This paper constructed random media models using the Von Karman type autocorrelation function, discussed the model

characteristics by two model parameters of autocorrelation length and spectrum exponent and analyzed the distribution and

variation of velocities in the models under the conditions of different variances. The results show that the variations of random

media models of heterogeneity scales in lateral and longitudinal directions are all produced by changing autocorrelation length

and lateral and longitudinal spectrum exponent. The disturbance range of the random perturbation is different if the disturbance

variance is different, and such a difference results in fluctuation of velocities in models around the background velocity. The

modeling figures demonstrate that random medium models can vividly describe real media.