A fluctuation-based method for tonal source depth discrimination using a vertical line array in shallow ocean

The difference in amplitude fluctuations caused by surface and submerged source depth variations provides a viable mechanism for binary source depth discrimination in shallow ocean. However, its performance is limited due to the fluctuation of modal interference. Different from the amplitude fluctuation difference, the modal scintillation difference has been exploited to avoid the limitation via modal decomposition. Nevertheless, its discrimination performance degrades severely with decreasing vertical line array (VLA) span. To improve the depth discrimination performance, this paper analyzes the physical mechanisms of amplitude fluctuations and exploits the modal orthogonality to enhance the fluctuation difference using a VLA without modal decomposition. Modal orthogonality enables the integration of the signal power across the receiving array to suppress range-dependent interferences while preserving depth-dependent amplitude fluctuations. A normalized amplitude fluctuation index applicable to the VLA is designed to quantify the amplitude fluctuation. Simulation results demonstrate that the distinction between surface and submerged amplitude fluctuation index metrics is robust against the source range. The proposed method outperforms the Modified Modal Scintillation Index method in depth discrimination under limited array span conditions. Experimental data from SWellEx-96 further validate the proposed method's capability to improve discrimination performance.