{"Bibliographic":{"Title":"Delta-k acoustic sensing of ocean surface waves","Authors":"","Publication date":"1997","Publisher":""},"Administrative":{"Date created":"08-20-2023","Language":"English","Rights":"CC 0","Size":"0000028146"},"Pages":["14/91\n6198\nOF\nCOMMUNITY\n*\n*\nNOAA Technical Memorandum ERL ETL-280\nAvenue\nSTATES\nOF\nDELTA-k ACOUSTIC SENSING OF OCEAN SURFACE WAVES\nA.J. Palmer\nM.V. Trevorrow\nEnvironmental Technology Laboratory\nBoulder, Colorado\nJune 1997\nQC\n807. 5\nU6\nnoaa\nNATIONAL OCEANIC AND\nEnvironmental Research\nW6\nATMOSPHERIC ADMINISTRATION\nLaboratories\nno.280","018194\nNOAA Technical Memorandum ERL ETL-280\nDELTA-k ACOUSTIC SENSING OF OCEAN SURFACE WAVES\nA.J. Palmer\nEnvironmental Technology Laboratory\nM.V. Trevorrow\nInstitute for Ocean Sciences\nSidney, B.C., Canada\nEnvironmental Technology Laboratory\nBoulder, Colorado\nJune 1997\nAND AT MOSPHERIC\nUNITED STATES\nNATIONAL OCEANIC AND\nAMOUNT NOAA SCHOOL\nEnvironmental Research\nDEPARTMENT OF COMMERCE\nATMOSPHERIC ADMINISTRATION\nLaboratories\nWilliam M. Daley\nD. JAMES BAKER\nJames L. Rasmussen\nS. DEPARTMENT OF\nSecretary\nDirector\nUnder Secretary for Oceans\nand Atmosphere/Administrator\nProperty of\nATMOSA\nNOAA Miami Library / AOML\nPresident\n4301 Rickenbacker Causeway\nMiami, Florida 33149","QC\n807.5\n, 46\nW6\nno 280\nNOTICE\nMention of a commercial company or product does not constitute an endorsement\nby NOAA/ERL. Use for publicity or advertising purposes of information from\nthis publication or concerning proprietary products or the tests of such products\nis not authorized.\nii","CONTENTS\nABSTRACT\n1\n1. INTRODUCTION\n1\n2. THE AK METHOD\n2\n3. HIGH-FREQUENCY Ak-ACOUSTICS\n3\n3.1 Spatial Coherence\n3\n3.2 Temporal Coherence\n4\n4. GEORGIA STRAIT EXPERIMENT\n5\n5. OPEN OCEAN EXPERIMENT\n7\n6. CONCLUSIONS\n8\n7. ACKNOWLEDGMENT\n8\n8. REFERENCES\n9\nFIGURES\n10\niii","Delta-k acoustic sensing of ocean surface waves\nA. J. Palmer and M. V. Trevorrow 1\nABSTRACT. A high-frequency acoustic method for measuring ocean directional wave spectra is\nput forward. The method is termed Ak-acoustics and is analogous to the Ak-radar and Ak-lidar\ntechniques for measuring ocean directional wave spectra. Significant practical differences between\nhigh-frequency Ak-acoustics and Ak-radar are quantified. The most important of these differences\nis the ability of high-frequency Ak-acoustics to measure the orbital velocity of a surface wave when\nscattering from subsurface scattering elements such as air bubbles. Experimental measurements of\ncoherent high-frequency acoustic backscatter from ocean surface-wave-induced advection of bubble\nclouds are shown to support the proposed Ak-acoustic method. Results of an open-ocean experiment\ndesigned to demonstrate the Ak-acoustic method are reported. The failure to see a Ak resonance line\nwas traced to unfavorable wind direction during the experiment.\n1. INTRODUCTION\nHigh-frequency ocean acoustics has a history of applications which includes both\nincoherent and coherent sounding, and has been used to study both surface and internal waves1-4\nThese applications make use of the fact that high-frequency acoustic signals scatter from\nsubsurface scattering elements such as biota and bubbles as well as from the surface itself. In\nparticular, bubbles exhibit resonantly enhanced acoustic scattering cross sections for acoustic\nfrequencies in the tens to hundreds of kilohertz regime1. In this paper, we describe a method for\nextending the wave sensing capabilities of high-frequency ocean acoustics.\nThe method is termed Ak-acoustics, and makes use of a fringe pattern formed by two\nfrequency-separated transmitted fields. The fringe pattern serves as a narrow band spatial filter.