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A physics-informed neural network (PINN) enables the estimation of horizontal modal wavenumbers using ocean pressure data measured at multiple ranges. Mode representations for the ocean acoustic pressure field are derived from the Hankel transform relationship between the depth-dependent Green's function in the horizontal wavenumber domain and the field in the range domain. We obtain wavenumbers by transforming the range samples to the wavenumber domain, and maintaining range coherence of the data is crucial for accurate wavenumber estimation. In the ocean environment, the sensitivity of phase variations in range often leads to degradation in range coherence. To address this, we propose using OceanPINN [Yoon, Park, Gerstoft, and Seong, J. Acoust. Soc. Am. 155(3), 2037–2049 (2024)] to manage spatially non-coherent data. OceanPINN is trained using the magnitude of the data and predicts phase-refined data. Modal wavenumber estimation methods are then applied to this refined data, where the enhanced range coherence results in improved accuracy. Additionally, sparse Bayesian learning, with its high-resolution capability, further improves the modal wavenumber estimation. The effectiveness of the proposed approach is validated through its application to both simulated and SWellEx-96 experimental data. [ABSTRACT FROM AUTHOR]

A self-reciprocity method is described for calibrating a spherical transducer in a spherical shell. The reciprocity constant is calculated using Green's function and the electroacoustic reciprocal principle in the spherical shell. A sensitivity correction is developed by calculating the transducer's receiving force in different fields. An experimental measurement setup is described to calibrate transducers with diameters of 20 and 30 mm in the frequency range from 25 to 63 kHz, calibrated in a 500 mm diameter spherical shell with a thickness of 2 mm. The largest discrepancy in calibration results between the self-reciprocity and three-transducer spherical-wave reciprocity method is around −1.4 dB. The self-reciprocity calibration method, with a smaller volume required than the three-transducer spherical-wave reciprocity method, has a potential advantage in calibrating the transducer at high hydrostatic pressure and varying water temperatures. [ABSTRACT FROM AUTHOR]

Laser-induced ultrasound is based on the thermo-elastic conversion of absorbed short light pulses to pressure pulses. In the work presented here, laser-induced ultrasound in a planar structure of interconnected layers with variations in optical, thermal, and mechanical properties is studied. Layered structures can be used for generating wideband ultrasonic pulses specific to a chosen application. An analytical time-domain solution is derived for the resulting pressure transmitted from the layered structure. The solution is derived for an arbitrary number of layers with an arbitrary optical absorption profile. Free space Green's functions with image sources are used to derive the solution. A solution employing the Beer–Lambert law is also proposed. The simplification with reflections only at the boundaries is in agreement with previous published results. The spectral properties of the generated pulse are derived, where the effects of optical absorption coefficients and layer thicknesses are shown. The analytical solution is compared to one-dimensional (1D) simulations and a three-dimensional (3D) simulation, realised as a two-dimensional (2D) axially symmetric case, using the matlab toolbox k-Wave. The 3D simulation on-axis pressure agrees well with the 1D analytical solution when the diameter of the laser beam is larger by approximately 1 order of magnitude than the thickness of the planar layered structure. [ABSTRACT FROM AUTHOR]

Applications of acoustic noise interferometry to passive remote sensing of the ocean rely on retrieval of empirical Green's functions (EGFs) from cross-correlations of ambient sound at spatially separated points. At ranges of tens of ocean depths, obtaining stable and accurate EGF estimates usually requires noise averaging periods of hours or days. Using data acquired in the Shallow Water 2006 experiment on the continental shelf off New Jersey, it is found that at ranges of 40–70 ocean depths, the EGFs can be retrieved with noise averaging times as short as 64 s. The phenomenon is observed for various receiver pairs but does not occur simultaneously in all azimuthal directions. The rapidly emerging EGFs have a wider frequency band and a richer normal mode content than the EGFs obtained in previous studies using long averaging times and are better suited for monitoring physical processes in the water column. Available acoustic and environmental data is examined to understand the conditions leading to rapid EGF emergence from diffuse noise. Strong intermittency is observed in the horizontal directionality of ambient sound. Rapid emergence of EGF in shallow-water waveguide is found to occur when the directionality of diffuse ambient noise is favorable. [ABSTRACT FROM AUTHOR]

This article investigates the interactions of two-plane waves in weakly nonlinear elastic solids containing quadratic and cubic nonlinearity. The analytical solutions for generated combined harmonic waves are derived using the Green's function approach applied to a generated system of quasi-linear equations of motion. Wave mixing solutions are obtained and include shape functions that permit closed-form solutions for a variety of interaction geometries. An explicit example is highlighted for a spherical interaction volume assuming isotropic elastic constants. Several parameters of the generated field after mixing are analyzed including resonant and nonresonant mixing, the role of interaction angle, and the frequencies of the two incident waves. Wave mixing offers the potential for sensing localized elastic nonlinearity and the present model can be used to help design experimental configurations. [ABSTRACT FROM AUTHOR]

A new approach that determines the contribution of aeroacoustic sources to sound power is presented. The method combines the Lighthill source distribution with an acoustic impedance matrix constructed from radiation kernels of the free-field Green's function. To demonstrate the technique, the flow noise produced by a pair of co-rotating vortices is examined. Results are initially compared with those obtained using Möhring's analogy of two-dimensional vortex sound radiation. The contribution to sound power for each component of the Lighthill tensor is presented for a range of wave numbers and vortex separation distances. For acoustically compact cases, the aeroacoustic source contributions for the diagonal components of the Lighthill tensor show a similar trend observed in sound maps for longitudinal quadruples. In contrast to the acoustically compact cases where the central focal area is mostly unchanged with variation in Mach number, significant variation in the focal areas occurs for non-acoustically compact cases. Using the aeroacoustic source contribution technique, the nature and location of dominant flow noise sources to sound power can be identified. [ABSTRACT FROM AUTHOR]

