The structure of raylike arrivals in a shallow-water waveguide

The structure of raylike arrivals in a shallow-water waveguide Philippe Rouxa兲 LGIT, Université Joseph Fourier, CNRS UMR 5559, Grenoble 38041, France

Bruce D. Cornuelle, W. A. Kuperman, and W. S. Hodgkiss Scripps Institution of Oceanography, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093-0230

共Received 7 February 2008; revised 30 July 2008; accepted 4 September 2008兲 Acoustic remote sensing of the oceans requires a detailed understanding of the acoustic forward problem. The results of a shallow-water transmission experiment between a vertical array of sources and a vertical array of receivers are reported. The source array is used to provide additional degrees of freedom to isolate and track raylike arrivals by beamforming over both source and receiver arrays. The coordinated source-receiver array processing procedure is presented and its effectiveness in an example of tracking raylike arrivals in a fluctuating ocean environment is shown. Many of these arrivals can be tracked over an hour or more and show slowly varying amplitude and phase. The use of a double-beamforming algorithm lays the foundation for shallow-water acoustic remote sensing using travel time and source and receive angles of selected eigenrays. © 2008 Acoustical Society of America. 关DOI: 10.1121/1.2996330兴 PACS number共s兲: 43.30.Cq, 43.60.Fg 关WLS兴

I. INTRODUCTION

Ocean acoustic tomography was introduced by Munk and Wunsch1 as a remote-sensing technique for large-scale monitoring of the ocean interior using low-frequency sound. This method depends on identification and tracking of stable ray arrivals and uses the arrival time changes to estimate ocean variability. It is typically performed between a few widely separated sources and receive arrays and can provide rapid surveys2 in deep or shallow water.3,4 Acoustic propagation at smaller scale and higher frequency can be similar to deep water based on wavelength scaling. Deep water refracted rays do not resemble shallowwater bottom-reflected rays, but in both cases 共deep water or shallow water兲, there are multiple eigenrays between a source and a receiver. These eigenrays provide more information than a single direct path, but also create difficulties in terms of identification and separation. The advantages of the smaller scale are easier measurement of the environment parameters such as bathymetry and the sound-speed fluctuations. Array deployments are also simpler in shallow water since array lengths can be shorter. For an arrival to be useful, it must also be stable enough to track over time and be identifiable unambiguously with a ray path 共or ray sampling kernel5兲 so that the sampling of the ocean sound-speed field is known. With a single source and receiver it can be difficult to identify each multipath with calculated arrivals from an ocean model. This problem may be eased with an array of receivers using time-delay beamforming.2 In this case two wave fronts arriving on the receive array at the same time but different angles can be identified and used as observations. However, depending on the complexity of the sound-speed structure, distinct wave

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front arrivals may seem to share the same arrival angle and time on the receive array due to the resolution limits imposed by the pulse bandwidth and the array size. In this work, we present experimental results obtained between two source/ receive arrays. Time-delay beamforming is performed simultaneously on both the source and receive arrays, allowing us to identify each acoustic ray by its launch angle, receive angle, and arrival time. This is related to the problem of underwater communications in shallow water with receiver arrays,6,7 and where source arrays can be used to achieve enhanced channel capacity.8 In the past few years, a series of broadband shallowwater acoustic experiments has been performed, employing both source and receive arrays and focusing on time reversal.9–15 Typical geometries for these experiments range from 1 to 8 km of acoustic propagation in a 50– 120 m deep waveguide with a set of transducers and hydrophones on two vertical arrays spanning most of the water column. The broadband signals were designed to estimate the impulse response of the ocean acoustic waveguide in the kilohertz frequency range. The observed impulse responses were first used for time-reversal focusing of the arrivals, studying time evolution of time-reversal focusing in a fluctuating environment.16 Time reversal implies a forth and back propagation through the waveguide. When a time-reversed signal is sent repeatedly over time, the degradation of the time-reversal focus with time results from the growing phase and amplitude differences of the acoustic field between the initial and actual propagation. Experimental results confirmed the stability of time-reversal focusing despite sound-speed fluctuations that were strongly affecting the acoustic forward propagation. On the other hand, the degradation of the timereversal focus did not provide straightforward information on the location and amplitude of the sound-speed fluctuations in the waveguide.17

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© 2008 Acoustical Society of America

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FIG. 1. 共Color online兲共a兲 Cartoon of experimental layout, showing source and receiver arrays. 共b兲 Mean 共black兲 and rms 共gray兲 sound-speed profiles for the region. The rms sound-speed axis is shown on the top and the mean sound-speed axis is presented on the bottom. Source and receiver depths are indicated by the plus signs to the left and right of the figure, respectively.

