Acoustic Green Research Articles

A noise-based high-resolution time-reversal method for acoustic defect localization in water pipes.

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.

Volume Flow Rate Estimation for Small Explosions at Mt. Etna, Italy, From Acoustic Waveform Inversion

AbstractRapid assessment of the volume and the rate at which gas and pyroclasts are injected into the atmosphere during volcanic explosions is key to effective eruption hazard mitigation. Here, we use data from a dense infrasound network deployed in 2017 on Mt. Etna, Italy, to estimate eruptive volume flow rates (VFRs) during small gas‐and‐ash explosions. We use a finite‐difference time‐domain approximation to compute the acoustic Green's functions and perform a full waveform inversion for a multipole source, combining monopole and horizontal dipole terms. The inversion produces realistic estimates of VFR, on the order of 4 × 104 m3/s and well‐defined patterns of source directivity. This is the first application of acoustic waveform inversion at Mt. Etna. Our results demonstrate that acoustic waveform inversion is a mature and robust tool for assessment of source parameters and holds potential as a tool to provide rapid estimates of VFR in near real time.

Sound from aeroelastic vortex-fibre interactions.

The motion of a line vortex moving past a one-dimensional flexible fibre is examined theoretically. A Schwarz-Christoffel conformal mapping enables the analytical solution of the potential flow field and its hydrodynamic moment on the flexible fibre, which is composed of a rigid segment constrained to angular motions on a wedge. The hydroelastic coupling of the vortex path and fibre motion affects the noise signature, which is evaluated for the special case of acoustically compact fibres embedded in a half plane. Results from this analysis attempt to address how the coupled interactions between vortical sources and flexible barbules on the upper surface of owl wings may contribute to their acoustic stealth. The analytical formulation is also amenable to application to vortex sound prediction from flexible trailing edges provided that an appropriate acoustic Green's function can be determined. This article is part of the theme issue 'Frontiers of aeroacoustics research: theory, computation and experiment'.

Ray-tracing semiclassical (RTS) low frequency acoustic modeling validated for local and extended reaction boundaries

The recently introduced acoustic ray-tracing semiclassical (RTS) method is validated for a set of practically relevant boundary conditions. RTS is a frequency domain phased geometrical acoustics method which directly reproduces the acoustic Green's function. As previously demonstrated for a rectangular room and weakly absorbing boundaries with a real and frequency-independent impedance, RTS is capable of modeling also the lowest modes of such a room, which makes it a useful method for low-frequency sound field modeling in enclosures. In practice, rooms are bounded with diverse types of materials, resulting in a frequency-dependent, phase-modifying absorption/reflection. In a realistic setting, we test the RTS method with two additional boundary conditions: a local-reaction boundary simulating a resonating absorber and an extended-reaction boundary representing a porous layer backed by a rigid boundary described within the Delany-Bazley-Miki model, as well as a combination thereof. The RTS-modeled spatially dependent pressure response, frequency-band decay curves and reverberation times are compared to those obtained by the finite element method. The RTS results show systematic agreement for all boundary conditions and disclose some interesting particularities of the method.

Rayleigh scattering of a cylindrical sound wave by an infinite cylinder.

Rayleigh scattering, in which the wavelength is large compared to the scattering object, is usually studied assuming plane incident waves. However, full Green's functions are required in a number of problems, e.g., when a scatterer is located close to the ocean surface or the seafloor. This paper considers the Green's function of the two-dimensional problem that corresponds to scattering of a cylindrical wave by an infinite cylinder embedded in a homogeneous fluid. Soft, hard, and impedance cylinders are considered. Exact solutions of the problem involve infinite series of products of Bessel functions. Here, simple, closed-form asymptotic solutions are derived, which are valid for arbitrary source and receiver locations outside the cylinder as long as its diameter is small relative to the wavelength. The scattered wave is given by the sum of fields of three linear image sources. The viability of the image source method was anticipated from known solutions of classical electrostatic problems involving a conducting cylinder. The asymptotic acoustic Green's functions are employed to investigate reception of low-frequency sound by sensors mounted on cylindrical bodies.