The auxiliary superfield approach is proposed as a method to obtain statistical predictions of the acoustic response of complex elastic structures. The potential advantage of the method is the full retention of interference and resonance effects associated with the degrees of freedom being averaged over. It is not known whether this approach leads to tractable problems for structural acoustics systems, however. We have applied the method to the idealized case of an infinite, thin plate with attached oscillators to obtain the mean Green's function. The oscillators are assumed to have an uncorrelated, Gaussian distributed mass and stiffness distribution representing a simple form of complex internal structure. Using the auxiliary superfield approach, the mean Green's functions are expressed exactly as a functional integral. For relatively small disorder, the integral may be estimated by a saddle point approximation which leads to coupled integral equations for effective mass and stiffness matrices that can be solved numerically for a given spatial distribution of the disorder. With the solutions for these matrices, one obtains a self-consistently determined, generalized fuzzy structure model. We give analytical solutions for the simple case of a uniform spatial distribution. The results are promising for the application of the method to more challenging geometries. [ABSTRACT FROM AUTHOR]

This work presents theoretical and numerical models for the backscattering of two-dimensional Rayleigh waves by an elastic inclusion, with the host material being isotropic and the inclusion having an arbitrary shape and crystallographic symmetry. The theoretical model is developed based on the reciprocity theorem using the far-field Green's function and the Born approximation, assuming a small acoustic impedance difference between the host and inclusion materials. The numerical finite element (FE) model is established to deliver a relatively accurate simulation of the scattering problem and to evaluate the approximations of the theoretical model. Quantitative agreement is observed between the theoretical model and the FE results for arbitrarily shaped surface/subsurface inclusions with isotropic/anisotropic properties. The agreement is excellent when the wavelength of the Rayleigh wave is larger than, or comparable to, the size of the inclusion, but it deteriorates as the wavelength gets smaller. Also, the agreement decreases with the anisotropy index for inclusions of anisotropic symmetry. The results lay the foundation for using Rayleigh waves for quantitative characterization of surface/subsurface inclusions, while also demonstrating its limitations. [ABSTRACT FROM AUTHOR]

In contrast-enhanced echography, the simulation of nonlinear propagation of ultrasound through a population of oscillating microbubbles imposes a computational challenge. Also, the numerical complexity increases because each scatterer has individual properties. To address these problems, the Iterative Nonlinear Contrast Source (INCS) method has been extended to include a large population of nonlinearly responding microbubbles. The original INCS method solves the Westervelt equation in a four-dimensional spatiotemporal domain by generating increasingly accurate field corrections to iteratively update the acoustic pressure. The field corrections are computed by the convolution of a nonlinear contrast source with the Green's function of the linear background medium. Because the convolution integral allows a coarse discretization, INCS can efficiently deal with large-scale problems. To include a population of microbubbles, these are considered as individual contrast point sources with their own nonlinear response. The field corrections are computed as before, but now, in each iteration, the temporal signature of each contrast point source is computed by solving the bubble's Marmottant equation. Physically, each iteration adds an order of multiple scattering. Here, the performance of the extended INCS method and the significance of multiple scattering is demonstrated through various results from different configurations. [ABSTRACT FROM AUTHOR]

We study the transition from ballistic to diffusive to equipartitioned waves in scattering media using the acoustic radiative transfer equation. To solve this equation, we first transform it into an integral equation for the specific intensity and then construct a time stepping algorithm with which we evolve the specific intensity numerically in time. We handle the advection of energy analytically at the computational grid points and use numerical interpolation to deal with advection terms that do not lie on the grid points. This approach allows us to reduce the numerical dispersion, compared to standard numerical techniques. With this algorithm, we are able to model various initial conditions for the intensity field, non-isotropic scattering, and uniform scatterer density. We test this algorithm for an isotropic initial condition, isotropic scattering, and uniform scattering density, and find good agreement with analytical solutions. We compare our numerical solutions to known two-dimensional diffusion approximations and find good agreement. We use this algorithm to numerically investigate the transition from ballistic to diffusive to equipartitioned wave propagation over space and time, for two different initial conditions. The first one corresponds to an isotropic Gaussian distribution in space and the second one to a plane wave segment. We find that diffusion and equipartitioning must be treated as local rather than global concepts. This local behavior of equipartitioning has implications for Green's functions reconstruction, which is of interest in acoustics and seismology. [ABSTRACT FROM AUTHOR]

A number of one-dimensional models have been developed to inform the design of piezoelectric transducers. The majority of these models are in the frequency domain. In this paper, we develop a one-dimensional time-domain model for the mechanical response of a piezoelectric layer. Secondary effects, resulting from feedback between the acoustic and electric variables, are included in the model. Our approach utilizes Green's function for the Helmholtz equation with radiation boundary conditions and the methods of complex analysis. The model predictions are validated by comparison with a finite-difference time-domain numerical simulation of the governing acoustic equations in and outside the layer. This time-domain model enables efficient calculation of the secondary piezoelectric action effects and provides the mechanical response to an arbitrary electrical source. [ABSTRACT FROM AUTHOR]

