations should be performe d in the discrete medium because observational data are discrete and b and-limited. This constraint results in inaccurate results in modeling and estimation. In addition, the interaction between the methods of t he modeling and the medium properties gives another constraint. In thi s paper, a discrete random medium, approximated to multi-scale behavio r, is modeled. The method is based on the superposition of a Gaussian medium with different scale of heterogeneity and derives a discrete mu lti-scale random medium which shows band-limited characteristics betwe en the period of the model and the Nyquist period determined by the sa mpling interval.