A Nonstationary Random Medium Modeling Method Based on FFT Moving Average and U-Net

Numerical simulation and analysis are effective means to explore the basic laws of the world, in which a synthetic model provides a model basis for research. A random medium model can effectively characterize the small-scale heterogeneity in artificial or natural complex media and has been widely used in reservoir, deposit, material, engineering, and other fields. Many efficient and accurate modeling methods have been proposed for stationary random medium models. However, the modeling efficiency of a random medium with nonstationary statistical characteristics is very low. In this paper, an efficient nonstationary random medium modeling method based on Fast Fourier transform moving average (FFT-MA) method and convolutional neural network is proposed. FFT-MA is used to quickly simulate a low-resolution random medium model, which satisfies the change of large-scale statistical characteristics. Then we transform the low-resolution model into a high-resolution model by a convolutional neural network. The convolutional neural network is trained using a set of stationary random medium models. The modeling experiments show that this method can accurately construct a nonstationary random medium model meeting the nonstationary statistical characteristics and improves the modeling efficiency.