Detecting acoustic signals in the ocean is crucial for port and coastal security, but existing methods often require informative priors. This paper introduces a new approach that transforms acoustic signal detection into network characterization using a MCN construction method. The method constructs a network representation of the acoustic signal by measuring pairwise correlations at different time scales. It proposes a network spectrum distance method that combines information geometry and graph signal processing theory to characterize these complex networks. By comparing the spectra of two networks, the method quantifies their similarity or dissimilarity, enabling comparisons of multi-scale correlation networks constructed from different time series data and tracking changes in nonlinear dynamics over time. The effectiveness of these methods is substantiated through comprehensive simulations and real-world data collected from the South China Sea. The results illustrate that the proposed approach attains a significant detection probability of over 90% when the signal-to-noise ratio exceeds −18 dB, whereas existing methods require a signal-to-noise ratio of at least −15 dB to achieve a comparable detection probability. This innovative approach holds promising applications in bolstering port security, facilitating coastal operations, and optimizing offshore activities by enabling more efficient detection of weak acoustic signals.

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