\nThe Ak method has previously been applied to radar5-7, laser8,9, and low frequency acoustic10\nsensing of surface gravity waves. The principal advantage of the method is the potential for\nobtaining rapid, quantitative directional measurement of ocean waves with a large range of\nwavelengths much longer than the carrier wavelength. The ability of the method to isolate the\nwavevector and frequency of a single wave from an ensemble of waves in a real sea allows an\naccurate measurement of the phase velocity of the wave, and hence a determination of the\nunderlying surface current5-7,11 A particular advantage of high-frequency Ak-acoustics not\nshared by Ak-radar is the ability to obtain a phase coherent signal from subsurface scattering\nelements which allows the measurement of the wave's orbital velocity.\nBelow we review the principles of the Ak method. We then discuss features unique to the\nhigh-frequency Ak-acoustic method including both limitations and advantages of the method.\nNext, we present results from a coherent high-frequency sensing experiment of ocean surface\nwaves that support the use of the high-frequency Ak-acoustic method to determine absolute wave\n1Institute for Ocean Sciences, 9860 W. Saanich Rd., Sidney, B.C., Canada V8L 4B2.","heights when the scattering elements are below the surface. Finally, we present the results of an\nopen-ocean experiment designed to demonstrate the Ak-acoustic method.\n2. THE Ak METHOD\nFigure 1 illustrates the basic elements of the Ak method. Figure 1a depicts an\nunderwater acoustic application that utilizes scattering either from the surface itself or from\nparticulate and bubble clouds lying below the surface. Acoustic frequencies in the range ~50-\n400 kHz corresponding to ranges ~400 - 50 m are typical of high frequency acoustic sensing in\nthe ocean. Above water Ak acoustic sensing of surface waves is clearly also possible when\nsurface Bragg structure exists. As indicated in Fig. 1a, the Ak acoustic method utilizes two\ntransmitted, collimated acoustic beams with slightly different frequencies. The use of two\nfrequencies causes a fringe pattern moving with the acoustic phase speed to be projected into the\nscattering volume and onto the surface. The two frequencies can be broadcast simultaneously or\nalternately in time-gated bursts provided their time separation is shorter than the backscatter\nphase decorrelation time. Also the pulses need to be longer than typically used in high-frequency\nbackscatter acoustics so that several surface waves are illuminated by the insonified patch. The\nwavevector of the fringe pattern is Ak = k1 - k2 where k1 and k2 are the wavevectors of the two\nfrequency beams. When an ocean wave which modulates the acoustic backscatter power, passes\nthrough the scattering volume, the interaction of the wave with the fringe pattern produces a\nmodulation of the frequency difference component of the backscattered signal which is the\ncomponent that contains the fringe pattern. When the wavevector of this modulation wave\nsatisfies a Ak Bragg condition, the modulation will be spatially coherent throughout the\nscattering volume and will produce a resonance line in the power spectrum of this frequency\ndifference signal as indicated in Fig. 1b. For backscattering, the Ak Bragg condition is 5-9\n(1)\nkgw=2Akcos(9)\nwhere ksw is the wavenumber of the surface wave, and 0 is the grazing angle of the acoustic\npropagation vector with the surface. The amplitude of the resonance line is determined by the\nacoustic reflectivity modulation at the surface. This modulation is caused primarily by a\ncombination of long-wave induced tilt and strain of the smaller scale surface Bragg structure.