Study on spatially varying convolution modeling based on anisotropic covariance functions

Abstract Nonstationary random-media modeling is a key technique for characterizing complex subsurface heterogeneity; however, in practical applications, it is often necessary to balance geological realism and computational efficiency. Based on spatial-domain process convolution theory, this study establishes a parameterized control framework for spatially varying convolution kernels and systematically analyzes, through sensitivity experiments, the regulatory mechanisms of parameters such as the anisotropy ratio, correlation angle, kernel-size scaling factor, and kernel type on the macroscopic structures and microscopic textures of random fields. On this basis, this study focuses on comparing two convolution-kernel construction strategies: the approximate convolution-kernel method and the anisotropic covariance convolution-kernel method. The approximate convolution-kernel method rapidly constructs spatially varying convolution kernels through geometric rotation and scale stretching, offering advantages such as computational simplicity, good model continuity, and strong stability, and is suitable for modeling scenarios with relatively gentle geological structures and weak textural variations. In contrast, the anisotropic covariance convolution-kernel method is based on an elliptic anisotropic spatial correlation structure, calculates the equivalent correlation length in different directions point by point, and further constructs the covariance convolution kernel, thereby enabling a more accurate description of complex geological textures and spatial statistical characteristics. Comparative studies using the Marmousi model and field seismic data show that the approximate convolution-kernel method can generate continuous and stable random-media models, whereas the anisotropic covariance convolution-kernel method exhibits stronger capability in characterizing spatial structures under geologically fractured and texturally complex conditions, and its generated results are more consistent with the spatial variation patterns of real data. This study deepens the understanding of the intrinsic mechanism of the spatially varying convolution method and provides a reliable theoretical basis and technical support for high-fidelity random-media modeling in complex nonstationary geological environments.