Anisotropic Fractional Brownian Field Synthesis via Curvelet Transform

Abstract

The proposed model employs curvelet-based techniques to generate anisotropic Fractional Brownian Fields, simulating systems with orientation-dependent self-similar properties. Curvelets are a mathematical tool that allows for an efficient representation of data with edges and other anisotropic singularities, being essential for capturing the directional complexity in the self-similar properties of the modeled systems. The synthesis procedure involves generating coefficients in curvelet space with a zero-mean Gaussian distribution. This approach is tailored to depict the stochastic behavior of natural systems, particularly in scenarios where angular distributions of correlations are critical. The main contribution of this paper is presenting a novel method for generating 2-D anisotropic Fractional Brownian Fields (AFBFs) using the Curvelet Transform, demonstrating the Curvelet Transform’s efficiency in modeling anisotropic properties. Potential applications include modeling heterogeneous geological structures, anisotropic materials, and complex disordered media.