Source depth estimation based on higher-order pressure vectors of sound field by deep learning

This paper presents a deep learning approach for estimating narrow-band source depth in the deep ocean using higher-order pressure vectors of the sound field. The method employs a ResNet-18 neural network to learn the nonlinear correlation between the first- and second-order pressure vectors and the source depth. Compared to traditional methods that estimate source depth based on the incident angle spatial variation trajectory, this approach does not require long-duration monitoring and provides more accurate depth estimations. First, the feasibility of using higher-order pressure vectors for source depth estimation is demonstrated through the Matched Field Processing (MFP) method. A ResNet-18 neural network is then trained using higher-order pressure vector replicas generated by the BELLHOP model, establishing a mapping between sound pressure vector features and source depth. Simulations indicate that pressure vectors in the depth z-direction contribute more significantly to depth estimation. The approach also considers the impact of variations in source depths, source frequencies, receiver depths, and sound velocity profiles. In most scenarios, the Root Mean Square Error (RMSE) for source depth estimation remained below 20 m, demonstrating stable and reliable performance. Finally, experimental data from the South China Sea, utilizing first-order pressure vectors in the depth z-direction, further validated the feasibility and effectiveness of this deep learning approach for source depth estimation.