Statistical Responses of Different Multifractal Estimators and Their Physical Interpretation in Solar Wind Turbulence

Abstract

Solar-wind turbulence often exhibits multifractal behavior, but the statistical sensitivities and physical interpretations of different multifractal estimators remain insufficiently understood. Using Parker Solar Probe magnetic-field observations together with shuffle and random-phase (RP) surrogate tests, we systematically compare multifractal estimators based on structure functions (SF), partition functions (PF), and multifractal detrended fluctuation analysis (MF-DFA). The surrogate analysis reveals that the three estimators respond differently to long-range correlations and non-Gaussian statistics, and the PF results are further compared with a local energy transfer (LET) proxy. SF multifractality is strongly suppressed after RP (0.057 → 0.006), indicating dominant sensitivity to scale-dependent heavy-tailed increment statistics. In contrast, the strong reduction of PF multifractality after shuffle processing (0.527 → 0.235) indicates primary sensitivity to correlation-induced heterogeneity. MF-DFA multifractality decreases progressively from the original data to RP and to shuffle surrogate (0.313 → 0.186 → 0.140), reflecting mixed sensitivity to both effects. PF also correlates with the LET variance (r = 0.454), especially after RP (r = 0.552), suggesting that the correlation-related multifractal component is linked to the inhomogeneity of turbulent energy transfer. These results demonstrate that different multifractal estimators respond to different statistical manifestations of turbulent fluctuations and therefore emphasize different physical aspects. The proposed framework helps distinguish increment intermittency from correlation-induced heterogeneity and clarifies the physical interpretation of multifractal measurements in solar wind turbulence.