Applications of Time-Reversal to Underwater Acoustics

J.F. Lingevitch, C.F. Gaumond, D.M. Fromm, and B.E. McDonald
Acoustics Division

Introduction

A time-reversal mirror (TRM) is an array of source-receiver elements that can be precisely controlled to project a desired acoustic wavefront. The Naval Research Laboratory has recently purchased a 64-element source-receive array (SRA) to test time-reversal methods on problems of interest to the Navy, including antisubmarine warfare, acoustic detection methods, remote bathymetry mapping, geo-acoustic inversion, and underwater communications. Time-reversal mirrors are an active area of investigation for these problems because of their capability for focusing acoustic energy in heterogeneous propagation environments such as shallow-water continental shelf areas in the ocean.

Acoustic propagation in shallow water is complicated by strong interactions with both the surface and the bottom, leading to extended multipath echoes. In addition, inhomogeneities in the water column distort the propagation paths. For these reasons, simple beam steering is not effective for ensonifying a desired location when it is away from the vicinity of the array. Time-reversal (phase conjugation) techniques have been demonstrated to focus acoustic energy in the ocean up to 30-km away by using a probe source. This method requires positioning a probe source at the desired focal point and measuring the propagated acoustic field from the probe source to the TRM. The measured signal on the TRM is then time-reversed and retransmitted from each element of the array. The new signal propagates through the waveguide and is observed to focus both spatially and temporally at the probe source location.

One key advantage of time-reversal techniques is that they require no a priori knowledge of the ocean propagation environment. The method is applicable to areas with variable ocean bathymetry, range-dependent sound speed, and geo-acoustic properties. Time-reversal focusing follows from the fact that when a solution of the linear wave equation is played backwards in time, wavefronts will retrace their paths. Attenuation and time variability of the ocean will degrade the reversibility of acoustic waves by a TRM, but recent observations have shown that the time scale of the focal smearing ranges from many hours for frequencies below 1 kHz to tens of minutes at 3.5 kHz.

The Naval Research Laboratory conducted an at-sea time-reversal experiment during May/June 2003 (TREX-03) on the New Jersey continental shelf near the Hudson Canyon. Figure 1 shows the 64-channel SRA during one of its deployments from the R/V Endeavor. The transducers are 6-in. spheres, spaced evenly at 1.25-m intervals along the 80-m aperture of the array. The array is deployed in a vertical configuration by suspending it from the stern of the ship. It is being modified for autonomous bottom-moored deployments in future experiments. The bandwidth of the array is 500-3500 Hz; each element is an independently controllable source/receiver so that the array can be used to implement a TRM. The R/V Oceanus was also on-site for a portion of the experiment to deploy an NRL echo repeater.

FIGURE 1
Deployment of the NRL 64-channel SRA from the stern of the R/V Endeavor during the TREX-03 time-reversal experiment.

Below we describe several applications of time-reversal to ocean acoustics that are being studied at NRL. The first is a rapid wide-area bathymetry mapping technique with a TRM. This technique uses the reverberation from a TRM that is focused near the seafloor to construct a map of the azimuthal variation in bathymetry. Time-reversal techniques are also being applied to enhance the performance of active sonar systems in acoustic detection problems. The multiple guide source (MGS) method uses the principle of time-reversal with in situ data to generate a detector that is matched to the local propagation. Broadband time-reversal operator decomposition (DORT) is a processing technique based on the mathematical decomposition of acoustic data that is designed to separate scatterers at different depths into different beams. We are also exploring applications of time-reversal to develop an "acoustic searchlight" device that could be used to acoustically sweep large regions of the ocean floor for partially buried mines. To make this method practical, we are studying ways to focus a TRM in an unknown environment without using a probe source.