A single-sided representation for passive and active Green's function retrieval, time-reversal acoustics, and holographic imaging

The homogeneous Green's function, defined as the superposition of the Green's function and its time-reversal, plays an important role in a variety of acoustic applications, such as passive and active acoustic Green's function retrieval, seismic interferometry, time-reversal acoustics, and holographic imaging. An exact representation of the homogeneous Green's function originates from the field of optical holographic imaging (Porter, 1970, JOSA). In this representation, the homogeneous Green's function between two points A and B is expressed as an integral along an arbitrary boundary enclosing A and B. This implies that the Green's function between A and B can be retrieved from measurements carried out at a closed boundary, or, via reciprocity, from passive observations at A and B of the responses to sources on a closed boundary. In practical situations, the closed-boundary integral usually needs to be approximated by an open-boundary integral. This can lead to significant artifacts in the retrieved Green's function. I will discuss a new, single-sided, representation of the homogeneous Green's function, which obviates the need for omnidirectional access. Like the classical closed-boundary representation, this new single-sided representation fully accounts for multiple scattering. I will indicate applications of this new representation in the aforementioned fields.

The acoustic Green's function for swirling flow in a lined duct

This paper considers the acoustic field inside an annular duct carrying mean axial and swirling flow and with either acoustically hard or lined walls. The particular aim is to compute the Green's function, which is required for predicting the noise generated by known acoustic sources, both approximately and numerically. Asymptotic approximations for first the eigenmodes and then the Green's function are derived in the realistic limit of high reduced frequency, which are found to agree very favourably with results determined numerically, even for relatively modest frequencies. Using a blend of uniform WKB asymptotics and numerics, singular cases in which multiple turning points are present are treated, allowing computation of accurate results across a very wide range of parameter values and flows.

Ocean remote sensing with acoustic daylight: Lessons from experiments in the Florida Straits

Ambient and shipping noise in the ocean provides acoustic illumination, which can be used, similarly to daylight in the atmosphere, to characterize the environment. Phase information, which is particularly sensitive to sound speed variations and current velocity, can be retrieved from noise observations by the process known as noise interferometry. Approximations to acoustic Green's functions, which describe sound propagation between two locations, are estimated by cross-correlating time series of diffuse noise measured at those locations. Noise-interferometry-based approximations to Green's functions can be used as the basis for a variety of inversion algorithms, thereby providing a purely passive alternative to active-source ocean acoustic remote sensing. This paper gives an overview of results from noise interferometry experiments conducted in the Florida Straits at 100 m depth in December 2012, and at 600 m depth in September/October 2013. Under good conditions for noise interferometry, estimates of cross-correlation functions are shown to allow one to perform advanced phase-coherent signal processing techniques to: perform waveform inversions; estimate currents by exploiting nonreciprocity; perform time-reversal/back-propagation calculations; and investigate modal dispersion using time-warping techniques. Conditions which are favorable for noise interferometry are identified and discussed. [Work supported by NSF and ONR.]

Ray-trace modeling of acoustic Green's function based on the semiclassical (eikonal) approximation.

The Green's function (GF) for the scalar wave equation is numerically constructed by an advanced geometric ray-tracing method based on the eikonal approximation related to the semiclassical propagator. The underlying theory is first briefly introduced, and then it is applied to acoustics and implemented in a ray-tracing-type numerical simulation. The so constructed numerical method is systematically used to calculate the sound field in a rectangular (cuboid) room, yielding also the acoustic modes of the room. The simulated GF is rigorously compared to its analytic approximation. Good agreement is found, which proves the devised numerical approach potentially useful also for low frequency acoustic modeling, which is in practice not covered by geometrical methods.

Waveform inversion of acoustic waves for explosion yield estimation

AbstractWe present a new waveform inversion technique to estimate the energy of near‐surface explosions using atmospheric acoustic waves. Conventional methods often employ air blast models based on a homogeneous atmosphere, where the acoustic wave propagation effects (e.g., refraction and diffraction) are not taken into account, and therefore, their accuracy decreases with increasing source‐receiver distance. In this study, three‐dimensional acoustic simulations are performed with a finite difference method in realistic atmospheres and topography, and the modeled acoustic Green's functions are incorporated into the waveform inversion for the acoustic source time functions. The strength of the acoustic source is related to explosion yield based on a standard air blast model. The technique was applied to local explosions (<10 km) and provided reasonable yield estimates (<∼30% error) in the presence of realistic topography and atmospheric structure. The presented method can be extended to explosions recorded at far distance provided proper meteorological specifications.

