Correlation of random wavefields: An interdisciplinary review

Time reversal acoustic (TRA) focusing allows concentration of elastic energy at a location in the soil being investigated to detect landmines. The TRA process is conducted by broadcasting a wide bandwidth signal and recording the surface vibration by a Laser Doppler Vibrometer (LDV). The system impulse response from speaker to the LDV output can then be computed by cross correlating the original and recorded signals for each channel. Each transducer re-radiates the time reversal impulse response. This provides efficient focusing of the seismic wave in both space and time, thus enhancing the nonlinear effects associated with soil and landmine vibrations. Using orthogonal initial signals the suggested TRA procedure can be implemented simultaneously with multiple transmitters to increase the scanning speed. The nonlinear effects were investigated using a phase inversion method where the TRA signal is broadcast a second time with an opposite sign and the two received signals are added in post processing. The summed signal contains mainly the results of nonlinear wave interaction and tends to cancel the linear response. Small scale land mine detection experiments were conducted using a laser Doppler vibrometer and an array of speakers in the frequency band 50-500Hz. They demonstrate that the TRA system provides high concentration of elastic wave energy in the tested area. The measurements of spectral density of the TRA focused signal reveal increased spectral density in the vicinity of mine resonance frequencies. The nonlinear TRA phase inversion method shows higher contrast between mine and no mine than the linear TRA method.

Time reversal acoustics is based on the time reversal symmetry of the acoustic fields. A detailed description of the acoustic field equation showing the time reversal symmetry property of S the solution is given. A geometric structure of a metamaterial for both an electromagnetic wave and acoustic wave is given. Then, the geometric structure of the metamaterial to implement time reversal acoustics is given. Time reversal acoustics has been successfully applied to non-destructive testing, medical ultrasound imaging, and underwater acoustics. The advantage of using metamaterial in time reversal acoustics is that it supports modes which radiate spatial information of the near field of a source efficiently in the far field.

We investigate some of the limitations of time reversal acoustics (TRA) in solid media with transducers attached to the surface. In particular, we consider the limitations due to the finite size of the transducers and elastic wave propagation. Using a theoretical approach, numerical simulations and validation from laboratory ultrasound experiments, we find that finite size transducers and the existence of longitudinal and shear waves play significant roles in perturbing the time reversal process. Despite these limitations, we show that TRA in solids is very robust, providing the means to reconstruct the main features of the source signal. The analysis of TRA retro-focusing properties in solid specimens is of foremost importance for the development of new non-destructive evaluation techniques.

This chapter contains sections titled: Introduction Theory of Time-Reversal Acoustics Application of TR to Medical Ultrasound Imaging Application of Time-Reversal Acoustics to Ultrasonic Nondestructive Testing Application of TRA to Landmine or Buried Object Detection Application of Time-Reversal Acoustics to Underwater Acoustics References

There are numerous medical applications of ultrasound radiation force (RF) which could be made more effective using the time reversal acoustics (TRA) principles. This paper gives an overview of research into physical and technical bases of RF generation in heterogeneous biological media using TRA focusing systems. A custom-designed compact multichannel TRA system for receiving, digitizing, storing, time reversing, and transmitting acoustic signals in a wide frequency range from 0.01 to 10 MHz has been developed and extensively tested in model systems and ex vivo tissues and bones. Shear strain and shear waves remotely induced in soft tissues and bones by radiation force were detected using various acoustical and optical means. Experimental studies fully confirmed the feasibility of TRA generation of RF and demonstrated several advantages over conventional means of remotely inducing shear stress in biological media. These advantages include a possibility to create highly localized (close to diffraction limit) shear stress in heterogeneous media stir focused ultrasound beam in 3-D volume using very simple hardware. [Work supported by NIH grant.]