Controlled Reverberation as a Bathymetry Probe

In ocean acoustic experiments, boundary reverberation (echo) is usually a source of interference to be mitigated. Time-reversal techniques, however, can control the locations where reverberation originates and use it to explore the environment. Figure 2 illustrates how this is done. Parameters are descriptive of actual ocean experiments performed in the Mediterranean by the NATO Undersea Research Center with NRL participation. First, a probe source of modest amplitude placed 1 m above the ocean bottom emits a pulse of a few milliseconds duration that is recorded on a vertical SRA 5 km away. The SRA time-reverses the signal, amplifies it, and retransmits it in all directions. As illustrated in Fig. 3, the returning signal along the path back toward the probe source focuses tightly, ensonifying the bottom near the probe source location. In other directions, however, the focus is shifted by sloping bathymetry (green area of Fig. 2). The broken blue circle in Fig. 2 illustrates where the focal region would occur if the ocean bottom were flat.

FIGURE 2
Plan view of the ocean bottom for a controlled reverberation experiment. The propagation path from probe source to SRA is in red; the path of the time-reversed back propagation is in blue. Reverberation from the green focal annulus returns along the blue paths and is represented by unfilled arrows.

FIGURE 3
Backpropagation from the SRA to the probe source at 5-km range calculated by a parabolic equation acoustic model using an experimentally measured environment. The blue curve gives the acoustic intensity incident on the bottom to reveal a tight focus at the probe source location.

The reverberant return to the SRA (unfilled blue arrows in Fig. 2) arrives at different times from different directions because of the bathymetic focal shift. If the returns from the reverberating annulus are analyzed by an appropriate horizontal array, the two-way travel time variation with direction can be extracted. A basic result from waveguide propagation theory then allows the travel time differences to be inverted to yield the bathymetic variation within the green band of Fig. 2.

This method, while still in the developing stages, has the potential of yielding bathymetric variation over many square kilometers of ocean in a matter of seconds in regions of unknown or shifting bathymetry. Traditional swath bathymetry from a moving ship would take many hours to complete.

Multiple Guide Sources

Multiple Guide Sources (MGS) is a new technique for improving sonar detection in shallow-water environments. It is designed to compensate for the effects of channel spreading (the dispersion of sound as it propagates through the waveguide) by using a set of experimentally measured channel responses in a matched-filter detector. Channel spreading is more pronounced for signals that have larger bandwidth, lower frequencies, and longer propagation paths; these are also the signals that have potential benefits for active sonar. Conceptually, the matched filter emphasizes the portions of the spectrum where the signal resides without increasing the magnitude of the noise. It is implemented by filtering a received noisy signal with the time-reversed replica of the expected signal, thus matched filtering can be thought of as a time-reversal technique. To use this conceptual solution, the expected echo from the target must be known. However, since the echo depends on many unknown target and waveguide parameters, it is necessary to approximate the matched filter by using the incident signal, numerical modeling, or direct measurement.

MGS is a technological approach to finding the matched filter from in situ measurements, and is adaptable to different sonar configurations and designs. The concept is to measure the channel spreading due to propagation by deploying several probe sources in the ocean volume where detection is required. The probe sources emit signals that are then measured with the TRM. The received signals are the one-way responses of the environment at a set of positions that are used to estimate the matched filter.

The program at NRL has focused on the scientific problems associated with this process: How many probe sources are needed to characterize a typical shallow-water environment? How does this number vary with bandwidth, frequency, and range? What is the expected improvement in detection from the use of MGS? We have focused on understanding the pro-cesses involved as well as determining a methodology for determining the answers.

Even though acoustic propagation in shallow-water regions is complicated, a large number of MGS is not necessarily required. In the recent TREX-03 experiment, data were taken to determine the number of MGS required for detection of targets at ranges between 2 and 4 km with a band of frequencies from 3 to 3.5 kHz. In this higher frequency, broader bandwidth case, only 10 MGS were required to cover 80% of the received echo. This small number of MGS is sufficient to increase the signal-to-noise ratio by 30 to 40 dB (assuming white Gaussian noise or reverberation). The implication of this result is that for realistic frequencies and bandwidths, a manageable number of probe sources, perhaps as few as five per kilometer, are required to estimate the environmental spreading caused by acoustic propagation in shallow water. Furthermore, a detection algorithm that is based on these in situ environmental estimates can significantly improve detection over noise, and possibly over reverberation also.