The repeated acquisition of the acoustic transfer matrix between the two arrays was also performed during the experiment for estimation of the waveguide itself, using the evolution of the transfer matrix to estimate the evolving sound-speed field. Having both source and receive arrays enables array processing at both source and receive locations, enhancing the arrival identification process that is the starting point for time-of-arrival based estimates of ocean structure. In the following, we describe observations of stable identifiable arrivals and show that the rapid sampling and high signal-to-noise ratio of the observations provide for high precision measurements of arrival time changes. The goal of this paper is to study forward propagation between the two arrays using a double-beamforming algorithm that allows us to separate and identify each ray path between the source and receive arrays. Travel-time measurements on these ray paths could be used for shallow-water ocean remote sensing in a fluctuating environment. II. EXPERIMENT

We have performed an experiment in July 2005 north of Elba Island, Italy with the same equipment, location, and basic setup as discussed in previous work.16 As shown in Fig. 1共a兲, there was a vertical line array of Ns = 29 equally spaced transducers 共SA兲 spanning 78 m in 120 m water depth and Nr = 32 equally spaced receiving hydrophones 共RA兲 covering 62 m 关Fig. 1共b兲兴. We record the time domain pressure field p共t , zr , zs兲 transmitted from a point source at depth zs on a vertical line array to a receiver at depth zr. The arrays were linked to the ship via two-way radio telemetry, so the data were recorded on the ship in real time. The range between the two arrays was 4.071 km. The transducers had a central frequency of 3.2 kHz with a 1 kHz bandwidth. The pulses transmitted during the experiment were 200 ms linear frequency modulated chirps that were compressed after reception to their pulse equivalent by matched filtering. This produced broadband receptions with signal-to-noise ratio greater than 40 dB with power-limited transmissions. The coded pulse signal is transmitted sequentially by each element of the SA with a separation between transmissions of 250 ms to allow for maximum channel dispersion of 200 ms 共Fig. 3兲. J. Acoust. Soc. Am., Vol. 124, No. 6, December 2008

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FIG. 2. 共Color online兲 Group velocity vs phase velocity for the mean soundspeed profile shown in Fig. 1. The dotted line indicates the dividing line between surface-reflected rays to the right and refracted rays to the left.

The acquisition of the transfer function between each source of the SA and each receiver of the RA thus requires about 7 s to complete. The transfer function is recorded every 20 s to monitor fluctuations of the oceanic waveguide. During the 7 days of the experiment, 26 conductivitytemperature-depth 共CTD兲 casts and 32 expendable bathythermograph 共XBT兲 casts were taken at multiple locations 共and times of day兲 in the area. The average depth-dependent sound-speed profile measured by CTD is shown in Fig. 1共b兲. The water column is stratified in both temperature and salinity, with warm, fresher water on top of colder saltier water. Salinity was supplied for the XBT casts from the observed T-S relation from the CTD data, but the salinity variation had a relatively small effect on sound speed. The sound-speed profile is downward refracting, with high gradients in the thermocline between 30 and 60 m. The buoyancy frequency 共not shown兲 of the mean profile has a maximum of 20 cycles/ h near 38 m depth, allowing for a rich spectrum of internal wave variability. The sound-speed profile was qualitatively similar throughout the transmission experiments reported below, but showed significant variability in the region of strong gradients, as shown by the root-mean-square 共rms兲 sound speed plotted in the same figure. Peak rms variability is 2.3 m / s at about 35 m, reducing to less than 1 m / s below 41 m and less than 0.1 m / s below 90 m. The analysis of the sources of the sound-speed variability is outside the scope of this paper, but the main contributors are adiabatic internal wave 共and tide兲 displacement of the isopycnals, diabatic processes 共heating, cooling, and wind mixing兲 in the upper 20 m, and horizontal advection. The acoustic propagation predicted from the reference sound-speed profile must be matched to the observed impulse responses to confirm that the arrivals are understood. The vertical arrays provide critical information for identification of the observed arrival peaks with theoretical arrivals. Group velocity versus phase velocity is shown in Fig. 2 from a ray-tracing numerical simulation based on the average sound speed. For comparison with a ray representation, group velocity can be matched to range divided by travel time, while phase velocity is related to local sound speed Roux et al.: Shallow-water rays