An exact analytical three-dimensional time-domain Green's function is introduced for the van Wijngaarden wave equation when the coefficients of the two loss terms satisfy a specific relationship. This analytical Green's function, which describes frequency-squared attenuation in acoustic media such as water, enables the subsequent derivation of new expressions that describe the lossy spatial impulse response for a circular piston. Initial time-domain assessments, which compare the Green's functions for the van Wijngaarden, Stokes, and power law wave equations using the attenuation and sound speed for water, indicate that these three lossy wave equations yield nearly identical results at distances greater than or equal to 10 μm. Lossy spatial impulse responses are also evaluated with increasing distance in and near the paraxial region of a circular piston radiating in water to reveal some interesting time-domain interactions between frequency-squared attenuation and diffraction. Similar behaviors are also demonstrated for the lossy far-field spatial impulse. In addition, the convergence is demonstrated for two analytically equivalent expressions applied to numerical computations of the lossy spatial impulse response. The results show that these new expressions are ideal for describing and explaining fundamental interactions between frequency-squared attenuation and diffraction in the time-domain. [ABSTRACT FROM AUTHOR]

Pressurized water supply pipeline systems (PWSPS) are quintessential to human development and sustenance, but suffer a multitude of unresolved defects (i.e., leaks, blockages, etc.) due to aging and inaccessibility. In this paper, the ubiquitous high-frequency background noise in PWSPS is harnessed to introduce a high-resolution, passive defect detection technique. The relation between the acoustic Green's and cross correlation functions for a pressurized water pipe is derived for the case of high frequency waves, i.e., acoustic wavelengths smaller than the pipe diameter. This relation is subsequently used to formulate a time-reversal technique for localizing anomalies such as small variations in pipe wall impedance and through-wall defects (i.e., leaks). It is shown that the derived relationship between the cross correlation and acoustic Green's functions enables very accurate defect detection and localization by measuring the background noise at two locations along a pipe. This is an important result given that (i) there is limited access to buried PWSPS to conduct high-frequency active defect detection, and (ii) traditional methods to actively probe pipes (e.g., valve maneuverer) are low-resolution (tens to hundreds of meters) and often result in pipe overloading and fatigue. [ABSTRACT FROM AUTHOR]

A seismic reflection survey conducted directly over two bottom-mounted hydrophones in the north-east Pacific Ocean is used to explore how surface source locations affect ambient noise interferometry for the two hydrophones. The airgun shots are used as an approximation of an impulsive sound source at a discrete location, which allows us to investigate spatial contributions to the cross correlation between the two hydrophones. Simulated and experimental results are presented. The contributions to the cross correlations are explained by different reflections off the surface or bottom of the ocean, and a discussion about what can and cannot be inferred about the emergence to the Green's function is presented. [ABSTRACT FROM AUTHOR]

Cross correlations of diffuse noise can be utilized to recover the time domain Green's function (TDGF) between two points. This principle allows for a variety of practical applications, such as seismic tomography, ocean thermometry, passive localization, etc. However, in the real ocean environment, loud interference noise sources usually bias the travel time estimates of the TDGF or result in poor recovery quality. To deal with this issue, a diffuse noise reconstruction approach is proposed to eliminate the influence of the strong interference noise by utilizing the time domain statistical property of ocean ambient noise recorded on single hydrophones with the help of random matrix theory. Simulation and experimental data analysis indicate that this algorithm can effectively extract the diffuse noise component from the ocean ambient noise field and retrieve the TDGF with a higher signal-to-noise ratio when coherent accumulation of cross correlations of the reconstructed diffuse noise is performed. [ABSTRACT FROM AUTHOR]

We investigate the feasibility of using a known elastic target located near the seabed for the purpose of inferring characteristics of marine sediment. In the problem considered the object position and its burial depth are not known with precision. First, the admittance matrix of the elastic object is determined (numerically or experimentally) over a wide frequency range in the structural acoustic regime. Then, the equivalent source method (ESM) coupled with a spectral representation of the Green's functions in stratified domains is used to predict the object acoustic signature in various environments and experimental configurations. The resulting solver takes into account all multiple scattering between target (buried or not), sea floor, and sea surface and is not limited to short distances. After presenting the solution to the forward problem several synthetic inversions for sediment characteristics are shown. They are based upon a resonance-based misfit function we describe. The Bayesian procedure also infers object burial and source-object range, broadening its range of application. [ABSTRACT FROM AUTHOR]

A parametric approach based on parametric analysis of the acoustical properties of a layered media is proposed to derive a reduced layered Green's function. The approach relies on the smallness of one of the problem parameters and allows a simpler form of Green's function by disregarding the smaller parametric terms. Several illustrative examples comparing the amplitudes of exact and reduced Green's function for small parameter of density ratio in various source and observation location setups are presented. It is demonstrated that the CPU times calculated at different points decrease considerably for the reduced Green's function, further justifying the presented method. [ABSTRACT FROM AUTHOR]