\nFor surface scattering, the description thus far is the same as for Ak-radar sensing of the\nocean surface. In fact, because the wavelength of high-frequency ocean acoustics systems and\nocean sensing radars are comparable (a few centimeters) the surface scattering elements\n(centimeter-scale Bragg structure) and modulation processes (tilting and straining of this Bragg\nstructure by the long waves) are also the same. However, important practical differences exist\nbetween Ak-radar and high-frequency Ak-acoustics, especially when the acoustic scattering\nelements lie below the surface. Below, we focus on these differences in order to place the high-\nfrequency Ak-acoustic method in perspective with the already established theory and applications\nof Ak-radar.\n2","3. HIGH-FREQUENCY Ak-ACOUSTICS\nFrom a practical standpoint, one of the most important areas of difference between high-\nfrequency Ak-acoustics and Ak-radar is in their coherence properties - both in the spatial\ncoherence of the Ak-fringe pattern and the temporal coherence of the scattering elements. The\nspatial coherence of the high-frequency Ak-acoustics fringe pattern is generally less than that of\nits counterpart in Ak-radar, and this gives rise to generally larger linewidths for the Ak-resonance\nline. On the other hand, for subsurface scattering elements, the temporal coherence of high-\nfrequency Ak-acoustics can greatly exceed that for Ak-radar and Ak-acoustic scattering from the\nsurface. As we see below, this allows for the possibility of measuring absolute wave orbital\nvelocity with high-frequency Ak-acoustics which is not possible for Ak scattering from the\nsurface, because of phase jitter caused by the motion of the small scale surface Bragg structure\n(sea clutter).\n3.1. Spatial Coherence\nAs with any narrow band filter, the linewidth of the Ak filter depends on the filter's\nstability and coherence properties, the latter of which is controlled by the spatial coherence of the\nAk fringe pattern interaction with the Ak Bragg-resonant surface waves. This spatial coherence\ncan be divided into longitudinal and transverse coherences. The familiar longitudinal coherence\ncontributes a fractional wavenumber linewidth to the filter given by\n8k/k ~ 1/(N)\n(2)\nwhere N is the number of fringe wavelengths in the illuminated scattering volume.\nThe three most important transverse coherence limits are due to (1) the spherical shape of\nthe Ak fringe pattern wavefronts, (2) the loss of directional discrimination caused by the\nnarrowness of the fringe pattern, and 3 - the angular separation between the fringe pattern and\nsurface-wave wave fronts through a finite depth of scatterers. The third decoherence problem\nwas noted also for Ak-lidar sensing of ocean surface waves 12. The fractional linewidths\nassociated with these three spatial coherence limits can be estimated from simple geometric\nconsiderations. They are, respectively,\nok/k ~ 0B2/2\nSpherical Fringe Wavefronts:\n(3)\n8k/k ~ [A/(RO)]²\nNarrow Fringe Wavefronts:\n(4)\nFinite Depth of Scatterers:\n8k/k ~ OG D/A\n(5)\n3","where 2 is the fringe wavelength, R is the transmitter range to the scattering volume, 0 is\nangular beam width of the radiation source, OG is the grazing angle, and D is the depth of the\nscatterers. Note that the first two transverse linewidths have opposite trends with respect to the\ntransducer beam-width, SO the minimum of the sum of these two linewidths define an optimal\nbeam-width angle. As an example, for a typical high-frequency ocean acoustic range of R = 200\nm, and surface wave wavelength, 2 = 3 m, the optimal beamwidth is given by:\n~ 0.15 rad\n(6)\nThe Ak linewidth resulting from these combined coherence limits is likely to exceed that for the\nlonger range Ak-radar applications.