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FIG. 3. 共Color online兲 The logarithm of the intensity of the pressure field received on the RA for a source on the SA at 96 m depth plotted as a color image for depth and arrival time. 共a兲 Field received from a single transmission. 共b兲 Incoherent average of 60 transmissions over 1 h 共averaging one transmission per minute兲. 共c兲 Numerical simulation of the field using a highangle broadband PE code. Computation has been performed for a 1 kHz bandwidth Gaussian pulse centered at 3 kHz using the sound-speed profile shown in Fig. 1共b兲. Bottom sound speed is uniform and equal to 1600 m / s.

divided by the cosine of the angle the ray makes with the horizontal axis. Path length increases with increasing phase velocity, so group speed can only increase if the mean sound speed along the ray path increases faster than the path length. The arrivals to the left of the vertical dashed line at a phase velocity of 1536 m / s are refracted in the upper ocean, while those to the right are surface reflected. The group velocity increases sharply near the point of surface reflection because of the strong increase in sound speed near the surface and decreases after surface reflection due to increased path length. The figure shows that several different phase velocities 共rays兲 can have the same group velocity 共arrival time兲 for group velocities above about 1496 m / s 共arrival times earlier than about 2.72 s兲. The logarithm of the intensity of the pressure field received on the RA for a source on the SA at 96 m depth is shown in Fig. 3共a兲 for depth and arrival time. The acoustic field is a mixture of clear wave fronts spanning the RA and speckle due to interference between acoustic paths. The maximum signal-to-noise ratio is around 40 dB. The field received from a single transmission is shown in Fig. 3共a兲 while Fig. 3共b兲 is an incoherent average of 60 transmissions over 1 h. The average filters out some of the speckle observed in single transmissions, emphasizing the strong wave front arrivals. A numerical simulation of the field using a high-angle broadband PE code18 is shown in Fig. 3共c兲 using the sound3432

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speed profile seen in Fig. 1共b兲. There is visual agreement between the numerical simulation and the incoherently averaged field at least in the arrival structure of the multiply reflected/refracted paths. This agreement is due in part to the monotonicity of the observed sound-speed profiles. In other experiments, surface cooling created a sound-speed minimum near the surface, leading to complicated arrival patterns with strong sensitivity of the arrival pattern to small changes in the sound-speed profile. In these cases, identification of the superposed timefronts was much more difficult because small differences between the estimated and actual sound-speed field resulted in significant mismatches between observed and calculated arrival patterns. Because of the structure of the sound-speed profile, the earliest arrivals correspond to ray paths which nearly touch the surface, as seen in Fig. 2. These have the least travel time because the sound energy propagates in the high-speed region of the waveguide enough to more than compensate for the increased path length. The direct path can be seen to arrive at about 2.7 s 共group velocity of 1507.8 m / s兲, overlapping with surface-reflected energy, so that there is considerable difficulty in unscrambling the superposed arrivals. The incoherently averaged beamformer output for the 96 m source using a dRA = 16 m aperture subarray of the RA centered at 96 m depth is shown in Fig. 4. There are three clear arrival spots at about 2.719 s travel time, which is in the region of no multivalued group velocities. The later arrivals are also clearly separated and show the array side lobes. We also see the early arrivals from the ray共s兲 that turn near the surface, as seen in Fig. 3 around 2.69 s, the direct path at near-zero angle and travel time of 2.7 s, and some well-separated arrivals for times after about 2.706 s. However, the array side lobes 共the large patches between ⫾10° – 15° on each side of the zero-angle intensity maximum at 2.7 s兲 and the superposition of high- and low-angle arrivals at similar times complicate the beamformed output in the region of overlap. The group velocity versus phase velocity plot 共Fig. 2兲 is easier to interpret. The observed data set is four dimensional, consisting of acoustic pressure as a function of source, receiver, travel time, and transmission time, but only two-dimensional slices can be displayed on paper. The arrival pattern for a single source-receiver pair is more difficult to decipher without the array information. The matched-filtered 共but not demoduRoux et al.: Shallow-water rays

