Modeling three-dimensional underwater acoustic propagation over multi-layered fluid seabeds using the equivalent source method.

This paper develops an efficient three-dimensional (3D) underwater acoustic propagation model with multi-layered fluid seabeds based on the equivalent source method (ESM). It solves the Helmholtz equation exactly by a superposition of fields generated by equivalent sources. A linear system coupling ESM equations is derived by imposing boundary conditions and solved iteratively using the generalized minimum residual method. Unlike a direct ESM solver, matrix-vector products in each iteration are evaluated by a pre-corrected fast Fourier transformation (PFFT), significantly reducing the numerical cost and enabling efficient solution of 3D large-scale propagation. Moreover, sound speed profiles can be taken into account by dividing the water column into sub-layers, each of which requires an individual PFFT procedure using an FFT subgrid scheme. Simulations of propagation over a Gaussian canyon validate the PFFT-accelerated ESM (PFFT-ESM). The capability of the PFFT-ESM for 3D scattering problems is demonstrated by further presenting the Gaussian canyon simulations with corrugated surface waves.

Modeling propagation in shallow water with the range-dependent sea surfaces and fluid seabeds using the equivalent source method.

This paper describes a shallow water range-dependent propagation model (RPM) based on the equivalent source method (ESM). The proposed model allows both the sea surface and fluid seabed to vary with the propagation range. The proposed equivalent source method-based range-dependent propagation model (ESM-RPM) utilizes three sets of equivalent sources, placed above the sea surface, below the seabed, and above the seabed, which replace the sea surface reflection, seabed reflection, and seabed transmission, respectively. The unknown strengths of the equivalent sources can be determined by solving an inverse problem based on the boundary conditions. The capability of the ESM-RPM for propagation in refractive water is demonstrated by evaluating the Green's function using a modal projection method. Numerical simulations are conducted in iso-velocity and refractive shallow water with an underwater canyon and corrugated surface waves, including two-dimensional (2-D) propagation across the canyon and three-dimensional (3-D) propagation along the canyon. Further simulations demonstrate the 2-D across-canyon and 3-D along-canyon propagations with random rough sea surfaces. The results show that the proposed ESM-RPM provides efficient, benchmark-quality numerical solutions that accurately capture the mode coupling associated with the varying cross section of the waveguide. Thus, the model has great potential to be applied in benchmarking propagation in shallow water with the varying sea surface and seabed.

Three-dimensional sound scattering from transversely symmetric surface waves in deep and shallow water using the equivalent source method.

This paper proposes a propagation model to calculate the three-dimensional (3-D) sound scattering from transversely symmetric sea surface waves in both deep and shallow water using the equivalent source method (ESM). The 3-D sound field is calculated by integrating an assembly of two-dimensional (2-D) transformed fields with different out-of-plane wavenumbers through a cosine transform. Each 2-D solution is calculated using the ESM incorporating a complex image method that can efficiently and accurately solve the 2-D water/seabed Green's function. The oscillatory cosine integral is accurately calculated using a segmented integral scheme requiring relatively few 2-D solutions, which can be further improved through the use of parallel computation. The model is validated by comparison with a 3-D Helmholtz-Kirchhoff method for deep water and a finite element method for a shallow water wedge with both a fluid and an elastic seabed. The model is as accurate as the finite element approach but more numerically efficient, which enables Monte Carlo simulations to be performed for random rough surfaces in order to study the scattering effects at a reasonable computational cost. Also, 3-D pulse propagation in the shallow water wedge is demonstrated to understand the out-of-plane scattering effects further.

Frequency Invariant Beamforming for a Small-Sized Bi-Cone Acoustic Vector-Sensor Array.

In this work, we design a small-sized bi-cone acoustic vector-sensor array (BCAVSA) and propose a frequency invariant beamforming method for the BCAVSA, inspired by the Ormia ochracea's coupling ears and harmonic nesting. First, we design a BCAVSA using several sets of cylindrical acoustic vector-sensor arrays (AVSAs), which are used as a guide to construct the constant beamwidth beamformer. Due to the mechanical coupling system of the Ormia ochracea's two ears, the phase and amplitude differences of acoustic signals at the bilateral tympanal membranes are magnified. To obtain a virtual BCAVSA with larger interelement distances, we then extend the coupling magnified system into the BCAVSA by deriving the expression of the coupling magnified matrix for the BCAVSA and providing the selecting method of coupled parameters for fitting the underwater signal frequency. Finally, the frequency invariant beamforming method is developed to acquire the constant beamwidth pattern in the three-dimensional plane by deriving several sets of the frequency weighted coefficients for the different cylindrical AVSAs. Simulation results show that this method achieves a narrower mainlobe width compared to the original BCAVSA. This method has lower sidelobes and a narrower mainlobe width compared to the coupling magnified bi-cone pressure sensor array.