Exact analytical expressions for the spatial impulse response are available for certain transducer geometries. These exact expressions for the spatial impulse response, which are only available for lossless media, analytically evaluate the Rayleigh integral to describe the effect of diffraction in the time domain. To extend the concept of the spatial impulse response by including the effect of power law attenuation in a lossy medium, time-domain Green's functions for the Power Law Wave Equation, which are expressed in terms of stable probability density functions, are computed numerically and superposed. Numerical validations demonstrate that the lossy spatial impulse for a circular piston converges to the analytical lossless spatial impulse response as the value of the attenuation constant grows small. The lossy spatial impulse response is then evaluated in different spatial locations for four specific values of the power law exponent using several different values for the attenuation constant. As the attenuation constant or the distance from the source increases, the amplitude decreases while an increase in temporal broadening is observed. The sharp edges that appear in the time-limited lossless impulse response are replaced by increasingly smooth curves in the lossy impulse response, which decays slowly as a function of time. [ABSTRACT FROM AUTHOR]

The envelope of the time-lagged cross-correlation of an underwater noise field between two hydrophones can under certain conditions be used as a proxy for active acoustic receptions between the two locations enabling the study of ocean variability. Previous work looked at the sensitivity of cross-correlation peak amplitudes with respect to the distribution of the noise sources. The present study examines the sensitivity of the cross-correlation envelope peak times with respect to changes in the sound-speed distribution. A wave-theoretic scheme allowing for finite-frequency calculations in two and three dimensions, combined with the Born approximation for perturbations of the Green's function and the peak arrival approach, is used to obtain sensitivity kernels with respect to environmental (sound-speed) changes. These kernels provide a way to infer ocean structure from the cross-correlation peaks, considered as observables on their own and valid even in cases where the cross-correlation function does not approximate the time-domain Green's function between the two receivers. The sensitivity behavior is studied for different propagation conditions and noise-source distributions, ranging from spatially distributed uncorrelated noise sources to point sources, such as individual ships. Deviations from linearity are addressed and discussed. [ABSTRACT FROM AUTHOR]

An in vivo range verification technology for proton beam cancer therapy, preferably in real-time and with submillimeter resolution, is desired to reduce the present uncertainty in dose localization. Acoustical imaging technologies exploiting possible local interactions between protons and microbubbles or nanodroplets might be an interesting option. Unfortunately, a theoretical model capable of characterising the acoustical field generated by an individual proton on nanometer and micrometer scales is still missing. In this work, such a model is presented. The proton acoustic field is generated by the adiabatic expansion of a region that is locally heated by a passing proton. To model the proton heat deposition, secondary electron production due to protons has been quantified using a semi-empirical model based on Rutherford's scattering theory, which reproduces experimentally obtained electronic stopping power values for protons in water within 10% over the full energy range. The electrons transfer energy into heat via electron-phonon coupling to atoms along the proton track. The resulting temperature increase is calculated using an inelastic thermal spike model. Heat deposition can be regarded as instantaneous, thus, stress confinement is ensured and acoustical initial conditions are set. The resulting thermoacoustic field in the nanometer and micrometer range from the single proton track is computed by solving the thermoacoustic wave equation using k-space Green's functions, yielding the characteristic amplitudes and frequencies present in the acoustic signal generated by a single proton in an aqueous medium. Wavefield expansion and asymptotic approximations are used to extend the spatial and temporal ranges of the proton acoustic field. [ABSTRACT FROM AUTHOR]

Classical acoustic wave-field representations consist of volume and boundary integrals, of which the integrands contain specific combinations of Green's functions, source distributions, and wave fields. Using a unified matrix-vector wave equation for different wave phenomena, these representations can be reformulated in terms of Green's matrices, source vectors, and wave-field vectors. The matrix-vector formalism also allows the formulation of representations in which propagator matrices replace the Green's matrices. These propagator matrices, in turn, can be expressed in terms of Marchenko-type focusing functions. An advantage of the representations with propagator matrices and focusing functions is that the boundary integrals in these representations are limited to a single open boundary. This makes these representations a suitable basis for developing advanced inverse scattering, imaging and monitoring methods for wave fields acquired on a single boundary. [ABSTRACT FROM AUTHOR]

Acoustic noise interferometry is applied to retrieve empirical Green's functions (EGFs) from the ambient and shipping noise data acquired in the Shallow Water 2006 experiment on the continental shelf off New Jersey. Despite strong internal wave-induced perturbations of the sound speed in water, EGFs are found on 31 acoustic paths by cross-correlating the noise recorded on a single hydrophone with noise on the hydrophones of a horizontal linear array about 3.6 km away. Datasets from two non-overlapping 15-day observation periods are considered. Dispersion curves of three low-order normal modes at frequencies below 110 Hz are extracted from the EGFs with the time-warping technique. The dispersion curves from the first dataset were previously employed to estimate the seabed properties. Here, using this seabed model, we invert the differences between the dispersion curves obtained from the two datasets for the variation of the time-averaged sound speed profile (SSP) in water between the two observation periods. Results of the passive SSP inversion of the second dataset are compared with the ground truth derived from in situ temperature measurements. The effect of temporal variability of the water column during noise-averaging time on EGF retrieval is discussed and quantified. [ABSTRACT FROM AUTHOR]

This article derives the radiation impedance for two parallel pistons in two different configurations: baffled and unbaffled. For the former, the cylindrical system of coordinates is adapted to compute the self and mutual impedance of a piston between perfectly rigid infinite parallel planes. For the latter, spheroidal coordinates are used and declined for the case of two disks in free-space. The formulae for Green's function that respects Neumann boundary conditions are established in both configurations in order to compute the pressure field using the Huygens-Fresnel principle. Contrasting with the radiation impedance obtained for one single radiator, both systems exhibit resonant frequencies. The result of this study, validated in each case by a numerical method, can be used to predict the acoustic interaction of two vibrating systems for which their radiation surfaces are facing each other. [ABSTRACT FROM AUTHOR]

