Transmission mode time-reversal super-resolution imaging

The theory of time-reversal super-resolution imaging of point targets embedded in a reciprocal background medium [A. J. Devaney, "Super-resolution imaging using time-reversal and MUSIC," J. Acoust. Soc. Am. (to be published)] is generalized to the case where the transmitter and receiver sensor arrays need not be coincident and for cases where the background medium can be nonreciprocal. The new theory developed herein is based on the singular value decomposition of the generalized multistatic data matrix of the sensor system rather than the standard eigenvector/eigenvalue decomposition of the time-reversal matrix as was employed in the above-mentioned work and other treatments of time-reversal imaging [Prada, Thomas, and Fink, "The iterative time reversal process: Analysis of the convergence," J. Acoust. Soc. Am. 97, 62 (1995); Prada et al., "Decomposition of the time reversal operator: Detection and selective focusing on two scatterers," J. Acoust. Soc. Am. 99, 2067 (1996)]. A generalized multiple signal classification (MUSIC) algorithm is derived that allows super-resolution imaging of both well-resolved and non-well-resolved point targets from arbitrary sensor array geometries. MUSIC exploits the orthogonal nature of the scatterer and noise subspaces defined by the singular vectors of the multistatic data matrix to form scatterer images. The time-reversal/MUSIC algorithm is tested and validated in two computer simulations of offset vertical seismic profiling where the sensor sources are aligned along the earth's surface and the receiver array is aligned along a subsurface borehole. All results demonstrate the high contrast, high resolution imaging capabilities of this new algorithm combination when compared with "classical" backpropagation or field focusing. Above and beyond the application of seismo-acoustic imaging, the time-reversal super-resolution theory has applications in ocean acoustics for target location, and ultrasonic nondestructive evaluation of parts.     

Including dispersion and attenuation directly in the time domain for wave propagation in isotropic media

When sound propagates in a lossy fluid, causality dictates that in most cases the presence of attenuation is accompanied by dispersion. The ability to incorporate attenuation and its causal companion, dispersion, directly in the time domain has received little attention. Szabo [J. Acoust. Soc. Am. 96, 491-500 (1994)] showed that attenuation and dispersion in a linear medium can be accounted for in the linear wave equation by the inclusion of a causal convolutional propagation operator that includes both phenomena. Szabo's work was restricted to media with a power-law attenuation. Waters et al. [J. Acoust. Soc. Am. 108, 2114-2119 (2000)] showed that Szabo's approach could be used in a broader class of media. Direct application of Szabo's formalism is still lacking. To evaluate the concept of the causal convolutional propagation operator as introduced by Szabo, the operator is applied to pulse propagation in an isotropic lossy medium directly in the time domain. The generalized linear wave equation containing the operator is solved via a finite-difference-time-domain scheme. Two functional forms for the attenuation often encountered in acoustics are examined. It is shown that the presence of the operator correctly incorporates both, attenuation and dispersion.     

Modeling of nonlinear ultrasound propagation in tissue from array transducers

A computationally efficient model capable of simulating finite-amplitude ultrasound beam propagation in water and in tissue from phased linear arrays and other transducers of arbitrary quasiplanar geometry is described. It is based on a second-order operator splitting approach [Tavakkoli et al., J. Acoust. Soc. Am. 104, 2061-2072 (1998)], with a fractional step-marching scheme, whereby the effects of diffraction, attenuation, and nonlinearity can be computed independently over incremental steps. This approach is an extension to that of Christopher and Parker [J. Acoust. Soc. Am. 90, 507-521; 90, 488-499 (1991)], wherein linear and nonlinear effects are propagated separately over incremental steps, and the computation of the diffractive substeps are based on an angular spectrum technique with a modified sampling scheme for accurate and efficient implementation of diffractive propagation from nonradially symmetric sources. Results of the model are compared with published data. Predicted field profiles for nonlinear propagation in tissue from realistic array transducers using the pulse inversion method are presented.     

Source ranging with minimal environmental information using a virtual receiver and waveguide invariant theory