Acoustic time reversal is a promising technique for spatial and temporal focusing of sound in unknown environments. Acoustic time reversal can be implemented with an array of transducers that listens to a remote sound source and then transmits a time-reversed version of what was heard. In a noisy environment, the performance of such a time-reversing array (TRA) will be degraded because the array will receive and transmit noise, and the intended signal may be masked by ambient noise at the retrofocus location. This article presents formal results for the signal-to-noise ratio at the intended focus (SNRf) for TRAs that receive and send finite-duration broadband signals in noisy environments. When the noise is homogeneous and uncorrelated, and a broadcast power limitation sets the TRA's electronic amplification, the formal results can be simplified to an algebraic formula that includes the characteristics of the signal, the remote source, the TRA, and the noisy environment. Here, SNRf is found to be proportional to the product of the signal bandwidth and the duration of the signal pulse after propagation through the environment. Using parabolic-equation propagation simulations, the formal results for SNRf are illustrated for a shallow water environment at source-array ranges of 1 to 40 km and bandwidths from several tens of Hz to more than 500 Hz for a signal center frequency of 500 Hz. Shallow-water TRA noise rejection is predicted to be superior to that possible in free space because TRAs successfully exploit multipath-propagation.

: Acoustic time reversal is of interest to the United States Navy because it is an effective means for focusing sound in unknown underwater environments. For the last nine years, the Office of Naval Research has supported theoretical and numerical investigations at the University of Michigan into the performance of time reversing arrays in the ocean. This report summarizes the research accomplishments of these investigations.

In percutaneous procedures there is often a need to focus therapeutic ultrasound to a predefined area without affecting surrounding tissues. Focusing based on Time Reversal Acoustics (TRA) principles constitutes a promising approach for generating high intensity ultrasound field tailored to the shape of the predefined area. Conventional TRA technique enables ultrasound focusing only at a site, where there is an ultrasound beacon, e.g. piezo-transducer mounted at the tip of a catheter. We developed a method of steering the focus away from the beacon location. The method is based on the measurements of impulse response (IR) in several reference points and calculating virtual IRs for the points outside the reference beacon location. The IR for the point away from the beacon is constructed based on mathematical extrapolation of the measured reference IRs frequency spectra, particularly phases. The effectiveness of extrapolated TRA focusing is explored experimentally and by computer simulation. Potential applications include ultrasounda-ssisted drug delivery, artery recanalization and tumor ablation.

Time reversal acoustics (TRA) techniques provide a means to focus energy at a localized time and space, or at an unknown location (i.e., source or scatterer not known a priori) without the need to calculate time delays, as is necessary for phased arrays. The experiments demonstrate that time reversal focusing provides localized surface vibration with amplitude sufficient to induce measurable nonlinear effects and does so over a wide frequency band. Because the amplitude is spatially focused, time reversal enables local probing of this nonlinearity that can be used for nonlinear imaging. The nonlinear effects for wide band frequency signals were measured by phase-inversion method combining two signals of opposite sign in order to cancel the linear response and preserve quadratic nonlinearities. The method works effectively for nonlinear NDE of thin plates where laser Doppler Vibrometer can be used for measurements of the surface vibration and TRA focusing of acoustic waves. Presented results include crack and delamination diagnostic is epoxy graphite composites, diffusion bonded metallic disks and impact surface damage in glass. Scanning electron microscopy and optical images are also shown to demonstrate the types of damage features detected using this method.

Based on principles from time reversal acoustics, a new acoustics based touchscreen technology has entered the marketplace. Based on accounts of key contributors, this paper presents a history of the developments behind the invention, development and commercialization of this new touchscreen technology. This illustrates innovation from lab to marketplace.

The presence of strong sources of elastic waves often makes it impossible to localize weaker ones, which are sometimes the most meaningful, e.g. in the characterization of complexity of active Earth faults or of microdamage in a composite structural material. To address this problem, a selective source reduction method is proposed here which, applied in conjunction with time reversal acoustics (TRA), provides the means to selectively reduce the contribution of strong sources allowing full illumination of the weak ones. The method is complementary to other methods based on TRA which aim at the selective illumination of scatterers in the propagation medium. In this paper, a description of the method is given along with presentation of a few numerical results to demonstrate its usefulness for localization of sources. Validation and some experimental results are also presented.