The purpose of the paper is twofold. First, a modified Green's function (MGF) approach is described for solving the time-independent inhomogeneous optoacoustic (OA) wave equation. The performance of this technique has been assessed with respect to the exact, traditional Born series and convergent Born series methods for an acoustically inhomogeneous spherical source. Second, we apply the same approach for calculating time domain signal from a blood vessel network consisting of an ensemble of acoustically homogeneous/inhomogeneous randomly positioned disks resembling cells. The predicted signals have been compared with those generated by the exact method and a freely available standard software. The OA spectra for a spherical source demonstrated excellent agreement with the exact results when sound-speed for the source was varied from −20% to 30% compared to that of the surrounding medium. The simulated OA signals also followed the same trend as that of the exclusively used software for the acoustically homogeneous blood vessel network. Future work will focus inclusion of a suitable phase factor within the MGF facilitating OA pulses building up at correct temporal locations for an acoustically inhomogeneous source. [ABSTRACT FROM AUTHOR]

A strategy of spatial distortion to make an anisotropic problem become isotropic has been previously validated in two-dimensional transverse isotropic (TI) viscoelastic cases. Here, the approach is extended to the three-dimensional problem by considering the time-harmonic point force response (Green's function) in a TI viscoelastic material. The resulting wave field, exactly solvable using a Radon transform with numerical integration, is approximated via spatial distortion of the closed form analytical solution to the isotropic case. Different distortions are used, depending on whether the polarization of the wave motion is orthogonal to the axis of isotropy, with the approximation yielding differing levels of accuracy. [ABSTRACT FROM AUTHOR]

A method is presented for estimating the range of a distant ship in shallow water using a vertical array and a guide ship at a known range close to the array. The method involves a combination of four different approaches: blind deconvolution, waveguide invariant, virtual receiver (VR), and array invariant. (1) Blind deconvolution extracts a time-domain Green's function from the broadband acoustic source (guide ship). (2) The Green's function is extrapolated into adjacent ranges using the waveguide invariant, generating a horizontal array of synthetic guide sources. (3) Each guide source then turns into a VR where the output approximates the signal that the distant (objective) ship will produce at the location of the guide source. (4) The horizontal virtual array around the guide ship applies the blind deconvolution again to estimate the Green's function for the objective source, followed by the array invariant to estimate the distance between the two ships. The proposed method is demonstrated using a ship of opportunity radiating broadband noise (100–500 Hz) and a 56.25-m long vertical array in approximately 100-m water. [ABSTRACT FROM AUTHOR]

In physical acoustic laboratories, wave propagation experiments often suffer from unwanted reflections at the boundaries of the experimental setup. We propose using multidimensional deconvolution (MDD) to post-process recorded experimental data such that the scattering imprint related to the domain boundary is completely removed and only the Green's functions associated with a scattering object of interest are obtained. The application of the MDD method requires in/out wavefield separation of data recorded along a closed surface surrounding the object of interest, and we propose a decomposition method to separate such data for arbitrary curved surfaces. The MDD results consist of the Green's functions between any pair of points on the closed recording surface, fully sampling the scattered field. We apply the MDD algorithm to post-process laboratory data acquired in a two-dimensional acoustic waveguide to characterize the wavefield scattering related to a rigid steel block while removing the scattering imprint of the domain boundary. The experimental results are validated with synthetic simulations, corroborating that MDD is an effective and general method to obtain the experimentally desired Green's functions for arbitrary inhomogeneous scatterers. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The Green's function retrieval in media with horizontal boundaries usually only considers the extraction of direct and reflected waves but ignores the virtual head waves, which have been observed experimentally from ocean ambient noise and used to invert for geometric and environmental parameters. This paper derives the extraction of virtual head waves from ocean ambient noise using a vertically spaced sensor pair in a Pekeris waveguide. Ocean ambient noise in the water column is a superposition of direct, reflected, and head waves. The virtual head waves are produced by the cross-correlations between head waves and either reflected waves or other head waves. The locations of sources that contribute to the virtual head waves are derived based on the method of stationary phase. It is the integration over time of contributions from these sources that makes the virtual head waves observable. The estimation of seabed sound speed with virtual head waves using a vertical line array is also demonstrated. The slope of the virtual head waves is different from that of direct and reflected waves in the virtual source gather; it is therefore possible to constructively stack the virtual head waves. The predictions are verified with simulations. [ABSTRACT FROM AUTHOR]

A theoretical method for estimating the Green's function between two points in an acoustic waveguide was proposed using a vertical source array that spans sufficient waveguide depth [Roux and Fink, J. Acoust. Soc. Am. 113, 1406–1416 (2003)]. This paper shows that by reversing the role of sources and receivers, the Green's function between two ships (sources) can be extracted using a vertical receiver array with a limited aperture. First, the Green's functions from each ship are estimated along the array via blind deconvolution. Then the Green's function between two ships is obtained by either correlation or convolution of the individual Green's functions summed over the array, depending on the array position with respect to the ships. The feasibility of extracting Green's functions between ships of opportunity radiating random broadband (100–500 Hz) noise is demonstrated using a 56.25-m aperture vertical array in approximately 100-m shallow water. [ABSTRACT FROM AUTHOR]