A method is presented for estimating the range of an unknown broadband acoustic source in a waveguide, using a vertical array and a signal sample from another broadband source at a known location relative to the array. The method requires no modeling of the acoustic field, and little to no environmental information for flat bathymetries. Waveguide invariant theory [e.g., D'Spain and Kuperman, J. Acoust. Soc. Am 106, 2454-2468 (1999)] is applied to the "virtual receiver" [Siderius et al., J. Acoust. Soc. Am. 102, 3439-3449 (1997)] to create a "virtual aperture" (VA). In effect, the method effectively converts a source at known range r(g) into a continuum of receivers lying between ranges (1 +/- alpha/beta)*r(g), where beta is a scalar parameter called the acoustic invariant, and alpha approximately 0.1. This effective displacement is achieved by correlating the known source field, measured at frequency component omega, with the unknown source field, measured at frequency component omega + omegas. When the VA output is plotted as a function of omega and omegas, the slope of the resulting correlation contours yields the unknown source range. The concept is illustrated via both simulation and analysis of data collected from a pseudo-random noise source with 75-150-Hz bandwidth during SWellEx-3, a shallow water experiment conducted off the San Diego coast. The virtual aperture can be reformulated for range-dependent environments, if adiabatic propagation assumptions are valid, and if the bathymetry surrounding the array is known.     

Characterization of subwavelength elastic cylinders with the decomposition of the time-reversal operator: theory and experiment

The decomposition of the time-reversal operator provides information on the scattering medium. It has been shown [Chambers and Gautesen, J. Acoust. Soc. Am. 109, 2616-2624 (2001)] that a small spherical scatterer is in general associated with four eigenvalues and eigenvectors of the time-reversal operator. In this paper, the 2D problem of scattering by an elastic cylinder, imbedded in water, measured by a linear array of transducers is considered. In this case, the array response matrix has three nonzero singular values. Experimental results are obtained with linear arrays of transducers and for wires of different diameters smaller that the wavelength. It is shown how the singular value distribution and the singular vectors depend on the elastic velocities cL, cT, the density rho of each wire, and on the density rho0 and velocity c0 of the surrounding fluid. These results offer a new perspective towards solution of the inverse problem by determining more than scattering contrast using conventional array processing like that used in medical ultrasonic imaging.     

Compilation of empirical ultrasonic properties of mammalian tissues. II

The compilation of the literature on ultrasonic propagation properties of mammalian tissues [J. Acoust. Soc. Am. 64, 423 (1978)] is continued with the addition of 45 papers yielding over 700 lines of parametric data.     

The acoustic reflex threshold in aging ears

This study investigates the controversy regarding the influence of age on the acoustic reflex threshold for broadband noise, 500-, 1000-, 2000-, and 4000-Hz activators between Jerger et al. [Mono. Contemp. Audiol. 1 (1978)] and Jerger [J. Acoust. Soc. Am. 66 (1979)] on the one hand and Silman [J. Acoust. Soc. Am. 66 (1979)] and others on the other. The acoustic reflex thresholds for broadband noise, 500-, 1000-, 2000-, and 4000-Hz activators were evaluated under two measurement conditions. Seventy-two normal-hearing ears were drawn from 72 subjects ranging in age from 20-69 years. The results revealed that age was correlated with the acoustic reflex threshold for BBN activator but not for any of the tonal activators; the correlation was stronger under the 1-dB than under the 5-dB measurement condition. Also, the mean acoustic reflex thresholds for broadband noise activator were essentially similar to those reported by Jerger et al. (1978) but differed from those obtained in this study under the 1-dB measurement condition.     

On boundary conditions for the diffusion equation in room-acoustic prediction: Theory, simulations, and experiments

This paper proposes a modified boundary condition to improve the room-acoustic prediction accuracy of a diffusion equation model. Previous boundary conditions for the diffusion equation model have certain limitations which restrict its application to a certain number of room types. The boundary condition employing the Sabine absorption coefficient [V. Valeau et al., J. Acoust. Soc. Am. 119, 1504-1513 (2006)] cannot predict the sound field well when the absorption coefficient is high, while the boundary condition employing the Eyring absorption coefficient [Y. Jing and N. Xiang, J. Acoust. Soc. Am. 121, 3284-3287 (2007); A. Billon et al., Appl. Acoust. 69, (2008)] has a singularity whenever any surface material has an absorption coefficient of 1.0. The modified boundary condition is derived based on an analogy between sound propagation and light propagation. Simulated and experimental data are compared to verify the modified boundary condition in terms of room-acoustic parameter prediction. The results of this comparison suggest that the modified boundary condition is valid for a range of absorption coefficient values and successfully eliminates the singularity problem.     