Broadband Time-reversal

The Time-Reversal Operator Decomposition (DORT) method is a signal-processing algorithm developed to decouple overlapping time-domain signals due to multiple targets.1 To construct the time-reversal operator (TRO), a TRM is used to collect the backscattered signal from a collection of targets (Fig. 4). It has been shown previously that the eigenvectors of the TRO correspond to the scattered signals from the individual targets in the waveguide. This technique has potential application in the fields of medical ultrasound, communications, and sonar.

FIGURE 4
The two stages of forming a matrix of data from the scatterers. In the top panel, each source sequentially transmits a signal. After each source transmits, each receiver records the scattered data from each source (bottom panel). The figure shows two kinds of scatterer: one is the scatterer in the middle of the water column; the other is a collection of small scatterers located on the bottom of the water column.

In spite of the potential for isolating targets in shallow-water environments, there are several shortcomings of this method that we are addressing at NRL. The first is that a significant amount of time is still required to acquire the data necessary to construct a TRO. This is because a sequence of pings has to be emitted from the TRM and the resulting backscattered signal captured. However, the temporal variability of the ocean, as well as motion of the SRA and scatterers, can significantly affect the measured field during the data acquisition. A second shortcoming of the original method is that it uses narrowband signals. In shallow water, sonar systems are often reverberation limited, i.e., the dominant noise process is scattering from sources such as bottom roughness, bottom inhomogeneities, bubble plumes, and fish. To overcome them, broadband signals are typically used to better detect isolated targets from generally more distributed clutter. Broadband signals also typically contain more clues that can be used to classify the echo as originating from a target or clutter.

We have derived a broadband extension of the DORT algorithm. This method applies conventional DORT processing to the individual frequency components of a broadband signal and then transforms the resulting eigen-channels back into the time domain where existing broadband signal processing can be applied. We demonstrate this method using a numerical simulation with a probe signal of approximately 100 Hz bandwidth. The scatterers in this problem are positioned at different ranges except for two, which are located at 4500 m but at different depths (50 and 70 m), in order to more stringently test the isolation capability of this technique. Figure 5 shows backpro-pagation images (the TRM data propagated through the waveguide with a numerical model) generated from the first and second of the eigen-channels. In the upper panel, the first eigen-channel is backpropagated and two strong scatterers are apparent; the other weaker scatterers are not as evident due to the color scale. In the upper panel, only the deeper scatterer at the 4500-m range is imaged. In the lower panel, the second eigen-channel is backpropagated and now the 50-m deep scatterer at the 4500-m range is revealed. There is also a hint of the 70-m deep scatterer present in the second eigen-channel. This is caused by frequency-dependent fading that occurs in shallow-water propagation. Effectively, the fading causes the scatterer at 70-m not to be the strongest at all frequencies, and hence it appears in multiple eigen-channels. This is a well known problem in adaptive beamforming algorithms, notably in the area of teleconferencing with multiple microphones. Methods for overcoming this problem with shallow-water propagation are currently under investigation.

FIGURE 5
This broadband acoustic image is generated from two eigen-channel outputs of broadband DORT. The upper panel shows the image from the first singular vector and the lower panel shows the image from the second. Several scatterers are in the water column. In the upper panel, two large scatterers are particularly apparent. In the lower panel, a smaller scatterer is isolated from the stronger scatterer at the same range.

Broadband DORT also has the potential to overcome the problem of taking sequential data in shallow water, and it was tested experimentally during the TREX-03 experiment. The NRL SRA and an echo-repeater were deployed at ranges varying between 1 to 5 km. Linear frequency modulated and pseudorandom noise (PRN) signals in the 3.0-3.5 kHz band were transmitted from subapertures of the array to probe the environment. The PRN signals were designed to be approximately orthogonal to each other so that they could be simultaneously transmitted, with each group of sources having its unique PRN signal. In each case, the echoes from each were recorded from each element of the array. Preliminary results suggest that PRN signals are necessary to implement broadband DORT in shallow water.