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FIG. 5. 共Color online兲共a兲 Matched-filtered 共but not demodulated兲 time record for a single reception for source and receiver depths of 96 m. 共b兲 Logarithm of intensity of the envelope of the impulse response for this source-receiver pair for 1 h at a rate of one acquisition every 20 s. Acquisitions are missing at 8 and 16 min.

lated兲 time record for a single reception for source and receiver depths of 96 m is shown in Fig. 5. The carrier frequency is retained in the analysis below to clearly show phase shifts. This is an estimate of the instantaneous impulse response between the source and receiver. This depth is below most of the sound-speed variability observed over the course of the experiment which was concentrated at the depth of the thermocline and near the surface. The sound-speed variability produced significant changes to the measured impulse responses for all sourcereceiver pairs over time. The logarithm of intensity of the envelope of the impulse response for this source-receiver pair for 1 h at a rate of one acquisition every 20 s is shown in Fig. 5共b兲. Acquisitions are missing at 8 and 16 min. Strong acoustic interference is seen between refracted/reflected signals in the waveguide in the region of overlapping arrivals. The amplitude of the largest peak never fades out, but the width of the peak fluctuates due to interference between multiple ray paths as well. The time evolution of this impulse response due to the changing sound-speed field should be useful for estimating those sound-speed changes, but the complexity of the arrival makes it hard to interpret these changes as changes in arrival time for separated rays. Skarsoulis19 suggested using the peak arrivals as observations without needing to separate them, using the sensitivity kernel for the combined peak, but this requires a very good estimate of the background sound-speed field, which is not available in this case because of the strong thermocline variability. For this reason, we explore methods for separating the rays. III. RAY IDENTIFICATION THROUGH DOUBLE BEAMFORMING

In order to identify the arrivals by their reception angle on the array, we perform time-delay beamforming on the received field to transform depth into reception angle: J. Acoust. Soc. Am., Vol. 124, No. 6, December 2008

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where z0 is the depth of the sound channel axis 共or soundspeed minimum兲 chosen as a reference and c0 is the sound speed at the reference depth. The time delay ␶共␪r , zr兲 at the center of the vertical array is set to zero so that the arrival times are referenced to that center. Performing time-delay beamforming 共1兲 for a range of ␪r transforms the data from the 共t , zr , zs兲 domain to the 共t , ␪r , zs兲 domain. In the 共t , ␪r , zs兲 domain, each acoustic ray arrival from a particular source which spans the receive array in the 共t , zr , zs兲 domain 共Fig. 3兲 is localized around its reception time and angle. When ray theory is applicable to the data, time-delay beamforming allows an efficient ray identification that is limited by the array size. Distinct rays can arrive at the same time with similar receive angles, so that time-delay beamforming at the receiver is not always sufficient to separate arrivals. Taking advantage of the experimental configuration where both transmit and receive arrays are used, we perform a timedelay beamforming on both arrays. Time-delay beamforming over both arrays transforms the data from the 共t , zr , zs兲 physical domain to the 共t , ␪r , ␪s兲 domain where ␪s is the angle of the wave front at the source array. N

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1 r 1 s p共t, ␪r, ␪s兲 = 兺兺 p共t + ␶共␪r,zi兲 + ␶共␪s,z j兲,zi,z j兲. N i=1 Ns j=1 共3兲 In the 共t , ␪r , ␪s兲 domain, the acoustic wave fronts are identified by propagation time, receive, and transmit angle. This double beamforming was applied to the observations taken during a 2 h period. For each set of transmissions, the received waveforms as a function of arrival time and source and receiver depth were transformed to time and source and receiver angle space. The three-dimensional output fields must be shown in slices for two-dimensional representation. To show the angular structure of the arrivals, we sum the intensity over a 1 ms range of travel arrival times centered on ray arrivals. An example of double-beamforming output for a single set of transmissions between a dSA = 16.7 m aperture subarray of the SA and a dRA = 16 m aperture subarray of the RA both centered at 96 m depth is shown in Fig. 6. The subarray apertures were chosen to maximize the array gain provided by the time-delay beamforming algorithm.21 The fact that the Roux et al.: Shallow-water rays

