Acoustic Time-reversal Mirror Research Articles

Time reversal technique for gas leakage detection.

The acoustic remote sensing of subsea gas leakage traditionally uses sonars as active acoustic sensors and hydrophones picking up the sound generated by a leak as passive sensors. When gas leaks occur underwater, bubbles are produced and emit sound at frequencies intimately related to their sizes. The experimental implementation of an acoustic time-reversal mirror (TRM) is now well established in underwater acoustics. In the basic TRM experiment, a probe source emits a pulse that is received on an array of sensors, time reversed, and re-emitted. After time reversal, the resulting field focuses back at the probe position. In this study, a method for enhancing operation of the passive receiving system has been proposed by using it in the regime of TRM. Two factors, the local character of the acoustic emission signal caused by the leakage and a resonant nature of the bubble radiation at their birth, make particularly effective scattering with the conjugate wave (CW). Analytical calculations are performed for the scattering of CW wave on a single bubble when CW is formed by bubble birthing wail received on an array, time reversed, and re-emitted. The quality of leakage detection depends on the spatio-temporal distribution of ambient noise.

Ocean acoustic time reversal

A series of ocean acoustic time experiments have been jointly conducted in the last ten years by the NATO Undersea Research Centre and the Marine Physical Laboratory. The experiments demonstrated a robustness of the ocean acoustic time reversal mirror process similar to that found in more controlled, ultrasonic laboratory experiments. Results from these experiments have pointed to potential applications to SONAR signal processing methods and to acoustics communications. In addition, the experimental procedures themselves have yielded data that provide further understanding of the ocean acoustic environment and the increased stability of time reversal process over one way propagation in a fluctuating medium.

Time reversal mirrors and invariants of the time reversal operator: Application to detection and imaging in biological media

Acoustic time reversal mirrors have been developed in the Laboratoire Ondes et Acoustique for several years. In inhomogeneous media and especially in the presence of multiple scattering, these systems provide outstanding focusing properties. While used in pulse echo mode, the time reversal process can be iterated, leading to selective focusing on the most reflective point among a set of scatterers. This iteration is also used to enhance the echo from a defect like a kidney stone or a microcalcification in the breast. The iterative time reversal process is described by a matrix call the Time Reversal Operator (TRO). The eigenvectors of this matrix provide the invariants of the iterative time reversal process, their analysis is the base of the D.O.R.T. method. It allows the separation of the echoes from several scatterers in an inhomogeneous medium and the selective focusing on any of them. Furthermore, when an estimate of the medium’s Green function is available, high‐resolution and low‐noise images can be achieved using the backpropagation of the dominant eigenvectors. The principle of acoustic time reversal mirrors and the D.O.R.T. method will be described through several examples.

Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels

SUMMARY We draw connections between seismic tomography, adjoint methods popular in climate and ocean dynamics, time-reversal imaging and finite-frequency ‘banana-doughnut’ kernels. We demonstrate that Frechet derivatives for tomographic and (finite) source inversions may be obtained based upon just two numerical simulations for each earthquake: one calculation for the current model and a second, ‘adjoint’, calculation that uses time-reversed signals at the receivers as simultaneous, fictitious sources. For a given model, m, we consider objective functions χ(m) that minimize differences between waveforms, traveltimes or amplitudes. For tomographic inversions we show that the Frechet derivatives of such objective functions may be written in the generic form , where δ ln m=δm/m denotes the relative model perturbation. The volumetric kernel Km is defined throughout the model volume V and is determined by time-integrated products between spatial and temporal derivatives of the regular displacement field s and the adjoint displacement field s†; the latter is obtained by using time-reversed signals at the receivers as simultaneous sources. In waveform tomography the time-reversed signal consists of differences between the data and the synthetics, in traveltime tomography it is determined by synthetic velocities, and in amplitude tomography it is controlled by synthetic displacements. For each event, the construction of the kernel Km requires one forward calculation for the regular field s and one adjoint calculation involving the fields s and s†. In the case of traveltime tomography, the kernels Km are weighted combinations of banana-doughnut kernels. For multiple events the kernels are simply summed. The final summed kernel is controlled by the distribution of events and stations. Frechet derivatives of the objective function with respect to topographic variations δh on internal discontinuities may be expressed in terms of 2-D kernels Kh and Kh in the form , where Σ denotes a solid-solid or fluid-solid boundary and ΣFS a fluid–solid boundary, and ∇Σ denotes the surface gradient. We illustrate how amplitude anomalies may be inverted for lateral variations in elastic and anelastic structure. In the context of a finite-source inversion, the model vector consists of the time-dependent elements of the moment-density tensor m(x, t). We demonstrate that the Frechet derivatives of the objective function χ may in this case be written in the form , where e† denotes the adjoint strain tensor on the finite-fault plane Σ. In the case of a point source this result reduces further to the calculation of the time-dependent adjoint strain tensor e† at the location of the point source, an approach reminiscent of an acoustic time-reversal mirror. The theory is illustrated for both tomographic and source inversions using a 2-D spectral-element method.

