Biomedical subjects
Publications and source records attributed to Karim G Sabra.
It has been experimentally demonstrated that the Green's function between two points could be recovered using the cross-correlation function of the ambient noise measured at these two points. This paper investigates the theory behind this result in the simple case of a homogeneous medium with attenuation.
Coherent deterministic arrival times can be extracted from the derivative of the time-averaged ambient noise cross-correlation function between two receivers. These coherent arrival times are related to those of the time-domain Green's function between these two receivers and have been observed experimentally in various environments and frequency range of interest (e.g., in ultrasonics, seismology, or underwater acoustics). This nonintuitive result can be demonstrated based on a simple time-domain image formulation of the noise cross-correlation function, for a uniform distribution of noise sources in a Pekeris waveguide. This image formulation determines the influence of the noise-source distribution (in range and depth) as well as the dependence on the receiver bandwidth for the arrival-time structure of the derivative of the cross-correlation function. These results are compared with previously derived formulations of the ambient noise cross-correlation function. Practical implications of these results for sea experiments are also discussed.
Acoustic time reversal exploits reciprocity between sources and receivers to generate backward propagating waves that automatically focus at their point of origin. In underwater acoustics, an array of transducers that can both transmit and receive, referred to as a time reversing array (TRA) or time reversal mirror (TRM), generates the back-propagating waves. Such arrays have been shown to spatially and temporally focus sound in unknown complicated multipath environments, and are therefore of interest for active sonar and underwater communication applications. Although stationary vertical linear TRAs have been favored in prior studies, practical applications of acoustic time reversal in underwater environments are likely to involve towed, tilted, horizontal, or bottom-mounted arrays. In particular, array motion introduces Doppler effects and eliminates source-receiver reciprocity, two factors that potentially impact the automatic focusing capability of TRAs. This paper presents the results from a theoretical and computational investigation into how array motion and orientation influence TRA retrofocusing in the shallow ocean. Here, the TRA tow speed is assumed constant, and the array is assumed to be straight and linear (vertical, horizontal, or tilted). And, for simplicity, the TRA is assumed to respond to a stationary point source emitting a broadband pulse. When a TRA moves, the retrofocus is predicted to shift in the direction of array motion due to the translation of the array between its reception and broadcast times. In addition, the performance of a towed horizontal TRA is predicted to degrade more rapidly with towing speed than that of an equivalent (but clearly idealized) towed vertical array because of range-dependent Doppler phase differences that do not influence the vertical array. However, short tilted arrays may approach vertical array performance and appear to be a potentially versatile compromise for implementing TRA concepts in active sonar or underwater communication systems.
Active acoustic time reversal may be accomplished by recording sounds with an array of transducers--a time-reversing array (TRA) or time-reversal mirror (TRM)--and then replaying the recorded and time-reversed sounds from the same array to produce back-propagating waves that converge at the location(s) of the remote sound source(s). Future active sonar and underwater communication systems suitable for use in unknown shallow ocean waters may be developed from the automatic spatial and temporal focusing properties of TRAs. However, ocean currents affect time reversal because they alter acoustic reciprocity in the environment. This paper presents a theoretical and computational investigation into how ocean currents influence TRA retrofocusing in shallow ocean environments for various array orientations. The case of TRA retrofocusing in a three-dimensional range-independent sound channel with a steady horizontal ocean current is covered here, based on a normal-mode propagation model valid for low Mach number currents. The main finding is that in the presence of ocean currents (typically <1 m/s), a TRA performs well (the associated retrofocus amplitude decay is less than 1 dB) except that a retrofocus shift (up to a few wavelengths at 500 Hz at a range of 2.5 km) may occur due to the differing interaction between the ocean current profile and each acoustic normal mode. In addition, TRA performance is predicted to depend on the array orientation relative to the ocean current direction, especially for horizontal arrays.
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.