Spectral weighting strategies for sentences measured by a correlational method

Listeners' ability to understand speech in adverse listening conditions is partially due to the redundant nature of speech. Natural redundancies are often lost or altered when speech is filtered, such as done in AI/SII experiments. It is important to study how listeners recognize speech when the speech signal is unfiltered and the entire broadband spectrum is present. A correlational method [R. A. Lutfi, J. Acoust. Soc. Am. 97, 1333-1334 (1995); V. M. Richards and S. Zhu, J. Acoust. Soc. Am. 95, 423-424 (1994)] has been used to determine how listeners use spectral cues to perceive nonsense syllables when the full speech spectrum is present [K. A. Doherty and C. W. Turner, J. Acoust. Soc. Am. 100, 3769-3773 (1996); C. W. Turner et al., J. Acoust. Soc. Am. 104, 1580-1585 (1998)]. The experiments in this study measured spectral-weighting strategies for more naturally occurring speech stimuli, specifically sentences, using a correlational method for normal-hearing listeners. Results indicate that listeners placed the greatest weight on spectral information within bands 2 and 5 (562-1113 and 2807-11,000 Hz), respectively. Spectral-weighting strategies for sentences were also compared to weighting strategies for nonsense syllables measured in a previous study (C. W. Turner et al., 1998). Spectral-weighting strategies for sentences were different from those reported for nonsense syllables.     

Time reversed reverberation focusing in a waveguide

Time reversal mirrors have been applied to focus energy at probe source locations and point scatterers in inhomogeneous media. In this paper, we investigate the application of a time reversal mirror to rough interface reverberation processing in a waveguide. The method is based on the decomposition of the time reversal operator which is computed from the transfer matrix measured on a source-receiver array [Prada et al., J. Acoust. Soc. Am. 99, 2067-2076 (1996)]. In a similar manner, reverberation data collected on a source-receiver array can be filtered through an appropriate temporal window to form a time reversal operator. The most energetic eigenvector of the time reversal operator focuses along the interface at the range corresponding to the filter delay. It is also shown that improved signal-to-noise ratio measurement of the time reversal operator can be obtained by ensonifying the water column with a set of orthogonal array beams. Since these methods do not depend upon a priori environmental information, they are applicable to complex shallow water environments. Numerical simulations with a Pekeris waveguide demonstrate this method.     

Examining the use of a time-varying loudness algorithm for quantifying characteristics of nonlinearly propagated noise (L)

A previous letter by Gee et al. [J. Acoust. Soc. Am. 121, EL1-EL7 (2007)] revealed likely shortcomings in using common, stationary (long-term) spectrum-based measures to quantify the perception of nonlinearly propagated noise. Here, the Glasberg and Moore [J. Audio Eng. Soc. 50, 331-342 (2002)] algorithm for time-varying loudness is investigated. Their short-term loudness, when applied to a shock-containing broadband signal and a phase-randomized signal with equivalent long-term spectrum, does not show a significant difference in loudness between the signals. Further analysis and discussion focus on the possible utility of the instantaneous loudness and the need for additional investigation in this area.     

Optimal adaptive focusing through heterogeneous media with the minimally invasive inverse filter

The inverse filter is a technique used to adaptively focus waves through heterogeneous media. It is based on the inversion of the Green's functions matrix between the M transducers of a focusing array and N control points in the focal area. The inverse filter minimizes the pressure deposited around the focal point. However it is highly invasive, requiring the presence of N transducers or hydrophones in the focal area at the control points' locations to measure the Green's functions. This paper presents a way of reaching the inverse filter's focusing quality with a minimally invasive setup: only one transducer (at the desired focal location) is needed. This minimally invasive inverse filter takes advantage of the fact all the information about the propagation medium can be retrieved from the signals backscattered by the medium towards the focusing array, if the propagation medium is lossless. A numerical simulation is performed to test this minimally invasive inverse filter through a scattering, lossless medium. The focusing quality equals the conventional, highly invasive inverse filter's. The average spatial and temporal contrast is increased by up to 10 dB compared to the time reversal focusing.     

Experimental subwavelength localization of scatterers by decomposition of the time reversal operator interpreted as a covariance matrix

The D.O.R.T. method (French acronym for Decomposition of the Time Reversal Operator) is an active remote sensing technique using arrays of antennas for the detection and localization of scatterers [Prada et at., J. Acoust. Soc. Am. 99, 2067-2076 (1996)]. The analogy between the time reversal operator and the covariance matrix used for classical sources separation in passive remote sensing [Bienvenu et al., IEEE Trans. ASSP 31, 1235-1247 (1983)] is established. Then, an experiment of subwavelength detection and localization of point-like scatterers with a linear array of transducers is presented. Using classical estimators in reception like Maximum-Likelihood and Multiple Signal Characterization (MUSIC), two point-like scatterers separated by lambda/3 and placed at 100lambda from the array of transducers are resolved. In these experiments, the role of multiple scattering and the existence of additional eigenvectors associated with dipolar and monopolar radiation of each scatterer is discussed.     

