Parabolic equations (PEs) are useful for modeling sound propagation in a range-dependent environment. However, this approach entails approximating a leading-order cross-derivative term in the PE square-root operators. Deep operator networks (DeepONets) are designed to approximate operators. In this paper, we train DeepONets to take complex sound pressure and speed of sound at any depth location of interest as inputs and approximate the PE square operator in modeling two-dimensional sound propagation. Once trained, a network can predict the far field for a wide variety of environmental conditions, without needing to approximate the operator or calculate the whole mode trajectory and at a lower computational cost. The original DeepONet learns the operator of a single function. By contrast, the modified version presented here learns multiple-input operators with Fourier features. Using computational and theoretical examples, we demonstrate that DeepONet is efficient for learning complex ocean acoustic physics with good accuracy.

A mesoscale eddy is detected and tracked in the western North Pacific region. Within the life cycle of the cyclonic eddies, the intensities of eddies make a difference. Satellite images indicate the oceanic eddy keeps westward-moving until it disappears. Oceanographic and acoustic characteristics of the eddy are studied. The acoustic energy distribution results from the different intensity of both modelled eddy and measured eddy are calculated. With sound propagation through the cyclonic eddy and anticyclonic eddy, the position of convergence zone moves away from and towards the acoustic source compared with the sound propagation through background hydrography. The coupling coefficient of different orders of normal modes changes significantly. The closer to the centre of the eddy, the stronger the coupling coefficient.

Oceanic fronts involved by ocean currents led to strong gradients of temperature, density and salinity, which have significant effects on underwater sound propagation. This paper focuses on the impact of the oceanic front on three-dimensional underwater sound propagation. A joint experiment of ocean acoustic and physical oceanography at the western North Pacific fronts is introduced. The measurement data for sound waves passed through the oceanic front is processed. The results are analysed and compared with the numerical simulation. It was found that transmission loss presented some difference when the source was located in the front centre and sound waves propagated towards water mass on opposite sides of the front centre. And when the sound field is excited by the underwater explosion at a depth of 200 m, the effects of the horizontal refraction cannot be neglected. On the other hand, the transmission loss for sound pressure fell sharply and rose rapidly at the side of cold water masses.

Bayesian methodology is a good way to infer unknown parameters in a marine environment. A passive source location method in a shallow water waveguide with a single sensor based on Bayesian theory is presented in this paper. The input of a Bayesian inversion algorithm is received different normal mode impulse signals, which are separated and extracted with a warping transformation from received broadband impulse signals. The source range, depth, and other seabed parameters were estimated without prior knowledge of the seabed information. Different normal mode impulse acoustic signals travelling at different group speeds arrived at the sensor at different times because of the dispersion characteristics of the shallow water waveguide. The time delay of different modes can be used for the passive source location. However, normal mode group speeds are greatly affected by the environmental parameters. The performance of the passive location becomes negative when parameters mismatch. In this paper, the source location was transformed to the inversion of the source location and environmental parameters, which can be estimated accurately based on the multi-dimensional posterior probability density (PPD). This method is less limited by environmental factors, and the accuracy of inversion results can be analyzed according to the PPD of inversion parameters, which has higher reliability and a wider application scope. The effectiveness and robustness of the algorithm were quantified in terms of the root mean squared error (RMSE) at a variety of signal-to-noise ratios (SNRs) in 50 simulation sets. The RMSE values decreased with the SNR. The validity and accuracy of the method were proved by the results of simulation and experiment data.

The performance of active sonar detection systems is seriously affected by the reverberation at the bottom of the waveguide in shallow water. In order to improve the performance of active sonar detection, it is necessary to understand the horizontal correlation of shallow-water bottom reverberation in active towed-array processing technology. However, the current research on the spatial correlation of reverberation is mainly based on vertical correlation, little work has been done on the horizontal correlation characteristics of long-distance seabed reverberation, and there is no support from sea test data. In this paper, the coupled mode reverberation model is applied to the horizontal correlation, and is studied according to the receiving position, time, and frequency. The simulation results show that, for the long-range bottom reverberation, the lateral correlation is greater than the longitudinal correlation in the horizontal space. By introducing the adiabatic mode solution, the mathematical model of horizontal correlation in the range-dependent waveguide with depth is derived. The numerical results show that the influence of the seabed dip angle on the horizontal correlation should be considered and that the horizontal correlation is affected obviously by the propagation effects of the sloped sea floor. Finally, the experimental data processing and analysis are given and verify the correctness of the algorithm.

In this Letter, a three-dimensional beamforming method is proposed for a miniaturized aperture acoustic vector sensor (AVS) array. This method extracts the multipole modes using the AVS array, and then synthesizes the desired beam pattern according to the relation between multipole modes and spherical harmonics. Compared to the spherical harmonics decomposition of the sound field method, the proposed method achieves comparable array gain with higher white noise gain when the distance of adjacent elements d and the wavelength λ satisfy 0.01≤d/λ≤0.2. Experimental results also demonstrate the effectiveness of the proposed three-dimensional beamforming method at very low frequency.