Wavelet-Based Local Modulation and Non-Stationary Scaling Analysis of Multifractal Fields

Numerous natural and experimental systems, from turbulent flows and fracture surfaces to biological textures, exhibit multifractal structures with scale-dependent irregularities and long-range correlations. Standard multifractal models, assuming globally uniform scaling, fail to capture their spatially varying and non-stationary behavior. We propose a wavelet-based local multifractal framework to resolve these limitations by quantifying spatial variations in roughness and intermittency. The method employs undecimated discrete wavelet transforms (UDWT/SWT) with Daubechies db4–db8 wavelets to estimate local Hurst exponents H(r) and intermittency coefficients λ(r) within adaptive or sliding windows. Wavelet coefficients and scale-dependent regressions are used to robustly extract local scaling laws while mitigating boundary and noise effects. Validation will use synthetic multifractal fields to assess accuracy, robustness, and wavelet selection. Application to fracture-surface datasets will reveal spatial maps of H(r) and λ(r), linking heterogeneity in surface roughness and intermittency to fracture dynamics and material microstructure.