Acoustic radiation analysis for a control domain based on Green's function

The acoustic radiation problem in the control domain with complex boundaries is investigated. Acoustic Green's function for acoustic point sources in the control domain was obtained by using conformal transformation theory. The expression of the acoustic radiation function for the control domain was derived. The acoustic radiation characteristics of a pulsating sphere in a quarter-infinite domain and numerical simulations were compared to illustrate the effects of the boundary characteristic, location, and radiation frequency on acoustic radiation power and acoustic directivity. This study provides a new method to analyze the acoustic radiation problem with complex boundaries.

Acoustic Green's function extraction from ambient noise in a coastal ocean environment

AbstractWe report on the results of an underwater acoustic field experiment conducted in December 2012 on the continental shelf off the Florida Keys in water of approximately 100 m depth. Ambient noise was recorded concurrently on three moored near‐bottom instruments with horizontal separations of approximately 5 km, 10 km, and 15 km. We focus in this letter on instrument pairs with 5 km and 10 km separations. Consistent with theoretical predictions, coherent sums of many realizations of cross correlations of ambient noise records at two measurement locations are shown to yield approximations to deterministic acoustic Green's functions that describe propagation between those two locations. The results presented demonstrate the feasibility of extracting information suitable for use in tomographic inversions from measurements of underwater acoustic ambient noise.

Near-Field Representations of the Acoustic Green's Function in a Shallow Ocean with Infinite Elastic Seabed

In this paper, we show how to construct acoustic Green's functions for a water column atop an infinite elastic seabed using a generalization of the method by Ahluwalia and Keller.6Our goal is to obtain a representation of the acoustic Green's function which is valid in the near field. Such a representation is useful in the investigation of the inverse shape problem using the methodology we pioneered for waveguides with reflecting seabeds.

Acoustic noise interferometry in the Straits of Florida at 100 m depth: A ray-based interpretation

Cross-correlation function of ambient and shipping noise recorded simultaneously by two hydrophones provides an estimate of the acoustic Green's function, which describes deterministic sound propagation between the hydrophones and can be used to estimate physical parameters of the water column and seafloor. This paper presents results of an experimental investigation of acoustic noise interferometry in 100 m-deep water in the Straits of Florida. Acoustic noise was recorded continuously for about six days at three points near the seafloor. Coherent acoustic arrivals are successfully identified in the 20–70 Hz frequency band for pairs of hydrophones separated by ranges of 5.0 and 9.8 km. The measured noise cross-correlation functions are compared to ray-based simulations of Green's functions, with generally good agreement between correlation functions and simulations. Ray-based simulations are shown to reproduce multipath features of the measured correlation functions, which are due to multiple surface and bottom reflections. The feasibility of passive acoustic remote sensing using a few hydrophones in a shallow-water waveguide will be discussed. [Work supported by NSF, ONR, and NAVAIR.]

Spectral decompositions and nonnormality of boundary integral operators in acoustic scattering

Understanding the spectral properties of boundary integral operators in acoustic scattering has important practical implications, such as for the analysis of the stability of boundary element discretizations or the convergence of iterative solvers as the wave number k grows. Yet, little is known about spectral decompositions of the standard boundary integral operators in acoustic scattering. Theoretical results are mainly available on the unit circle, where these operators diagonalize in a simple Fourier basis. In this paper we investigate spectral decompositions for more general smooth domains. Based on the decomposition of the acoustic Green's function in elliptic coordinates, we give spectral decompositions on ellipses. For general smooth domains we show that approximate spectral decompositions can be given in terms of circle Fourier modes transplanted onto the boundary of the domain. An important underlying question is whether the operators are normal. Based on previous numerical investigations it appears that the standard boundary integral operators are normal only when the domain is a ball and here we prove that this is indeed the case for the acoustic single layer potential. We show that the acoustic single, double and conjugate double layer potential are normal in a scaled inner product on the ellipse. On more general smooth domains the operators can be split into a normal component plus a smooth perturbation. Numerical computations of pseudospectra are presented to demonstrate the nonnormal behaviour on general domains.

