Characterization of underwater acoustic fluctuations through the Hurst exponent: concept and application to experimental data

Overview & Synopsis

Underwater acoustic propagation in highly dynamic oceanic environments induces complex signal fluctuations. Analysis of continuous-wave transmissions (2.5 kHz) recorded during the NARVAL21 campaign across the Iceland-Faroe Front showed that classical statistical diagnos- tics (e.g., the Λ−Φ diagram and complex-plane representations) fail to fully capture the temporal organization of the signals, leading to difficulties to quantify and separate the stochastic infor- mation contained in multipath propagation. To overcome this limitation, this study introduces the Hurst exponent (H) as a compact descriptor of the scaling behavior and temporal memory of acoustic phase fluctuations. Using a multi-estimator approach (structure-function methods, detrended fluctuation analysis, and its variants) across four distinct source-receiver configura- tions, this study demonstrates that H successfully reveals distinct scaling regimes that standard metrics miss. While three configurations exhibit persistent dynamics (H > 0.5), the cross-front propagation at 100 m depth systematically transitions to an anti-persistent regime (H < 0.5), directly reflecting stronger local environmental variability. Furthermore, observed slope breaks before saturation indicate multi-scale behavior. These findings establish Hurst-based analysis as a powerful tool for discriminating propagation conditions, opening perspectives for environmen- tal monitoring and multifractal inverse problems.