\n3.2 Temporal Coherence\nOne of the most important practical benefits of high-frequency Ak-acoustics is the\npossibility of obtaining a temporally coherent Ak signal from subsurface scatterers. As\nmentioned above, this would allow the measurement of the orbital velocity of a selected surface\nwave, and hence the determination of the absolute waveheight. This is not possible with Ak-\nradar or Ak-acoustic sensing of the surface without knowledge of a modulation transfer function\nthat determines the backscatter power modulation as a function of wave amplitude5-7. To exhibit\nthe phase coherence, we write the frequency difference component of the received Ak-acoustic\npressure signal as,\np1(t)p2*(t) = exp(-2i1ww) Sexp(2i(k,°r1 - k2°r2)) g(r1)g(r2)s(r1,t)s(r2,t)dr1dr\n(7)\nwhere r are the position vectors to the scattering elements for the two different frequency fields,\ns(r,t) is a generalized scattering element strength (e.g., Bragg structure amplitude for surface\nscattering, monopole strength for bubbles, etc.), and g(r) is the antenna pattern. If we let\nr'=r2-r,\nthe signal can be written as\np1(t)p2*(t) = exp(-2i1ww) [exp(-2ik,\"r')g(r') s(r',t) dr'\nJexp(2iAkr1)g(r1)s(r1,t)dr\n(8)\nwhere we have assumed that s(r',t) and g(r') are spatially homogeneous on the scale of k2. The\nfirst integral is just the normal single-field scattering integral over the scattering volume. The\nsecond integral is the Ak fringe pattern filter.\n4","The long surface waves modulate both s(r1,t) and The phase modulation caused by the\norbital motion of r1 is\nso = 2Ak (Vorb/Wsw) cos(ksw°r\n(9)\nwhere Vorb is the amplitude of the long wave orbital velocity, and is its angular frequency.\nFor surface scattering, this phase modulation cannot be filtered by the second integral because of\nphase jitter induced by the random motion of the small-scale surface Bragg structure over times\nmuch shorter than the longwave phase modulation time. In other words, the signal given by Eq.\n(8) will phase average to zero over the long wave time scale. However, a time Fourier transform\nof the autocovariance of this signal (power spectrum) will succeed in revealing the Ak-filtered\ns(r,t) modulation at the frequency that the longwave passes through the filter. This is the\nstandard processing used for Ak-radar.\nOn the other hand, if there is no phase jitter on time scales less than the longwave period,\nthen both the 2Akevorb(t)/wsw phase modulations induced by longwave orbital velocity as well as\nthe s(r,t) modulation can be revealed by a coherent temporal Fourier transform of the signal\ngiven by Eq. (8). This will be the case for subsurface scattering elements that move only with the\nlongwave orbital motion. Expanding the exponent in the Ak filter integral shows that the phase\nmodulation will appear at 'sideband' frequencies separated from each other and from any uniform\ncurrent-induced Doppler frequency shift by the Ak resonant surface wave frequency as illustrated\nin Fig. 1c. From Eq. (9), the height of these sidebands is determined by the wave's peak orbital\nvelocity projected along Ak. Knowing Ak, we can then compute the absolute wave height. The\ns(r,t) amplitude modulation is expected to be zero for the high-frequency subsurface scatterers as\na consequence of the incompressibility of water; i.e., although there is advection of the\nsubsurface scatterers by the long waves, there is no coherent change in the scatterer concentration\nthat would be necessary to modulate the backscattered intensity.\n4. GEORGIA STRAIT EXPERIMENT\nIn this section we report the results of a non delta-k ocean acoustics experiment that\nsupports the phase-coherent delta-k acoustic application put forward above. The phase\nmodulation of single-frequency, coherent acoustic sounding of subsurface air bubbles was\nmeasured using 100 kHz sidescan sonars. These sidescan sonars (beamwidth to the -3 dB points\nequals 1.5° horizontal, 30° vertical) were incorporated into a self-contained high frequency\nacoustic platform, known as Susy13, that also supports six vertical sonars and several\nhydrophones. Susy freely drifts at 25 m depth suspended from a surface float. Under