The use of solid acoustic reverberators for temporal and spatial focusing of acoustic energy based on time reversal acoustic (TRA) principle was described in the literature. We experimentally and theoretically demonstrated that the liquid-filled TRA reverberators can also efficiently focus acoustic energy and compared the advantages of solid and water-filled reververators. A theoretical model was developed to explore the factors defining the efficiency of TRA focusing, providing the design constraint for the water-filled reververators. The model allows evaluation of the spatial and temporal characteristics of TRA focused acoustic field formed as a result of numerous reflections of ultrasound within the reverberator. The TRA focused field structure, its dependence on the shape and size of the resonator, ultrasound frequency, and attenuation were investigated for the standard and binary modes of TRA focusing. The experiments with custom built liquid-filled acoustic resonators confirmed the predictions of a developed theory, including sharpening of the focal area and increasing of the focal intensity in a binary mode of TRA focusing. The conducted research supports suggestion that such liquid-filled reverberators can be considered as a base for a miniature limited range ablation devices for biomedical applications.

Time-reversal (TR) processing is derived from the invariance of the wave equation for a lossless medium to change of the sign of the time variable. By retransmitting the TR version of the time-dispersed received signal propagated from a probe source (PS) to a source–receiver array (SRA), one can reacquire the probing pulse at the PS location (time compression and spatial focusing) when the waveguide environment is time invariant. However, if some environmental variations occur between the two transmissions, the retrofocusing signal will be defocused. This paper presents an inversion method of ocean environmental variations, which exploits the focusing/defocusing effect measured at the PS location in the presence of environmental perturbations between the PS transmission and the SRA retransmission. Specifically, inversion of the sound speed profile represented in terms of the empirical orthogonal functions is developed. Examples of the method applied to synthetic data are provided to demonstrate the method’s feasibility.

Gas condensate reservoirs are an essential part of Saudi Arabia's hydrocarbon resources. A good understanding of the effect of water on the phase behavior properties of these hydrocarbons is essential for carrying out accurate forecasts of the performance of these reservoirs using numerical simulators. In addition, the scaling and corrosion tendencies of the produced water are strongly influenced by mass transfer with the hydrocarbon phase. This paper presents unique experimental phase behavior data for a typical Saudi Arab gas condensate three-phase (water/condensate/gas) system. The objective of this work is to quantify the effect of water on gas condensate fluid properties. The results show that appreciable amount of carbon dioxide and methane partition from the gas condensate phase into the aqueous phase. Another important observation was the mass transfer of water into the condensate phase. The mass transfer between the condensate and aqueous phases results in a decrease in the gas/condensate ratio. The carbon dioxide in solution makes the brine acidic, and can dissolve carbonate minerals from the formation, for example, calcium carbonate. In addition, the acidic or sour brine will be quite corrosive. The experimental results are compared with equation-of-state and other correlations published in the literature.

A new echo-to-reverberation enhancement method with reverberation nulling constrains based on waveguide invariant is proposed to solve the problems of direct time reversal processing and the time reversal reverberation nulling method. Firstly, a 2-dimensional signal subspace for the range containing a target potentially is obtained by decomposition of time reversal operator at central frequency. And the bottom focusing weight vector for the target range is obtained by the decomposition of time reversal operator at another range near the target with a frequency-shift, according to the waveguide invariant. Then, combined the optimal array signal processing theory, a constrained optimal excitation weight vector of source receiver array is deduced from the signal subspace and the bottom focusing weight vector, so as to focus sound energy on target while null the sound energy on the seafloor below the target, resulting in echo-to-reverberation enhancement. This method not only remedies the shortages of conventional time reversal processing and the time reversal reverberation nulling, but also obtains an improved performance for echo-to- reverberation enhancement, because of the bottom reverberation nulling constrains at the target range. Numerical simulations in typical shallow water environments illustrate the effectiveness of the proposed method.