A hierarchical mixture model for sparse broadband scattering functions between moving platforms

A hierarchical mixture model is considered for sparse broadband acoustic Green's functions [J. Acoust. Soc. Am. 130, 2346, Canadian Acoust. 40(3)]. Such a mixture model can be employed to match arbitrary second order statistics of a channel over time-bandwidth and angle. The model matches these statistics while simultaneously admitting the degree of sparsity necessary to capture propagation between moving platforms through the ocean waveguide. The uppermost stage of the hierarchy is specified by a mean bulk relative platform speed. Conditioned on this is a structured field of beta distributions associated with the probabilities of ensonified paths over beam-Doppler and frequency. The mixture model of the response is built from Bernoulli indicator variables whose probabilities are drawn from the field of betas. Posterior mean and variance are reviewed and used in an underwater acoustic receiver structure to replace Kalman like estimators of response as well as phase looked loop structures for symbol timing. The performance in terms of mean squared error is 10 dB lower than conventional Wiener filtering schemes when the channel response is significantly sparse. Reduction of this margin occurs as either sparsity or SNR is degraded. This degradation in performance is quantified under a range of sparsity constraints associated with the beta variates. [Work supported by the Naval Innovative Science and Engineering Program and the Office of Naval Research.]

Rayleigh scattering of a spherical sound wave

Acoustic Green's functions for a homogeneous medium with an embedded spherical obstacle arise in analyses of scattering by objects on or near an interface, radiation by finite sources, sound attenuation in and scattering from clouds of suspended particles, etc. An exact solution of the problem of diffraction of a monochromatic spherical sound wave on a sphere is given by an infinite series involving products of Bessel functions and Legendre polynomials. In this paper, a simple, closed-form solution is obtained for scattering by a sphere with a radius that is small compared to the wavelength. Soft, hard, impedance, and fluid obstacles are considered. The solution is valid for arbitrary positions of the source and receiver relative to the scatterer. Low-frequency scattering is shown to be rather sensitive to boundary conditions on the surface of the obstacle. Low-frequency asymptotics of the scattered acoustic field are extended to transient incident waves. The asymptotic expansions admit an intuitive interpretation in terms of image sources and reduce to classical results in appropriate limiting cases.

Emergence of Acoustic Green's Functions from Time Averages of Ambient Noise

The emergence of deterministic Green's functions from cross-correlation of ambient noise is the physical basis for a number of passive remote sensing techniques. The data-accumulation time necessary for the Green's function emergence is of critical significance for the feasibility and implementation of the passive techniques. This paper re-examines calculation of the necessary data-accumulation times. Previously published estimates are extended to more general ambient noise fields and source-receiver geometries. The emergence time calculation is performed for arbitrary anisotropy of the noise field generated by random acoustic noise sources located on a surface or on a curve. The results apply to a general case of an inhomogeneous, moving or motionless medium with time-independent parameters. It is shown that in certain situations the emergence time estimates are influenced by the geometry (dimensionality) of the noise sources' layout, and not necessarily by the dimensionality of the propagation medium. A simpler technique using basic statistical principles is suggested for calculating the emergence time under rather general assumptions.

Crosscorrelation kernels in acoustic Green's function retrieval by wavefield correlation for point sources on a plane and a sphere

SUMMARY The far-field approximation is commonly assumed in the derivation of Green's function retrieval by wavefield correlation using reciprocity theorems. This approximation can result in erroneous amplitude of the retrieved seismic phases and generate artificial arrivals. In an open system, we show that the far-field approximation can be removed by the exact integral equation method and this leads to the crosscorrelation kernel. In previous work, kernels in 2-D space had been explicitly constructed. With the kernel, we can construct the Green's function by crosscorrelation even when the sources are not in the far field. Here we extended the 2-D case to 3-D for acoustic waves for point sources on a plane and on a sphere. For the spherical case, the kernel is expressed by spherical harmonics and it degenerates to the Dirac Delta distribution under the high-frequency case; however, for a fixed frequency, if we increase the radius of the sphere, it reduces to that of the plane boundary.

True amplitude imaging by inverse generalized Radon transform based on Gaussian beam decomposition of the acoustic Green's function

True amplitude migration is one of the most important procedures of seismic data processing. As a rule it is based on the decomposition of the velocity model of the medium into a known macrovelocity component and its sharp local perturbations to be determined. Under this decomposition the wavefield can be considered as the superposition of an incident and reflected/scattered waves. The single scattering approximation introduces the linear integral operator that connects the sharp local perturbations of the macrovelocity model with the multishot/multioffset data formed from reflected/scattered waves. We develop the pseudoinverse of this operator using the Gaussian beam based decomposition of acoustic Green's functions. The computation of this pseudoinverse operator is done pointwise by shooting Gaussian beams from the target area towards the acquisition system. The numerical implementation of the pseudoinverse operator was applied to the synthetic data Sigsbee2A. The results obtained demonstrate the high quality of the true amplitude images computed both in the smooth part of the model and under the salt body.