typical\nwindy ocean conditions, white-capping processes create copious quantities of microscopic air\nbubbles (10 - 200 um radius) that penetrate 1 to 5 m deep. Typically the resonant scattering from\nthese microbubbles makes them excellent acoustic tracers of the subsurface orbital motions\ninduced by surface gravity waves. In order to verify the above arguments concerning the phase\n5","modulation impressed by surface gravity waves on subsurface returns, we examined a short\nrecord of such vertical sonar and sidescan sonar backscatter signals taken under 10-12 m/s winds\nin Georgia Strait (British Columbia), November 24th, 1991. A 20 minute segment of 120 kHz\nupward-looking sonar intensity vs. depth is shown in Figure 2. The acoustic resonant bubble\nradius for this frequency is 38 micrometers. Waveheight effects are removed by referencing the\ndepth scale to the instantaneous free surface measured with the vertical sonars. This figure\nshows a clear presence of microbubble plumes, sometimes extending to more than 10 m, with a\nmean depth of approximately 4.5 m. In vertical incidence measurements the free surface is a\n:\nclearly identifiable feature; however for moderate to small grazing angles the resonant scattering\nfrom these microbubbles will completely dominate the Bragg scattering and obscure the surface.\nThe 100 kHz sidescan transmitted a phase-encoded pulse of 5.08 ms, which yields an estimated\nsingle-ping velocity uncertainty of 14 cm/s, with a pulse repetition period of 0.6 s. For a brief\nperiod one of the sidescan sonars was oriented roughly upwind, which yields estimates of the\norbital velocity of the wind-driven wave field. The vertical sonars give accurate (2 cm)\nmeasurements of the wave height above the instrument.\nWe processed the sidescan sonar backscatter signal in two different ways. In the first\ncase, we formed a time- and range-averaged low-frequency power spectrum of the backscattered\nintensity in 10 m range bins, using the 1.6 Hz ping rate as the sampling rate. Consistent with our\nexpectations above, we found no low-frequency modulation in the power spectrum signal in\nexcess of the expected noise background and range dependence caused by spherical spreading\nand sidescan beam geometry. In the second case, we used pulse-pair processing to extract the\nDoppler velocity in range bins equal to the pulse length (3.78 m). Low-frequency velocity\nspectra were formed from these Doppler velocities, then averaged in range and time. (note that\nAk processing would replace the range average with the Ak filter to select a single surface wave\nwavenumber.) We then converted this Doppler shift spectrum to a height spectrum a(Wsw) using\nthe relation (assuming linear wave theory and that the predominant scattering lies within the\nupper 1-2 m)\n(10)\nwhere u(Wsw) is the peak orbital velocity of the surface wave, and kac is the acoustic wavenumber.\nThis allows us to compare the derived height spectrum from the sidescan Doppler sonar with a\nheight spectrum estimated from the vertical sonars, as shown in Fig. 3. For this wave spectrum\nthe significant waveheight was 1.25 m with a peak period of 6.1 S. For a 10-12 m/s wind this is\nnot a fully developed sea. The agreement between the two height spectra is good for surface\nwave frequencies above about 0.2 Hz, illustrating that in this frequency regime the acoustic phase\nshifts imposed by bubble motions are due almost entirely to surface gravity wave orbital motions.\nThe disagreement in the spectra at low frequencies is due to the Doppler estimation noise being\naccentuated by the w-2 correction from velocity to height power. The original Doppler spectrum\ncontains little power below 0.15 Hz.