Journal of Theoretical and Computational Acoustics

The Viscous Grain Shearing (VGS) theory predicts the existence of a compressional wave and a shear wave in an unconsolidated marine sediment. Although it is known that, subject to certain constraints, the shear wave satisfies causality, the causal nature of the compressional wave is less well understood. In this paper, the VGS compressional-wave speed and attenuation are examined in three frequency regimes, where it is shown that they follow approximately frequency power laws. It is then proved that the VGS propagation factor, which is a combination of the phase speed and attenuation, is a causal transform: its inverse Fourier transform is zero for all times prior to the onset of the source. The derivation of this result, which is a necessary condition if the VGS compressional wave equation is to satisfy causality, includes the development of a technique for evaluating a class of previously unknown integrals. This integration procedure relies on a limiting argument combined with certain Fourier transforms, the latter taking the form of “improper” integrals, which, it is shown, can be expressed explicitly based on the properties of generalized functions. An expression for the impulse response of the VGS compressional wave is also developed and shown to satisfy causality, although the transition from zero to the peak level is abrupt, quite unlike the perfectly smooth behavior exhibited by the impulse response of the VGS shear wave, which is maximally flat everywhere in the medium at the instant the source is activated.

A new spectrally optimized physical dispersion relation preserving scheme has been introduced to solve computational acoustics and aeroacoustics problems, accurately. The derived fourth-order accurate scheme has significant spectral resolution and physical dispersion relation preserving (DRP) nature. The scheme displays neutral stability at high CFL numbers. The developed scheme has an ability to add numerical diffusion as and when required to attenuate spurious waves present in the computed solutions. These features make the proposed scheme suitable for solving computational aeroacoustic problems. The scheme has been validated by comparing solutions of model computational acoustic problems with the available analytical solutions. Scheme has also been tested to solve the incompressible flow field around a circular cylinder executing rotary oscillations. Ability of the scheme to perform direct simulation of the computational aeroacoustic problems has been shown by computing acoustic field triggered by a laminar flow past a stationary circular cylinder. Excellent match has been observed between the present computed results and the available results in the literature which justifies applicability of the present DRP scheme to solve complex flow and aeroacoustic problems.

In shallow-water waveguide, the normal mode information of acoustic signals plays an important role in localization research. In this paper, an extraction algorithm of modal intensity distribution based on horizontal circular array is proposed. By using the horizontal wavenumber of each mode, the modal domain beamforming is used to estimate the modal intensity distribution of the acoustic signal. The theoretical derivation, data simulation and experimental data are used to verify the feasibility of the algorithm based on circular array and the superiority compared with the line array extraction algorithm. At the last part of the paper, an application based on modal intensity distribution is proposed: water surface interference suppression, and the effectiveness of the interference suppression algorithm is verified from theoretical derivation and simulation experiments.

The acoustic propagation problem in the ocean is modeled via the wide angle parabolic equation with a Neumann to Dirichlet map bottom boundary condition. An environment consisting of the water column, a sediment layer and the semi-infinite sub-bottom region is considered. The derivatives of a new cost function with respect to the unknown environmental parameters are calculated analytically via the adjoint operator and incorporated numerically in an inversion scheme. Full geoacoustic inversion for eight bottom parameters is performed successfully, using experimental field data from the Yellow Shark experiment, for the first time according to the authors’ knowledge. Adjoint inversion for the water SSP, using the EOFs, is also presented and validated with simulated data.

Adiabatic approximation (AP) combined with perturbation theory gives a fast normal-mode solution of temporal coherence for sound field in a two-dimensional deep water with time-varying random internal waves. Internal waves induced mode changes are deduced using the first-order perturbation theory [C. T. Tindle, L. M. O’Driscoll and C. J. Higham, Coupled mode perturbation theory of range dependence, J. Acoust. Soc. Am. 108(1) (2000) 76–83]. And mode perturbations in amplitude are neglected by the adiabatic method with wavenumber perturbations in phase merely considered. The AP expression of temporal coherence function is theoretically identical to the adiabatic transport equation theory [J. A. Colosi, T. K. Chandrayadula, A. G. Voronovich and V. E. Ostashev, Coupled mode transport theory for sound transmission through an ocean with random sound speed perturbations: Coherence in deep water environments, J. Acoust. Soc. Am. 134(4) (2013) 3119–3133]. Numerical results of the adiabatic temporal coherence function for several low frequencies and ranges up to 1000km are calculated. Then the coherence time scales obtained from the calculations are examined by a one-way coupled theory considering forward scattering [A. G. Voronovich, V. E. Ostashev and J. A. Colosi, Temporal coherence of acoustic signals in a fluctuating ocean, J. Acoust. Soc. Am. 129(6) (2011) 3590–3597]. Comparisons demonstrate that the range and frequency dependence of coherence time for both methods are quite close. And this shows good agreement with the well-known inverse frequency and inverse square root range laws. In addition, the internal wave energy dependence of coherence time is also studied.