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FIG. 6. 共Color online兲 Example of double-beamforming output on a linear scale for a single set of transmissions between a dSA = 16.7 m aperture subarray of the SA and a dRA = 16 m aperture subarray of the RA both centered at 96 m depth. 共a兲 Average intensity in the 共␪r , ␪s兲 domain for a time window of 1 ms centered around the observed ray arrival time at 2.6948 s. The circle is centered at the launch and receive angles for a numerically calculated ray that propagates between the centers of the two subarrays. 共b兲 Associated ray path as depth vs range. 共c兲 Same as Fig. 6共a兲 but for a subset of the angle domain centered on the observed peak.

array gain saturates for subarrays larger than D ⬇ 16 m means that the acoustic field coherence vanishes for interelement distances larger than D. The average intensity in the 共␪r , ␪s兲 domain for a time window of 1 ms centered around the observed ray arrival time at 2.6948 s is shown in Fig. 6共a兲. This arrival corresponds to one of the two early arrivals seen in Figs. 3 and 5 and is a ray that nearly reaches the ocean surface. The green circle is centered at the launch and receive angles for a numerically calculated ray that propagates between the centers of the two subarrays 关Fig. 6共b兲兴. This ray path has been obtained with a ray trace code using the depth-dependent sound-speed profile of Fig. 1共b兲. Note in Fig. 6共a兲 the presence of angular side lobes due to the element spacing on the SA and RA. Calling ␦␪SA and ␦␪RA the angular separation between main lobe and side lobe for the SA and RA, respectively, we have ␦␪SA = sin−1共␭ / aSA兲 = 9.8° and ␦␪RA = sin−1共␭ / aRA兲 = 13.7°, where ␭ = 0.475 m is the wavelength of the center frequency and aSA = 2.786 m and aRA = 2 m are the interelement separation for the SA and RA. Finally, Fig. 6共c兲 shows a magnified image of the average intensity in a subset of the angle domain centered on the observed peak. The diffraction-limited angular width of the peak is deter3434


mined by the SA and RA subapertures as sin−1共␭ / dSA兲 ⬇ sin−1共␭ / dRA兲 ⬇ 1.7°. Given the estimated signal-to-noise ratio and peak width, we estimate the precision of source and receive angles at 0.25°. The ray selected in Fig. 6—with arrival time= 2.6948 s for a 96 m source and receiver depth—is well separated from other ray paths, as can be seen in Figs. 3共a兲, 3共b兲, and 5共b兲. As such, double beamforming was not necessary to isolate it from interference by other ray paths. Working with this ray path allows us then to compare the time-domain waveform obtained from the double-beamforming algorithm 关Fig. 7共a兲兴 to the time-domain signal obtained directly from the pointto-point source-receiver pair at 96 m 关Fig. 7共b兲兴. The amplitude of the matched-filtered arrival as a function of arrival 共travel兲 time and transmission time is shown as color in Fig. 7. A vertical slice of the plot at a single transmission time corresponds to an expanded plot of the region around t = 2.6948 s from the time-domain signal represented in Fig. 5共a兲. The evolution of this waveform over a 1 h set of transmissions shows the phase and amplitude effects of the ocean fluctuations since no multipath interference is expected for this isolated path. In the case of the double-beamforming algorithm 关Fig. 7共a兲兴, the waveform has Roux et al.: Shallow-water rays

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FIG. 7. 共Color online兲 Amplitude of the matched-filtered arrival as a function of arrival 共travel兲 time and transmission time for 1 h of transmissions. Color scale gives positive and negative pressures. 共a兲 Double-beamformed waveform for the source and receiver angles 共␪s = 10.2° and ␪r = 10.7°兲. 共b兲 Same as 共a兲, but for only 96 m source and receiver depths.

been extracted for the source and receiver angles 共␪s = 10.2° and ␪r = 10.7°兲. Figures 7共a兲 and 7共b兲 are very similar except for the improved signal-to-noise ratio for the doublebeamforming output due to the array gain associated with the processing. As a consequence, the time-domain waveform for each ray path can be tracked as a function of transmission time. In addition to variations in amplitude and phase of the arrival, the source and receiver angles vary in time. The evolution of the source and receive angles 共␪s and ␪r兲 for 1 h of transmissions for the ray arrival shown in Fig. 7 is shown in Fig. 8. For each transmission, the double beamforming has been performed on the two subarrays and the intensity in a limited angle range is plotted. This is the time behavior of a slice through the maximum intensity spots, as shown in Fig. 6共c兲. Figures 8共a兲 and 8共b兲 only show intensity values for the source and receive angle ranges that were above 80% of the maximum intensity 共at the time of the peak arrival兲 for this particular ray at each time.