Reverberation Focusing

It is not always possible or practical to position a probe source at a desired focusing location in the ocean. We are investigating time-reversal methods for focusing a TRM in an uncertain environment without placing a probe source.2 One idea is to obtain an estimate of the transfer function between a desired focal point on the ocean floor and the SRA by exploiting the boundary reverberation due to a known SRA incident pulse. For this measurement, the SRA will transmit a ping, or series of pings, and then record the resulting reverberant signal on all receiving channels. By filtering the reverberation signal with a time window corresponding to a desired focusing range, a map can be constructed that specifies the amplitude and phase of the SRA elements in order to focus back to the source of the reverberation. Several factors complicate a straightforward application of this approach. First, several scatterers from different depths and azimuths may contribute to a given time window of reverberation data. Secondly, the backscattered signal is typically weak and must be detected from sources of noise in the vicinity of the SRA. To overcome these difficulties, we are implementing broadband probe signals that can be detected with a matched-filtering approach.

During TREX-03, the NRL 64-channel SRA was deployed from a ship that was moored in approximately 80 m of water (only 56 of the 64 elements were in the water). A 1-s incident continuous wave pulse was transmitted from the array, and the resulting reverberation was received on the SRA. The amplitude of the reverberation time series was beamformed; Fig. 6 shows the time series for all beams. The energy summed over all of the array elements is shown in the bottom panel. Because of propagation effects in the waveguide, certain ranges are preferentially ensonified with more energy than other ranges. The peaks in the backscattered energy curve correlate well with the ranges where the incident beam strongly interacts with the bottom. Figure 7 shows the acoustic field that results when a segment of the captured reverberation is time-reversed and propagated through the ocean environment that was measured during this test. The top panel shows the transmission loss in a range-depth plot with a dynamic range of 20 dB where the SRA spans the water column at the origin of the range axis. The plot shows a partial focusing of energy at the bottom at approximately 1250 m from the SRA. The bottom panel of Fig. 7 shows the transmission loss at a depth of 81.5 m, near the sediment interface. At the focusing range, the transmission loss plot shows an enhanced ensoni-fication on the bottom of about 5 dB compared to the neighboring ranges.

FIGURE 6
Reverberation recorded on SRA after a 1-s CW ping centered at 1427 Hz. The top panel shows the received time series that has been beamformed. The bottom panel is the received energy summed over all array elements. The peaks in the received energy correlate with ranges where the incident beam interacts with the sediment interface.

FIGURE 7
Backpropagation of a time-reversed window of the reverberation signal shown in Fig. 6. The time window is approximately 1.87 ± 0.05 s, corresponding to a nominal range from the SRA of approximately 1400 m. The color plot shows the backpropagation of this reverberation segment through the environment that was measured during the experiment. The bottom curve is a plot of the transmission loss near the bottom (81.5-m depth) showing the increased ensonification of approximately 5 dB near the bottom at about 1250m from the array.

Conclusions

At NRL, the concept of a time-reversal mirror is being applied to acoustic detection and remote sensing applications in shallow-water ocean environments. These ideas are being tested in at-sea experiments with a unique 64-channel source-receiver array. Time-reversal processing offers potential benefits to Navy systems because it can focus acoustic energy in uncertain environments. Applications of this technology to antisubmarine warfare, wide-area bathymetry mapping, and mine hunting are being developed.

Acknowledgments

The authors thank E.R. Franchi and J.S. Perkins for their helpful comments in preparing this manuscript.

[Sponsored by ONR]

References
1C. Prada, S. Manneville, D. Spoliansky, and M. Fink, "Decomposition of the Time-Reversal Operator: Detection and Selective Focusing on Two Scatterers," J. Acoust. Soc. Am. 99, 2067-2076 (1996).
2J.F. Lingevitch, H.C. Song, and W.A. Kuperman, "Time Reversed Reverberation Focusing in a Waveguide," J. Acoust. Soc. Am. 111, 2609-2614 (2002).