Journal of Computational Acoustics

Spherical acoustic holography was utilized to reconstruct the interior sound field of an enclosed space with vibrating boundaries using an open spherical microphone array. The interior sound fields of vibrating shells, including a pulsating shell, a $z$-axis oriented oscillating shell, a partially vibrating shell and a point-excited vibrating shell, were reconstructed, and numerical simulations were carried out to examine the impact of reconstruction parameters, the radius of the microphone array, the number of microphones, the distribution of microphones on the array surface, the wave number, the number of basis functions used, and the radius of the reconstruction surface on the accuracy of reconstruction. In order to minimize the error of reconstruction caused by a variety of factors and uncertainties, such as the measurement noise, regularization treatments were introduced into the process of reconstructing, to suppress the divergent trends of the reconstruction error along with the increase of the wave number and the increase of the radius of the reconstruction surface. Results showed that a Tikhonov regularization method with generalized cross validation (GCV) could yield the least error of reconstruction among the investigated regularization methods.

The paper is devoted to modeling of the backscattered field from a spherical target immersed in a homogeneous waveguide covered with ice. A bottom of the waveguide and an ice cover are fluid, attenuating half-spaces. A target is assumed to be acoustically rigid or fluid. In particular, the properties of the ice cover and a scatterer may coincide. The emitted signal is a pulse with a Gaussian envelope. The normal mode evaluation is applied to the scattering coefficients of a sphere. The amount of normal modes forming the backscattered field is determined by a given directivity of the source. Computational results are obtained in a wide frequency range 8–12kHz for water depths equal to several hundreds of meters, and distances between a source/receiver and a target from 1km up to 10km. It is shown that in a range interval up to several kilometers the backscattered field can be calculated also using a simplified medium model consisting of a water half-space and an ice half-space. In this case the scattering coefficients of a sphere are evaluated by the steepest descent method. For the considered oceanic waveguide of 200m depth with a sandy bottom the use of the simplified medium model essentially shortens a computing time.

In this paper, we consider the Weak Trefftz Discontinuous Galerkin (WTDG) method, which enables one to use at the same time the Finite Element Method (FEM) or Variational Theory of Complex Rays (VTCR) discretizations (polynoms and waves), for vibration problems. It has already been developed such that the FEM and the VTCR can be used in different adjacent subdomains in the same problem. Here, it is revisited and extended in order to allow one to use the two discretizations in the same subdomain, at the same time. Numerical examples illustrate the performances of such an approach.

Finite-difference (FD) schemes have been used widely for solving wave equations in seismic exploration. However, the conventional FD schemes hardly guarantee high accuracy at both small and large wavenumbers. In this paper, we propose an optimal time-space domain FD scheme for acoustic vertical transversely isotropic (VTI) wave modeling. The optimal FD coefficients for the second-order spatial derivatives are derived by approaching the time-space domain dispersion relation of acoustic VTI wave equations with the combination of the Taylor-series expansion and the sampling interpolation. We perform numerical dispersion analyses and acoustic VTI modeling using the optimal time-space domain FD scheme. The numerical dispersion analyses show that the optimal FD scheme has smaller dispersion than the conventional FD scheme at large wavenumbers, and also preserves high accuracy at small wavenumbers. The acoustic VTI modeling examples also demonstrate that the optimal time-space domain FD scheme has greater accuracy compared with the conventional time-space domain FD scheme for the same modeling parameters.

The Neumann axisymmetric boundary value problem is considered for a vibrating thin clamped circular plate embedded in the flat rigid screen in the outlet of the circular cylindrical cavity. It is assumed that the two pistons, one cylindrical and the other one annular/circular, are vibrating inside the cavity with the same single frequency and different initial phases. The pistons are the only sources of excitation of the fluid. The acoustic pressure difference on both sides of the plate forces its vibrations. The acoustic waves are radiated into the half-space above it. A rigorous theoretical analysis of sound radiation has been performed based on the exact solution of the problem of free vibrations of the plate. The system of three coupled partial differential equations is solved. They are the two Helmholtz equations for the cavity and for the half-space, and the equation of motion of the plate. Consequently, the acoustic pressure distribution in both spaces is presented as well as the acoustic power radiated.

The accuracy of the seismo-acoustic parabolic equation is tested for problems involving sloping fluid–solid interfaces. The fluid may correspond to the ocean or a sediment layer that only supports compressional waves. The solid may correspond to ice cover or a sediment layer that supports compressional and shear waves. The approach involves approximating the medium in terms of a series of range-independent regions, using a parabolic wave equation to propagate the field through each region, and applying single-scattering approximations to obtain transmitted fields across the vertical interfaces between regions. The accuracy of the parabolic equation method for range-dependent problems in seismo-acoustics was previously tested in the small slope limit. It is tested here for problems involving larger slopes using a finite-element model to generate reference solutions.