Figure 8 shows that both source and receive angles of the maximum intensity vary by less than 1° peak to peak over 1 h. Part of this variability is due to the motion of the SA and RA in response to ocean currents. However, we expect that some of the variability of source and receive angles is due to variability of the sound-speed profile, so angle information could be used to estimate ocean structure in combination with waveform travel time. Assuming that the sound-speed fluctuations only occur at the turning point 共depth zt, grazing angle ␪t = 0兲 for a given eigenray with sound speed c共z0兲 and angle ␪0 at the source 共or receiver兲, Snell’s law gives ⌬c共z兲 = ⌬␪0c共z0兲sin共␪0兲/cos2共␪0兲.

共4兲

In the observations, c共z0兲 does not vary for z0 deeper than 90 m. We measure ⬇1° in source/receive angle maximum variation over time, as seen in Fig. 8. Taking ␪0 = 10°, Eq. 共4兲 gives ⌬c共z兲 ⬇ 4.5 m / s which is consistent with a 2.3 m / s rms fluctuation at a depth of 30 m.


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FIG. 8. 共Color online兲 Evolution of the source, 共a兲, 共left兲, and receive, 共b兲, 共right兲 angles 共␪s and ␪r兲 for 1 h of transmissions for the ray arrival shown in Fig. 7. For each transmission, the double-beamforming process has been performed on the two subarrays and only the intensity above 80% of the maximum intensity 共at the time of the peak arrival兲 for this particular ray at each time is shown. J. Acoust. Soc. Am., Vol. 124, No. 6, December 2008

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FIG. 9. 共Color online兲共a兲 Average result of a single 共receiver array only兲 time-delay beamforming for a 96 m source depth performed on the aforementioned dRA = 16 m aperture subarray of the RA centered at 96 m depth. The plot has been limited to the region in arrival time containing three rays that arrive near 2.7185 s. The intensity has been incoherently averaged over a 1 h set of transmissions. 共b兲 Intensity in the 共␪r , ␪s兲 domain after double beamforming. 共c兲 Ray paths between the source and receive subarray centers for the three rays.

In some cases double beamforming is necessary to isolate multiple paths that arrive at nearly the same time. An example is shown in Fig. 9. Figure 9共c兲 displays three ray paths between the source and receive subarray centers that each arrive near 2.7185 s. The source is on the left and the receiver is on the right. Figure 9共a兲 shows the average result of a single 共receiver array only兲 time-delay beamforming performed on the RA for a 96 m source depth. For clarity, the beamformed result has been limited to the region in arrival time containing only these peaks. The intensity has been incoherently averaged over a 1 h set of transmissions. Figure 9共a兲 shows that two of the rays have receive angles in the interval of 9°–12°. The angle separation between the centers of the rays is close to the 1.7° width of the peak in angle space. Knowing that source and receive angles vary with time 共Fig. 8兲, these two rays are likely to interfere over time, preventing the use of single time-delay beamforming for travel-time estimation. On the other hand, Fig. 9共b兲 shows that these two rays are well separated after beamforming on both the SA and RA. The intensity plot in the 共␪r , ␪s兲 domain matches the ray calculation for source and receive angles. 3436