Shear wave elasticity imaging (SWEI) uses an acoustic radiation force to generate shear waves, and then soft tissue mechanical properties are obtained by analyzing the shear wave data. In SWEI, the shear wave speed is often estimated with time-of-flight (TOF) calculations. To characterize the errors produced by TOF calculations, three-dimensional (3D) simulated shear waves are described by time-domain Green's functions for a Kelvin-Voigt model evaluated for multiple combinations of the shear elasticity and the shear viscosity. Estimated shear wave speeds are obtained from cross correlations and time-to-peak (TTP) calculations applied to shear wave particle velocities and shear wave particle displacements. The results obtained from these 3D shear wave simulations indicate that TTP calculations applied to shear wave particle displacements yield effective estimates of the shear wave speed if noise is absent, but cross correlations applied to shear wave particle displacements are more robust when the effects of noise and shear viscosity are included. The results also show that shear wave speeds estimated with TTP methods and cross correlations using shear wave particle velocities are more sensitive to increases in shear viscosity and noise, which suggests that superior estimates of the shear wave speed are obtained from noiseless or noisy shear wave particle displacements. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, a deep-learning-based method for sound field reconstruction is proposed. The possibility to reconstruct the magnitude of the sound pressure in the frequency band 30–300 Hz for an entire room by using a very low number of irregularly distributed microphones arbitrarily arranged is shown. Moreover, the approach is agnostic to the location of the measurements in the Euclidean space. In particular, the presented approach uses a limited number of arbitrary discrete measurements of the magnitude of the sound field pressure in order to extrapolate this field to a higher-resolution grid of discrete points in space with a low computational complexity. The method is based on a U-net-like neural network with partial convolutions trained solely on simulated data, which itself is constructed from numerical simulations of Green's function across thousands of common rectangular rooms. Although extensible to three dimensions and different room shapes, the method focuses on reconstructing the two-dimensional plane of a rectangular room from measurements of the three-dimensional sound field. Experiments using simulated data together with an experimental validation in a real listening room are shown. The results suggest a performance which may exceed conventional reconstruction techniques for a low number of microphones and computational requirements. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Empirical Green's functions are obtained for 31 paths in a highly dynamic coastal ocean by cross-correlation of ambient and shipping noise recorded in the Shallow Water 2006 experiment on a horizontal line array and a single hydrophone about 3600 m from the array. Using time warping, group speeds of three low-order normal modes are passively measured in the 10–110 Hz frequency band and inverted for geoacoustic parameters of the seabed. It is demonstrated that, despite very strong sound speed variations caused by nonlinear internal waves, noise interferometry can be successfully used to acoustically characterize the seafloor on a continental shelf. [ABSTRACT FROM AUTHOR]

Ultrasound computed tomography (USCT) is a noninvasive imaging modality that has shown its clinical relevance for breast cancer diagnostics. As opposed to traveltime inversions, waveform-based inversions can exploit the full content of ultrasound data, thereby providing increased resolution. However, this is only feasible when modeling the full physics of wave propagation, accounting for 3D effects such as refraction and diffraction, and this comes at a significant computational cost. To mitigate this cost, a crosstalk-free source encoding method for explicit time-domain solvers is proposed. The gradient computation is performed with only two numerical "super" wave simulations, independent of the number of sources and receivers. Absence of crosstalk is achieved by considering orthogonal frequencies attributed to each source. By considering "double-difference" measurements, no a priori knowledge of the source time function is required. With this method, full-physics based 3D waveform inversions can be performed within minutes using reasonable computational resources, fitting clinical requirements. [ABSTRACT FROM AUTHOR]

The broadband interference structure of sound propagation in a waveguide can be described by the waveguide invariant, β, that manifests itself as striations in the frequency-range plane. At any given range (r), there is a striation pattern in frequency (ω) , which is the Fourier transform of the multipath impulse response (or Green's function). Moving to a different range (r + Δ r) , the same pattern is retained but is either stretched or shrunken in ω in proportion to Δ r , according to Δ ω / ω = β (Δ r / r). The waveguide invariant property allows a time-domain Green's function observed at one location, g(r,t), to be extrapolated to adjacent ranges with a simple analytic relation: g (r + Δ r , t) ≃ g (r , α (t − Δ r / c)) , where α = 1 + β (Δ r / r) and c is the nominal sound speed of 1500 m/s. The relationship is verified in terms of range variation of the eigenray arrival times via simulations and by using real data from a ship of opportunity radiating broadband noise (200–900 Hz) in a shallow-water environment, where the steep-angle arrivals contributing to the acoustic field have β ≈ 0.92. [ABSTRACT FROM AUTHOR]

Ambient noise was recorded continuously for 9 months by two horizontal arrays deployed in shallow water with a horizontal separation of approximately 0.5 km. Stable empirical Green's functions (EGFs) were extracted from ambient noise correlations between the two arrays. The EGFs have three distinct envelopes which correspond to the head waves, direct waves, and surface-reflected waves. The arrival time of the head wave was almost constant with season. Corresponding simulations were carried out, and implied that the relatively small penetration depth of heat flow is the main reason for the seasonally-invariant head wave speed. [ABSTRACT FROM AUTHOR]

