Nonstationary Random Media Modeling Based on Statistical Characteristic Parameters

Summary Subsurface reservoirs generally exhibit pronounced nonstationarity and multiscale heterogeneity, and accurate construction of nonstationary random media models is fundamental for reservoir characterization and fracture prediction. In this study, a nonstationary random media modeling method based on spatially varying convolution (SVC) is proposed, in which locally adaptive structures are represented through convolution kernels that vary spatially according to statistical parameters. The proposed method is compared with the spectral decomposition method and the fast Fourier transform-moving average (FFT-MA) method and is validated using synthetic models, local update experiments, and real seismic data. Quantitative evaluation is conducted using metrics including root mean square error (RMSE), mean absolute error (MAE), structural similarity index (SSIM), and variogram-based L2 distance. The results show that the SVC method achieves the best structural similarity (SSIM = 0.7836) and exhibits clear advantages in matching variograms along the principal direction. In local update experiments, although all three methods successfully achieve localized updates, the proposed method demonstrates superior performance in terms of directional error and boundary transition. In addition, the method shows favorable computational efficiency under the current implementation. Compared with covariance-based and stochastic partial differential equation (SPDE)-based nonstationary models, the proposed method places greater emphasis on local structural representation and practical applicability. Overall, it provides an efficient and flexible solution for modeling complex heterogeneous reservoirs.