Comment on "The directionality of acoustic T-phase signals from small magnitude submarine earthquakes" [J. Acoust. Soc. Am. 119, 3669-3675 (2006)

In a recent paper, Chapman and Marrett [J. Acoust. Soc. Am. 119, 3669-3675 (2006)] examined the tertiary (T-) waves associated with three subduction-related earthquakes within the South Fiji Basin. In that paper it is argued that acoustic energy is radiated into the sound channel by downslope propagation along abyssal seamounts and ridges that lie distant to the epicenter. A reexamination of the travel-time constraints indicates that this interpretation is not well supported. Rather, the propagation model that is described would require the high-amplitude T-wave components to be sourced well to the east of the region identified, along a relatively flat-lying seafloor.     

An iterative implementation of rotated coordinates for inverse problems

A generalized inversion method is presented that uses a rotated coordinates technique [Collins and Fishman, J. Acoust. Soc. Am. 98, 1637-1644 (1995)] in simulated annealing to invert for both the location of an acoustic source and parameters that describe the ocean seabed. The rotated coordinates technique not only aids in the inversion process but also indicates the coupling of the source and environmental parameters and the relative sensitivities of the cost function to changes in the various parameters. The information obtained from the rotated coordinates provides insights into how the inversion problem can be effectively decoupled. An iterative process consisting of multiple simulated annealing runs that each use a different set of rotated coordinates is demonstrated. This multistep algorithm is called systematic decoupling using rotated coordinates and is especially helpful when inverting for a large number of unknown parameters. The cost function minimized in the inversion algorithm is model-data cross-hydrophone spectra summed coherently over frequency and receiver pairs. The results of applying this inversion method to simulated data are presented in this paper.     

On the interpretability of speech/nonspeech comparisons: a reply to Fowler

Fowler [J. Acoust. Soc. Am. 88, 1236-1249 (1990)] makes a set of claims on the basis of which she denies the general interpretability of experiments that compare the perception of speech sounds to the perception of acoustically analogous nonspeech sound. She also challenges a specific auditory hypothesis offered by Diehl and Walsh [J. Acoust. Soc. Am. 85, 2154-2164 (1989)] to explain the stimulus-length effect in the perception of stops and glides. It will be argued that her conclusions are unwarranted.     

Parabolic equation solution of seismo-acoustics problems involving variations in bathymetry and sediment thickness

Recent improvements in the parabolic equation method are combined to extend this approach to a larger class of seismo-acoustics problems. The variable rotated parabolic equation [J. Acoust. Soc. Am. 120, 3534-3538 (2006)] handles a sloping fluid-solid interface at the ocean bottom. The single-scattering solution [J. Acoust. Soc. Am. 121, 808-813 (2007)] handles range dependence within elastic sediment layers. When these methods are implemented together, the parabolic equation method can be applied to problems involving variations in bathymetry and the thickness of sediment layers. The accuracy of the approach is demonstrated by comparing with finite-element solutions. The approach is applied to a complex scenario in a realistic environment.     

Target detection and location with ambient noise

By placing a vertical array in an ambient noise field and forming an upward and a downward beam one obtains two time series which can be cross correlated to reveal a subbottom profile of the seabed [Siderius et al., J. Acoust. Soc. Am. 120, 1315-1323 (2006)]. Here the cross-correlation approach is applied to the location in range and bearing of a point target. An experiment was designed using floats and weights mounted (and dismounted) on the same cable as the vertical array. Careful measurements were made of the location of all likely floats, ballast weights, array terminations, and so on. After suitable coherent averaging, peaks were seen at delays (correlation offsets) agreeing with the reflector positions and were shown to be absent when reflectors were removed. A trivial extension of the theory developed in Harrison and Siderius [J. Acoust. Soc. Am. 123, 1282-1296 (2008)] is used to explain the rough amplitudes of the reflections. The approach differs from "acoustic daylight" principally in having a capability to determine a target range.     

Frequency-domain wave equation and its time-domain solutions in attenuating media

Our purpose in this paper is to describe the wave propagation in media whose attenuation obeys a frequency power law. To achieve this, a frequency-domain wave equation was developed using previously derived causal dispersion relations. An inverse space and time Fourier transform of the solution to this algebraic equation results in a time-domain solution. It is shown that this solution satisfies the convolutional time-domain wave equation proposed by Szabo [J. Acoust. Soc. Am. 96, 491-500 (1994)]. The form of the convolutional loss operator contained in this wave equation is obtained. Solutions representing the propagation of both plane sinusoidal and transient waves propagating in media with specific power law attenuation coefficients are investigated as special cases of our solution. Using our solution, comparisons are made for transient one-dimensional propagation in a medium whose attenuation is proportional to frequency with recently obtained numerical solutions of Szabo's equation. These show good agreement.