An analytical method has been proposed by using Green's function analysis to find the transmission loss (TL) of a concentrically multi-layered circular dissipative chamber. Each layer of the chamber is filled with a porous acoustic absorptive material and is separated from the adjacent one by a thin perforated screen. A tailored Green's function for this configuration, in the absence of mean flow, is expressed as the summation of eigenfunctions of the central duct. In the analysis, the walls of the chamber are assumed to be acoustically rigid. The cumulative effect of the layers has been incorporated in terms of the reflection coefficient in the eigenfunctions of the central duct. By using the piston analogy approach at the inlet and outlet ports of the chamber, the total velocity potential generated inside the central duct is estimated. Thence, the transfer matrix is evaluated to predict the TL. The results obtained from the current method are in good agreement with the numerical models and available literature. A parametric study has been conducted to investigate the effect of the number of layers, and their arrangement with respect to thickness and flow resistivity, on the acoustic performance of the chamber. [ABSTRACT FROM AUTHOR]

The cross correlation of the underwater noise field recorded at two receivers conveys information about the time-domain Green's function between the two locations, provided that sufficient energy is channeled into the acoustic paths connecting these. The efficiency of this procedure depends on the locations and characteristics of the receivers and noise sources, as well as on the refraction properties of the ocean sound channel. The sensitivity of the finite-frequency noise cross-correlation function with respect to the location and amplitude of the noise sources is studied here, taking into account the refractive features of the ocean environment. The sensitivity kernel describing changes in the cross-correlation envelope due to changes in the noise source distribution is used to highlight noise-source locations with maximum potential impact on the cross-correlation output. [ABSTRACT FROM AUTHOR]

In this paper, the authors introduce an algorithm for locating sound-producing fish in a small rectangular tank that can be used, e.g., in behavioral bioacoustical studies to determine which fish in a group is sound-producing. The technique consists of locating a single sound source in the tank using signals gathered by four hydrophones placed in the tank together with a group of fish under study. The localization algorithm used in this paper is based on a ratio of two spectra ratios: the spectra ratio between the sound pressure measured by hydrophones at two locations and the spectra ratio between the theoretical Green's functions at the same locations. The results are compared to a localization based on image processing technique and with video recordings acquired synchronously with the acoustic recordings. [ABSTRACT FROM AUTHOR]

An investigation of a wavepacket model for free-jet and jet-surface interaction noise was conducted. The source term for the axisymmetric mode was extracted from a Mach 0.9 jet large eddy simulation and employed to adjust the parameters of a simple source model. Streamwise coherence decay, in particular, was considered. The source model was propagated with both the free-field and tailored Green's function for a semi-infinite flat plate positioned at a distance of r/D = 1 from the jet axis. Significant deviations were observed in the prediction of the low-angle directivity of the isolated jet as well as in the reproduction of the characteristics of the source field. However, the effects of trailing edge noise were well reproduced. The installed jet case, at the region dominated by trailing-edge scattering, showed very little sensitivity to the coherence decay, a crucial feature in the isolated jet case. In this sense, the modelling of the installed-jet case proved to be much simpler. [ABSTRACT FROM AUTHOR]

A decomposition of the Navier-Stokes equations is used to identify the equivalent source term for broadband shock-associated noise (BBSAN). An analytical closed-form model to predict BBSAN is developed using an acoustic analogy based on the Navier-Stokes equations. The field-variables are decomposed into the base flow, aerodynamic fluctuations, and acoustic fluctuations. The spectral densities of fluctuating acoustic quantities are obtained by convolving the vector Green's function with the source terms involving the two-point cross-correlation of the aerodynamic quantities. The scaling of the source term with the off-design parameter β = (| M j 2 − M d 2 |) 1 / 2 is compared with experimental results. The base flow is obtained using a Reynolds-averaged Navier-Stokes solution, while the fluctuating statistical quantities are obtained using theoretical and experimental results. This paper identifies the equivalent source of BBSAN based on the scaling analysis and the physical mechanism of shock-associated noise. The identified source term resides within the Navier-Stokes equations without further rearrangement and correlates very highly with BBSAN. Predictions for BBSAN are made at multiple observer angles and nozzle pressure ratios using the identified source term, and these predictions compare favorably with the experimental results. Finally, identification of the source locations in the jet exhaust responsible for BBSAN at different Strouhal numbers is performed. [ABSTRACT FROM AUTHOR]

In a reverberant cavity, when a noise field is sufficiently diffuse, the correlation of the signal measured by two sensors provides an estimation of the Green's function (GF) between them. Here, the convergence of this passive estimation in the case of elastic waves on thin plates is studied. A statistical approach is proposed, which relates the similarity between the cross correlation and the GF to the structural properties of the plate and the number of uncorrelated sources. The analysis is sustained by experimental results obtained on an aluminum plate. This study allows us to evaluate the efficiency of passive structural health monitoring of plate-like structures based on noise correlation. Finally, a most interesting finding shows an absolute upper bound of the signal-to-noise ratio for GF quality reconstruction: 4 N s / 5 , independently of the plate properties. [ABSTRACT FROM AUTHOR]

This work deals with the sound wave propagation modeling in anisotropic and heterogeneous media. The considered scattering problem involves an infinite layer of finite thickness containing an anisotropic fluid whose properties can vary along the layer depth. The specular transmission and reflection of an acoustic plane wave by such a layer is modeled through the state vector formalism for the acoustic fields. This is solved using three different numerical techniques, namely, the transfer matrix method, Peano series, and transfer Green's function. These three methods are compared to demonstrate the convergence of the numerical solutions. Moreover, the implemented numerical procedures allow the authors to retrieve the internal acoustic fields and show their dependency along with the fluid anisotropic properties. Results are presented to illustrate the changes in absorption that can be achieved by tuning the fluid anisotropy as well as the variation of these properties across the depth of the layer. The results presented are in very good agreement across the different methods. Given that many porous materials can be modeled as equivalent fluids, the results presented show the potential offered by such numerical techniques, and can further give more insight into inhomogeneous anisotropic porous materials. [ABSTRACT FROM AUTHOR]

