Abstract：The paper first discussed the conception of stationary random medium model and pointed out that the stationary random medium model consists of non-homogeneous parts of large and small scale.Large-scaled non-homogeneous part describes the average nature of medium,i.e.geological model in traditional meaning j small-scaled non-homogeneous medium means the random disturbance added to geologic model that usually presented the non-homogeneity of medium in a small scale by a spatial random process that mean is equal to zero (description by a spatially correlated function),therefore,only using a small amount of statistics (spatially self-correlated function,correlation length,mean and standard deviation etc.) can describe the disturbance of elastic parameters of medium in small-scaled space but can’t flexibly describe real media characterized by non-stationary change.The paper presented the conception of non-stationary random medium model and considered statistic eigenvalues of medium disturbance (such as autocorrelation function,mean and standard deviation etc.) slowly change with spatial coordinate in large scale,which is essential different from the disturbance of medium in stationary random medium model.According to the theory of spectrum dissolution of random process,the paper put forward the conception of local autocorrelation function and showed the random disturbance of medium by a spatial random process that the mean is zero,autocorrelation function and standard deviation slowly changes with spatial coordinate in large scale and the constructing method of stationary random medium model is generalized to construct non-stationary random medium model as well as the algorithm of constructing non-stationary random medium model is gained.The modeling results showed that the nori-stationary random medium model presented by the paper can more flexibly and accurately describe all kinds of complex and non-homogeneous medium models,so it has stronger adaptability.