Algorithms that enable acoustic sensing vehicles to autonomously map acoustic fields are being developed, but some require an analytical representation of the data collected from the acoustic field with specific continuity properties. One optimal control technique that has these requirements and has been used in autonomous acoustic sensing algorithms is Pontryagin’s Maximum Principle (PMP). Given that most real-world fields are modeled by numerical methods, the need to create continuous analytical representations from data is a hurdle in realistic applications of these autonomous algorithms. In this work, finite series of basis functions are used to solve this problem. The basis functions are selected to meet the criteria of the PMP, and are used to approximate the field from the data collected. While this approach meets the criteria of the algorithm, it can be a computationally expensive approach for complex fields and large datasets. This paper looks at the trade off between accuracy and computational time, for different frequencies and levels of field complexity. A previously published ocean profile developed from data taken off the island of Elba is used in the normal mode software, Kraken, to generate the acoustic fields used to test this method. The candidate basis functions considered are trigonometric functions analogous to finite Fourier series, and Legendre polynomials. The Legendre polynomials are shown to have higher accuracy when used with a dynamically selected exclusion range at low frequencies and a cubic spline interpolation method for generating intermediate data points at higher frequencies. Run times are calculated and while both candidate basis functions are shown to meet the requirements of the PMP algorithm, the Legendre polynomials require the least amount of run time.

Conventional finite-difference or pseudo-spectral viscoacoustic modeling methods use uniform, rectangular grids to simulate wave propagation, leading to severe spurious diffractions at the surface topography. To overcome the problem, we mesh the velocity and quality factor $(Q)$ models into curvilinear grids and map the models and the first-order velocity-stress viscoacoustic equation into an auxiliary system. However, when imaging viscoacoustic media, the first-order velocity-stress viscoacoustic equation has difficulty in compensating the energy loss and correcting the phase effects because of the memory variables. To overcome the problem, we apply the first-order equation in the auxiliary coordinates to derive a second-order viscoacoustic quasi-differential equation without memory variables in the same system, with an attenuated term and a dispersion term separately. A new hybrid spatial partial derivative method is proposed to solve the equation. Error analysis, using a homogeneous model with different grids, demonstrates the accuracy and validity of our methods. The numerical examples on two models with topographic surfaces indicate that our method can obtain more stable and improving results for modeling the wave propagation in viscoacoustic media including surface topography.

The numerical determination of dispersion relations in periodic materials via the finite element method is a difficult task in most standard codes. Here, we propose a novel technique which allows the computation of these band structures from local elemental subroutines in contrast with existing methods which impose Bloch boundary conditions on the global arrays. The proposed local approach is thus readily applicable to several physical contexts and space dimensionalities. Here we present the details of this element-based algorithm and provide verification results for three different kinematic assumptions applied to phononic crystals in a classical and a micropolar elastic medium. The paper also includes in the form of supplementary material, a fully-coded user subroutine and a test-problem to be used in a commercial finite element code.

Kirchhoff approximations for the forward-scattering target strength of underwater objects are developed by combining Babinet’s principle and the Kirchhoff integral, where theoretical formulations and a numerical implementation are given in detail. The Kirchhoff approximation is found to be a high-frequency physical acoustic approximation. The forward-scattering target strength versus frequency and the spatial angles for spherical objects, prolate spheroids and the Benchmark Target Strength Simulation Submarine (BeTSSi-Sub) model are obtained by the Kirchhoff approximation and compared with results from theory, the deformed cylinder method (DCM) and the boundary element method (BEM). The Kirchhoff approximation shows considerable agreement with the theoretical and numerical approaches in a region of $+/-20^{\circ }$ from the rigorous forward-scattering direction. The forward-scattered field contour and the corresponding directivity for the BeTSSi-Sub model are also calculated as a demonstration. Mode coupling caused by the simulated target is clearly revealed. The results indicate that the Kirchhoff approximation can predict the forward-scattering target strength of complex underwater objects.

The radiated acoustic waves from impact pile driving produce high noise level into the water which may cause damage to marine mammals living close to the offshore construction location. In this paper, a linear, axisymmetric finite element (FE) model is applied to predict pile driving noise in the water. Measurement from bottom-mounted hydrophone deployed at a site 230 m from the source is used to validate the model results. The comparisons between model results and measurement, such as structure modal analysis, sound exposure level at different pile penetration and unweighted one-third octave band level, are presented and show useful predictions of noise level from the model. Furthermore, a time domain case is demonstrated to show Mach wave associated with the radial deformation of the pile and supersonic speed. Finally, analysis of variance (ANOVA) and linear regression are made after verifying the model prediction. The ANOVA results identifies some significant parameters on pile driving noise and the empirical equation from linear regression represents the noise level from pile driving impact at close range. These are possible metrics on offshore wind farm environment assessment in Taiwan.