Benchmark problems for acoustic scattering from elastic objects in the free field and near the seafloor

Bistatic scattering of an elastic object using the structural admittance and noise-based holographic measurements

This paper presents a method to calculate the bistatic response of an elastic object immersed in a fluid using its structural Green's function (in vacuo structural admittance matrix), calculated by placing the object in a spatially random noise field in air. The field separation technique and equivalent source method are used to reconstruct pressure and velocity fields at the object's surface from pressure measurements recorded on two conformal holographic surfaces surrounding the object. Accurate reconstruction of the surface velocity requires subtraction of the rigid body response computed using a finite element approach. The velocity and pressure fields on the surface lead to the extraction of the in vacuo structural admittance matrix of the elastic object, which is manipulated to yield the farfield bistatic response for a fluid-loaded target for several angles of incidence. This method allows the computation of the scattering properties of an elastic object using exclusive information calculated on its surface (no knowledge of the internal structure required). A numerical experiment involving a cylindrical shell with hemispherical caps is presented, and its bistatic response in water shows excellent agreement with a finite element solution.

Efficient, wide-band rigid-body and elastic scattering computations using transient equivalent sources

A previous paper by the author has shown that transient structural-acoustic problems can be solved using time stepping procedures with the structure and fluid modeled using finite elements and equivalent sources, respectively. Here, the analysis is extended to included scattering problems. Although scattering problems have been discussed extensively in the literature, the current formulation is unique because the acoustic coupling matrix is treated as sparse. Also, most of the previous analyses have assumed the problem is time harmonic, and there is an advantage to performing the computations in the time domain because only a limited number of time steps are required to obtain wideband frequency resolution. This is especially true if the main emphasis is on the mid- to high-frequencies since the ringing response is typically dominated by the lowest frequency modes. Several examples are solved to validate the computations and to document the computation times and solution accuracy.

In Design of an Ocean Bottom Seismometer Sensor: Minimize Vibration Experienced by Underwater Low-Frequency Noise

Ocean Bottom Seismometers (OBS) placed on the seafloor surface are utilized for measuring the ocean bottom seismic waves. The vibration of OBS excited by underwater noise on its surface may interfere with its measured results of seismic waves. In this particular study, an OBS was placed on the seabed, while ray acoustic theory was used to deduce the sound field distribution around the OBS. Then using this information, the analytical expression for the OBS vibration velocity was obtained in order to find various factors affecting its amplitude. The finite element computing software COMSOL Multiphysics^® (COMSOL) was used to obtain the vibration response model of the OBS which was exposed to underwater noise. The vibration velocity for the OBS calculated by COMSOL agreed with the theoretical result. Moreover, the vibration velocity of OBS with different densities, shapes, and characters were investigated as well. An OBS with hemispherical shape, consistent average density as that of the seafloor, and a physical structure of double tank has displayed minimum amplitude of vibration velocity. The proposed COMSOL model predicted the impact of underwater noise while detecting the ocean bottom seismic waves with the OBS. In addition, it provides significant help for the design and optimization of an appropriate OBS.

Direct simulation of acoustic scattering problems involving fluid-structure interaction using an efficient immersed boundary-lattice Boltzmann method

An efficient immersed boundary-lattice Boltzmann method (IB-LBM) is applied to carry out the direct simulation of acoustic scattering problems involving fluid-structure interaction. In the simulation, the lattice Boltzmann method is adopted for the fluid domain, the immersed boundary method is used to handle the fluid-structure interaction and the instantaneous fluid pressure perturbation is computed to obtain the acoustic field. Compared with the conventional IB-LBMs, a force correction technique is introduced in this method to enforce the non-slip boundary conditions at the immersed boundaries and the acoustic scattering field thus can be obtained more accurately. The study of the numerical result comparison with the conventional IB-LBMs or analytical solutions is conducted on four acoustic problems, such as acoustic radiation from a pulsing cylinder, acoustic scattering from a static cylinder with pulse, or harmonic Gaussian sources and a moving two-dimensional sedimentating particle. The better efficiency of the present method is validated.

A Fourier-based total-field/scattered-field technique for three-dimensional broadband simulations of elastic targets near a water-sand interface

The numerical simulation of acoustic scattering from elastic objects near a water-sand interface is critical to underwater target identification. Frequency-domain methods are computationally expensive, especially for large-scale broadband problems. A numerical technique is proposed to enable the efficient use of finite-difference time-domain method for broadband simulations. By incorporating a total-field/scattered-field boundary, the simulation domain is restricted inside a tightly bounded region. The incident field is further synthesized by the Fourier transform for both subcritical and supercritical incidences. Finally, the scattered far field is computed using a half-space Green's function. Numerical examples are further provided to demonstrate the accuracy and efficiency of the proposed technique.

