Long-range correlations in sound and silence dynamics across soundscapes

Recent studies employing statistical analyses of acoustic landscapes have revealed two universal patterns: the duration of quiet intervals follows a power-law distribution, whereas the duration of sound intervals exhibits a log-normal distribution. Building upon this framework, we investigate the temporal correlations between sound and silence events across three distinct environments: savanna, dry forest, and urban soundscapes. To characterize these correlations, we apply two complementary analytical methods: spectral (Fourier) analysis and Detrended Fluctuation Analysis (DFA). Our results show that the mean DFA exponents for the savanna, dry forest, and urban environments are approximately 0.92, 0.95, and 0.93, respectively, while spectral analysis reveals a consistent power-law behavior with average slopes of 0.85, 1.05, and 0.95. By comparing the DFA exponent α and the Fourier power spectrum slope β through the theoretical relation β=2α−1, we confirm the mutual consistency of the methods and the presence of a characteristic 1/f scaling behavior. Although the studied phenomenon presents an overall 1/f behavior, some deviation are observed, specially for the Urban soundscape. In this case, a crossover phenomenon is observed, with intermediate scales (0.8 s – 20 s) exhibiting a larger DFA exponent compared to the smaller and larger scales, which display weaker correlations. We hypothesize that this scale more clearly captures correlation effects in the soundscape, potentially linked to communication and human activities marked by high levels of order and coordination. These findings suggest that the temporal organization of acoustic landscapes is governed by long-range memory processes, where silences and sounds are sequentially correlated over multiple time scales.