Wavefront propagation in discrete random media via stochastic huygens' minor principle

A stochastic theory is presented for the propagation of wavefronts in spatially random media. The study is limited to a class of media that may be modeled, in a two-dimensional setting, as ensembles of convex polygons (grains) of random physical and geometrical properties. The wavefront is considered to be a pulse spread over a domain of finite thickness. Special attention is given to modelling any point of this pulse, called disturbance. The dynamics of the disturbance is governed by two processes-ray kinematics and amplitude modulation-both of which are Markov; their semi-group property represents the stochastic Huygens' minor principle. This approach permits the inclusion of microscale deterministic and random phenomena in an analysis of wavefront behavior, e.g. wavefront decay, broadening, random arrival times, in heterogeneous media.