The rays are now clearly identified and isolated, so that an unambiguous waveform extraction as shown in Fig. 7 is feasible. Figures 10共b兲–10共d兲 show expanded views of the incoherently averaged intensity spots in source angle-receiver angle space associated with each ray in Fig. 9. As expected, Fig. 10共a兲 exhibits array side lobes for each spot as in Fig. 6共a兲 and the spot widths in Figs. 10共b兲–10共d兲 are consistent with the diffraction limits. Figure 11共a兲 shows the pulse-compressed received waveform as a function of transmission time for the surfacereflected ray shown in Fig. 9共c兲. The time evolution of the waveform has been constructed by choosing angles of maximum intensity near ␪s = 12.3° and ␪r = 11.8° for each transmission during a 1 h period. The ray shown in Fig. 11共a兲 has a path that is distinct in space from the ray shown in Fig. 7共a兲, so the two rays are expected to experience different oceanic environments. The time evolution of the arrival amplitude and phase is very different from that shown in Fig. 7. The time variability of the ray source and receive angles is plotted in Figs. 11共b兲 and 11共c兲 as in Fig. 8. The source and Roux et al.: Shallow-water rays

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receive angle variability as a function of transmission time differs from Fig. 8, confirming that the time-evolving ocean sound-speed structure is important along with SA and RA 2.716 2.7165 Acquisition Time (s)

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FIG. 11. 共Color online兲共a兲 Pulse-compressed received waveform on a linear scale as a function of transmission time for the surface-reflected ray shown in Fig. 9共c兲. 关共b兲 and 共c兲兴 Time variability of the ray source and receive angles, respectively, as in Fig. 8. J. Acoust. Soc. Am., Vol. 124, No. 6, December 2008

motion. The intensity fluctuations vary more sharply from transmission to transmission in Figs. 11共b兲 and 11共c兲 than in Figs. 8共a兲 and 8共b兲 as could be expected because of surface scattering for this surface-reflected ray. The variability of angle for the refracted ray shown in green in Fig. 9共c兲 is shown in Fig. 12. In Fig. 12共a兲, the waveform has been extracted for the arrival angles with peak intensity near ␪s = 8.8° and ␪r = −9.1° for each transmission during a 1 h set of transmissions. This ray has a turning point near the depth of maximum sound-speed variability. Figure 12共a兲 shows very large intensity fluctuations during the 1 h interval. Figures 12共b兲 and 12共c兲 show the time evolution of the intensity in angle ranges near the peak intensity, as in Figs. 11共b兲 and 11共c兲. The evolution of the receiver angle shows two angle peaks at some times, with the peak at more negative receiver angle showing significant intermittency. An incoherent average of the power in a 1 ms time interval centered on the arrival time is shown in Figs. 12共d兲 and 12共e兲 for transmissions at 15 and 33 min, respectively. Figure 12共d兲 shows two peaks in angle-angle space as confirmed by the receive angle evolution in Fig. 12共c兲. The double peak is probably a signature of interfering micromultipaths for this particular ray resulting in a destructive interference between two out-of-phase waveforms. At a time when the arrival is not doubled 关Fig. 12共e兲兴, the intensity spot is similar in intensity to those obtained in Figs. 6 and 10 which shows that the double spot observed in Fig. 12共c兲 is not a consequence of the double-beamforming algorithm.

In this shallow-water propagation experiment, ray paths can be isolated, identified, and tracked over time, yielding time series of arrival time, amplitude, and even carrier phase for use in characterizing the channel. Double beamforming can isolate some arrivals not resolvable with single beamforming and increases signal-to-noise ratio. Peaks can be tracked for several hours and show phase stability for accurate travel-time measurements. Source and receive angles of a selected eigenray are also time-evolving observable that can be tracked with the double-beamforming algorithm. Internal wave displacements are expected to be the dominant source of sound-speed variability on hourly timescales, producing the largest changes in the thermocline. There is a Roux et al.: Shallow-water rays

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significant difference in the time stability of ray paths that remain below the thermocline 共most stable兲, refract in the thermocline, refract above the thermocline, and interact with the surface. Through the use of the double-beamforming algorithm, shallow-water acoustic remote sensing may be then revisited between densely sampled source and receive arrays from which travel time, source, and receive angles of a large number of eigenrays are monitored. ACKNOWLEDGMENTS

This work was performed in collaborative experiments with the NATO Underwater Research Center 共NURC兲, La Spezia, Italy, with Mark Stevenson as Chief Scientist. Scientists contributing to these experiments include Tuncay Akal, Pierrot Boni, Pierrot Guerreni, other NURC staff, and the officers and crew of the RV Alliance. The work was funded by the Office of Naval Research. 1

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