Acoustic Time Series Variability and Time Reversal Mirror Defocusing Due to Cumulative Effects of Water Column Variability

The variability of the arrival structure of narrow band waveforms is derived for adiabatic propagation in a fluctuating ocean channel. Expressions for the expected value of the signal intensity are obtained for sound speed fluctuations characterized in a second moment sense over range, depth and time. Similar expressions are obtained for the focus intensity of a time reversal mirror.

Detection and Selective Focusing on Scatterers Using Decomposition of Time Reversal Operator Method in Pekeris Waveguide Model

The decomposition of the time reversal operator (DORT) method is a selective detection and focusing technique for the pulse-echo mode that uses an array of transmit-receive transducers. Because it is an application of the acoustic time reversal mirror, the irregular shape of the array and the aberration of the propagation medium are compensated and the selective focusing on targets is made possible. In this paper, we examined the application of this method to the underwater acoustics and the application to active sonar and communication are made possible. To clarify the relationship between the focusing effect of the DORT method and the sound propagation property in shallow water, we examined the selective focusing effect with respect to the propagation distance by using the cylindrical spread model without the sea surface and bottom and the Pekeris model, which is typical of shallow water models. There are few influences of the propagation distance on the focusing effect in shallow water model as a result, and it is shown that the focusing effect improves with the increase of the sound velocity of the bottom.

Time-reversal mirrors and rough surfaces: Theory

A systematic study is presented of the sensitivity of acoustic time-reversal mirrors (TRMs) to errors. One result is a novel acoustic method for determining the root-mean-square, rms, height and the surface-height autocorrelation function of rough surfaces. In particular, the effects of misregistering a TRM are studied with respect to a rough surface—the reflected wavefield is recorded in one place, time reversed, and then rebroadcast in a second place. This displacement causes the signal to depend importantly on the surface’s rms height and autocorrelation function. Simple closed-form formulas are presented for determining the rms height and the normalized surface-height autocorrelation function for both deterministic and randomly rough surfaces. Also presented is a numerical study that illustrates the statistical uncertainty in and the spatial resolution of the proposed method. An accompanying experimental article tests the proposed method with measurements made on a number of different rough surfaces.

Characterization of a large vortex using acoustic time-reversal mirrors

We report new results on the ultrasonic characterization of a fluid flow using an acoustic time-reversal mirror (TRM). The structure of a large vortex generated by a rotating disk in a hollow cylinder is investigated both inside and below the cylinder. For mean-flow characterization, the TRM is shown to be a powerful vorticity detector. Experimental time-of-flight data are successfully compared to a numerical simulation of the flow and the orthoradial velocity is reconstructed using simple geometrical acoustics. Real-time measurements allow us to extract the precession motion of the vortex, providing direct, non-intrusive, and dynamical information on the flow.

Phase conjugation in the ocean: Experimental demonstration of an acoustic time-reversal mirror

An experiment conducted in the Mediterranean Sea in April 1996 demonstrated that a time-reversal mirror (or phase conjugate array) can be implemented to spatially and temporally refocus an incident acoustic field back to its origin. The experiment utilized a vertical source–receiver array (SRA) spanning 77 m of a 125-m water column with 20 sources and receivers and a single source/receiver transponder (SRT) colocated in range with another vertical receive array (VRA) of 46 elements spanning 90 m of a 145-m water column located 6.3 km from the SRA. Phase conjugation was implemented by transmitting a 50-ms pulse from the SRT to the SRA, digitizing the received signal and retransmitting the time reversed signals from all the sources of the SRA. The retransmitted signal then was received at the VRA. An assortment of runs was made to examine the structure of the focal point region and the temporal stability of the process. The phase conjugation process was extremely robust and stable, and the experimental results were consistent with theory.