A physical boundary mounted with active sources can cancel acoustic waves arriving at the boundary, and emit synthesized waves into the neighboring medium to fully control the acoustic wavefield in an experimental setup such as a water tank or air-filled cavity. Using the same principles, a physical experiment can be artificially immersed within an extended virtual (numerical) domain so that waves propagate seamlessly between the experimental setup and virtual domain. Such an immersive wave control experiment requires physical monopolar sources on the active boundary. However, real physical sources (e.g., piezoelectric transducers) project waves at middle-to-high sonic frequencies (e.g., 1–20 kHz) that do not fully conform to the theoretically required monopolar radiation pattern; if left uncorrected, this causes controlled wavefields to deviate from those desired in immersive experiments. A method is proposed to compensate for the non-monopole-like radiation patterns of the sources, and can be interpreted physically in terms of Huygens principle. The method is implemented as a pre-computation procedure that modifies the extrapolation Green's functions in the Kirchhoff-Helmholtz integral before the actual experiments take place. Two-dimensional finite-difference simulations show that the processing method can effectively suppress the undesired effect caused by non-monopolar active sources in immersive wave control experiments. [ABSTRACT FROM AUTHOR]

Interferometry of ambient and shipping noise in the ocean provides a way to estimate physical parameters of the seafloor and the water column in an environmentally friendly manner without employing any controlled sound sources. With noise interferometry, two-point cross-correlation functions of noise serve as the probing signals and replace the Green's function measured in active acoustic remote sensing. The amount of environmental information that can be obtained with passive remote sensing and the robustness of the estimates of the seafloor parameters increase when contributions of individual normal modes are resolved in the noise cross-correlation function. Using the data obtained in the 2012 noise-interferometry experiment in the Straits of Florida, dispersion curves of the first four normal modes are obtained in this paper by application of the time-warping transform to noise cross correlations. The passively measured dispersion curves are inverted for unknown geoacoustic properties of the seabed. Resulting thickness of the sediment layer and sound speed are consistent with the geoacoustic models obtained earlier by other means. [ABSTRACT FROM AUTHOR]

A method is presented for numerically determining Green's functions for the purpose of calculating the far-field scattering from objects resting on or buried within the seafloor. To obtain the far-field scattering, initial evaluation of the three-dimensional near-field solution is required, through finite element analysis or other means. The Green's function and its spatial derivatives are then numerically evaluated for input into the Helmholtz-Kirchhoff integral, yielding the far-field scattering solution. This numerical technique determines the Green's function directly and avoids requiring analytic forms of Green's functions, which may be difficult or time consuming to evaluate for complex environments. This paper demonstrates the effectiveness of applying the numerical Green's function determination technique in conjunction with near-field results from finite element models to determine the far-field scattering for various elastic targets in free-field and flat seafloor environments. The method may be generalizable to arbitrary targets at complicated interfaces, incorporating interface roughness, layering, and volume inhomogeneities. [ABSTRACT FROM AUTHOR]

The Chen-Holm and Treeby-Cox wave equations are space-fractional partial differential equations that describe power law attenuation of the form α (ω) ≈ α 0 | ω | y . Both of these space-fractional wave equations are causal, but the phase velocities differ, which impacts the shapes of the time-domain Green's functions. Exact and approximate closed-form time-domain Green's functions are derived for these space-fractional wave equations, and the resulting expressions contain symmetric and maximally skewed stable probability distribution functions. Numerical results are evaluated with ultrasound parameters for breast and liver at different times as a function of space and at different distances as a function of time, where the reference calculations are computed with the Pantis method. The results show that the exact and approximate time-domain Green's functions contain both outbound and inbound propagating terms and that the inbound component is negligible a short distance from the origin. Exact and approximate analytical time-domain Green's functions are also evaluated for the Chen-Holm wave equation with power law exponent y = 1. These comparisons demonstrate that single term analytical expressions containing stable probability densities provide excellent approximations to the time-domain Green's functions for the Chen-Holm and Treeby-Cox wave equations. [ABSTRACT FROM AUTHOR]

Acoustic imaging methods often ignore multiple scattering. This leads to false images in cases where multiple scattering is strong. Marchenko imaging has recently been introduced as a data-driven way to deal with internal multiple scattering. Given the increasing interest in non-reciprocal materials, both for acoustic and electromagnetic applications, a modification to the Marchenko method is proposed for imaging such materials. A unified wave equation is formulated for non-reciprocal materials, exploiting the similarity between acoustic and electromagnetic wave phenomena. This unified wave equation forms the basis for deriving reciprocity theorems that interrelate wave fields in a non-reciprocal medium and its complementary version. Next, these theorems are reformulated for downgoing and upgoing wave fields. From these decomposed reciprocity theorems, representations of the Green's function inside the non-reciprocal medium are derived in terms of the reflection response at the surface and focusing functions inside the medium and its complementary version. These representations form the basis for deriving a modified version of the Marchenko method to retrieve the wave field inside a non-reciprocal medium and to form an image, free from artefacts related to multiple scattering. The proposed method is illustrated at the hand of the numerically modeled reflection response of a horizontally layered medium. [ABSTRACT FROM AUTHOR]