Comparisons among ten models of acoustic backscattering used in aquatic ecosystem research

Analytical and numerical scattering models with accompanying digital representations are used increasingly to predict acoustic backscatter by fish and zooplankton in research and ecosystem monitoring applications. Ten such models were applied to targets with simple geometric shapes and parameterized (e.g., size and material properties) to represent biological organisms such as zooplankton and fish, and their predictions of acoustic backscatter were compared to those from exact or approximate analytical models, i.e., benchmarks. These comparisons were made for a sphere, spherical shell, prolate spheroid, and finite cylinder, each with homogeneous composition. For each shape, four target boundary conditions were considered: rigid-fixed, pressure-release, gas-filled, and weakly scattering. Target strength (dB re 1 m(2)) was calculated as a function of insonifying frequency (f = 12 to 400 kHz) and angle of incidence (θ = 0° to 90°). In general, the numerical models (i.e., boundary- and finite-element) matched the benchmarks over the full range of simulation parameters. While inherent errors associated with the approximate analytical models were illustrated, so were the advantages as they are computationally efficient and in certain cases, outperformed the numerical models under conditions where the numerical models did not converge.

Model-based waveform design for optimal detection: A multi-objective approach to dealing with incomplete a priori knowledge

This work considers the design of optimal, energy-constrained transmit signals for active sensing for the case when the designer has incomplete or uncertain knowledge of the target and/or environment. The mathematical formulation is that of a multi-objective optimization problem, wherein one can incorporate a plurality of potential targets, interference, or clutter models and in doing so take advantage of the wide range of results in the literature related to modeling each. It is shown, via simulation, that when the objective function of the optimization problem is chosen to maximize the minimum (i.e., maxmin) probability of detection among all possible model combinations, the optimal waveforms obtained are advantageous. The advantage results because the maxmin waveforms judiciously allocate energy to spectral regions where each of the target models respond strongly and each of the environmental models affect minimal detection performance degradation. In particular, improved detection performance is shown compared to linear frequency modulated transmit signals and compared to signals designed with the wrong target spectrum assumed. Additionally, it is shown that the maxmin design yields performance comparable to an optimal design matched to the correct target/environmental model. Finally, it is proven that the maxmin problem formulation is convex.

Prediction of a body's structural impedance and scattering properties using correlation of random noise

This paper derives a method to estimate the structural or surface impedance matrix (or equivalently the inverse of the structural Green's function) for an elastic body by placing it in an encompassing and spatially random noise field and cross-correlating pressure and normal velocity measurements taken on its surface. A numerical experiment is presented that utilizes a cross-correlation method to determine the structural impedance matrix for an infinite cylindrical shell excited by a spatially random noise field. It is shown that the correlation method produces the exact analytic form of the structural impedance matrix. Furthermore, using standard impedance formulations of the scattered and incident pressure fields at the object surface that are based on the equivalent source method and using this estimated structural impedance, a prediction of the scattered acoustic field at any position outside of the object can be made for any given incident field. An example is presented for a point (line) source near a cylindrical shell and when compared with the analytical result, excellent agreement is found between the scattered fields at a radius close to the shell.

Time and frequency constrained sonar signal design for optimal detection of elastic objects

In this paper, the task of model-based transmit signal design for optimizing detection is considered. Building on past work that designs the spectral magnitude for optimizing detection, two methods for synthesizing minimum duration signals with this spectral magnitude are developed. The methods are applied to the design of signals that are optimal for detecting elastic objects in the presence of additive noise and self-noise. Elastic objects are modeled as linear time-invariant systems with known impulse responses, while additive noise (e.g., ocean noise or receiver noise) and acoustic self-noise (e.g., reverberation or clutter) are modeled as stationary Gaussian random processes with known power spectral densities. The first approach finds the waveform that preserves the optimal spectral magnitude while achieving the minimum temporal duration. The second approach yields a finite-length time-domain sequence by maximizing temporal energy concentration, subject to the constraint that the spectral magnitude is close (in a least-squares sense) to the optimal spectral magnitude. The two approaches are then connected analytically, showing the former is a limiting case of the latter. Simulation examples that illustrate the theory are accompanied by discussions that address practical applicability and how one might satisfy the need for target and environmental models in the real-world.

Structural-acoustic modeling for three-dimensional freefield and littoral environments with verification and validation

This paper describes a high-order, finite-element-based, three-dimensional time-harmonic model for large-scale exterior structural-acoustics problems. It is applicable to both freefield and littoral environments. For the freefield case, the infinite exterior is treated as a homogeneous linear acoustic medium. For littoral applications, the water or air and the sediment domains are each treated as linear homogeneous, semi-infinite half-spaces with piecewise-constant properties. Both domains admit complex-valued wave speeds to enable the inclusion of damping. The finite element formulation uses a variational statement which naturally incorporates the transmission-condition at the water or air-sediment interface. The truncation of the infinite exterior is realized using an infinite-element for the freefield case, and the perfectly-matched-layer approximation for littoral applications. Computation of the farfield quantities is done based on an integral representation which, for the littoral cases, uses efficient approximations for the appropriate Green's function. Numerical computations are presented for a series of progressively more complex problems, and are used to verify the model against analytic and other numerical solutions and validate it based on the experimental data for scattering from elastic scatterers as measured in freefield and sediment pool laboratory facilities.