The D.O.R.T. method

The D.O.R.T. method (Décomposition de l’Opérateur de Retournement Temporel) generalizes the principle of acoustic time reversal mirrors. It applies to detection and focusing with large arrays of transducers [Prada et al., J. Acoust. Soc. Am. 99 (1996)]. A transducer array insonifying a scattering medium is characterized by its frequency-dependent transfer matrix K(ω). The time-reversal process is then described by time-reversal operator K(ω)K*(ω). The eigenvalue decomposition of this hermitian operator provides a classification and a localization of the scattering centers in the medium. The two main steps of the D.O.R.T. method are the measurement of the interelement impulse responses of each pair of elements in the array and the diagonalization of the corresponding time reversal operator at chosen frequencies. The method is efficient for the detection and selective focusing in an inhomogeneous multiple target medium. It also applies to the recognition of shells, in particular to the detection and characterization of circumferential waves propagating around the shell. The D.O.R.T. method and recent experiments of detection through channels and through inhomogeneous media will be presented.

Experimental demonstration of an acoustic time reversal mirror in the ocean

An experiment conducted in the Mediterranean Sea in April 1996 demonstrated that a time reversal mirror (or phase conjugate array) can be implemented to spatially and temporally refocus an incident acoustic field back to its origin. The experiment utilized a vertical source–receiver array (SRA) spanning 77 m of a 125-m water column with 20 sources and receivers and a single source/receiver transponder (SRT) co-located in range with another vertical receive array (VRA) of 46 elements spanning 90 m of a 145-m water column located 6.5 km from the SRA. Phase conjugation was implemented by transmitting a 50-ms pulse from the SRT to the SRA, digitizing the received signal and retransmitting the time-reversed signals from all the sources of the SRA. The retransmitted signal was then received at the VRA. An assortment of runs were made to examine the structure of the focal point region and the temporal stability of the process. The phase conjugation process was extremely robust and stable. There was also excellent agreement between experiment and theory.

Hot topics in engineering acoustics.

Engineering acoustics attempts to utilize contemporary developments in many areas of science, technology, and analysis to produce acoustical systems and products which address existing needs or create new opportunities. Topics in engineering acoustics become ‘‘hot’’ when there is a convergence which facilitates a ‘‘quantum leap’’ in some particular application area. Fusion of new sensor technologies, microprocessors, signal processing, and electronic data communication has produced new options in condition‐based monitoring of machinery and industrial processes. Advances in the speed and reduction of cost in A–D and D–A converters, coupled with high memory density, has permitted the development of acoustic time reversal mirrors which could have application to ultrasonic nondestructive evaluation of materials. Computing power, new inversion algorithms, and novel transducers have led to the commercialization of resonant ultrasound spectroscopy which can determine the complete set of elastic moduli for materials with sample sizes which can be less than 1 mg. The availability of fast, accurate one‐dimensional computer‐based acoustic modeling tools and new research results in studies of the transfer to heat from acoustically oscillating fluids to solid surfaces are providing a new foundation to design and optimize the next generation of thermoacoustic engines and refrigerators.

Ultrasonic beam steering through inhomogeneous layers with a time reversal mirror

Adaptive time delay focusing techniques allow an efficient correction of the effects due to an inhomogeneous layer close to the transducer array. If the layer is far from the array, these techniques are no longer appropriate to correct the diffraction effects between the layer and the transducer array. This problem was overcome by the use of acoustic time reversal mirrors. In this technique, the Green's function of a dominant scatterer available in the medium is recorded in digital memories and used to focus on the scatterer in both transmit and receive modes. We present in this paper an extension of this technique to focus, in the presence of an aberrating layer, not only on the dominant scatterer, but also around it in order to image the surrounding zone. From the knowledge of the Green's function needed to focus on the initial scatterer, we calculate the new Green's function matched to the new point of interest. The algorithm uses the concept of time reversal propagation, and we shall present here theoretical and experimental results obtained with this technique. Finally, the knowledge of each Green's function matched to each new desired focal point allows the realization of a B-scan image of the zone surrounding the reflector.

Robust Acoustic Time Reversal with High-Order Multiple Scattering.

We report the first experiments showing the reversibility of transient acoustic waves through high-order multiple scattering by means of an acoustic time-reversal mirror. A point source generates a pulse which scatters through 2000 steel rods immersed in water. The time-reversed waves are found to converge to their source and recover their original wave form, despite the high order of multiple scattering involved and the usual sensitivity to initial conditions of time-reversal processes. Surprisingly, the observed resolution was one-sixth of the theoretical limit for the mirror's aperture.

Inverse scattering analysis with an acoustic time-reversal mirror.

Time-reversal mirror (TRM) utilizes time-reversal invariance of wave equation. Acoustic TRM are made of large transducer arrays allowing the incident acoustic field to be sampled, time reversed, and reemitted. The ability of TRM to time reverse separately each scattered wave permits us to isolate spatially and temporally the equivalent sources of extended scatterer illuminated by broadband pulse. We investigate more particulary the problem of a cylindrical scatterer: We show that TRM allows us to determine the location of the mode conversions of incident waves into circumferential waves.