\n6","5. OPEN OCEAN EXPERIMENT\nAn open-ocean delta-k acoustic test was conducted as part of a multifaceted ocean remote\nsensing experiment known as the Coastal Ocean Probe Experiment (COPE). The experiment\nwas conducted on September 28, 1995 from the Floating Instrument Platform (RV FLIP) which\nwas moored about 30 km off the northern coast of Oregon. A schematic drawing of the\ntransducer placements is shown in Fig. 4.\nTwo transducers were used, one for transmit, the other for receive. The acoustic system\noperated at 120 kHz and 120 kHz + Af where Af ranged between 400 and 1000 Hz. The\ntransmitted pulse length was nominally 20 ms, allowing the fringe pattern filter to act along eight\ndelta-k resonant surface-wave wavelengths. The raw voltage from the receiver was digitized\nwith 12-bit resolution at 625,000 samples per second. After rejecting the first 50,000 samples\n(equivalent to 59.6 m in range), 20,000 samples from each ping were collected using a ping rate\nof 3.2 Hz corresponding to about a 10 min record. The digitized signal was first squared and\nthen mixed down by multiplying by a sine-wave of frequency, Af, in order to extract the\nfrequency difference component of the signal that contains the delta-k fringe pattern. Next, the\n2000 ping record was Fourier transformed using sampling at the 3.2 Hz ping rate. A total of\nfourteen 256 point FFT were averaged giving a frequency resolution of 0.0125 Hz. Each ping\nwas range averaged over four, Af cycles,\nWe now use a formula computed for the signal-to-clutter ratio derived for delta-k radar5\nto estimate the corresponding signal-to-noise ratio for the delta-k acoustic signal. In the\nfrequency domain, the formula is given by5\nSNR =2 Rt² 1/2 (YCLUTTER/YDELTA-K) m² ksw2 F(ksw)/A\n(11)\nHere, n is the number of spectra averaged, YCLUTTER and YDELTA-K are the frequency linewidths of\nthe clutter background and the delta-k resonance line respectively, m is the modulation transfer\ncoefficient for the long waves acting on the Bragg structure, ksw is the delta-k resonant surface\nwave, F is the amplitude spectrum of the surface-waves, and A is the area of the surface from\nwhich signal is received.\nWe now estimate the value of SNR for a typical record that used a 400 Hz frequency\ndifference, corresponding to a 1.875 m wavelength, 1.915 Hz, delta-k resonant surface wave. As\nalready stated, n = 14. YCLUTTER is given roughly by dividing the windspeed (~8 m/s) by the\nBragg wavelength (0.006 m), giving 1.3 kHz. However, the 3.2 Hz sampling totally aliases this\nlinewidth, so we must use YCLUTTER ~ 1.6 Hz. The largest contribution to the linewidth of the\ndelta-k line is given by Eq. (2) The corresponding frequency linewidth YDELTA-K = 1/2 fsw (1/N)\n~\n0.11 Hz. Since the phase velocity of the delta-k resonant waves are much less than the wind\nspeed, these waves are in a fully developed, equilibrium portion of the spectrum for which F is\nusually taken as5\n7","F(ksw)~0.05 cos4()/ksw4)\n(12)\nwhere © is the angle between the wind and the surface-wave propagation vector, which was\n60 degrees in this experiment. The area A is estimated from the range and transducer beamwidth\nto be 75 m². Finally, the modulation transfer coefficient is taken to be the same as the estimate\nfor delta-k radar5: m ~ 13. Putting all of these parameter estimates in Eq. (11) gives\nSNR - 0.6\n(13)\nThis estimate is consistent with the observed delta-k spectra in the experiment, as shown\nin Fig. 5; delta-k resonance lines were not seen to rise above the level of clutter. Had the\ntransducers faced directly upwind or downwind, the SNR estimate would be 16 times larger,\nprobably making the observation of the delta-k acoustic line possible.\n6. CONCLUSIONS\nWe have examined a potential new remote sensing method for measuring directional\nocean wave spectra. The method utilizes Ak detection of the modulation of high-frequency\nbackscattered acoustic returns from surface or subsurface scattering elements. It was shown that\nfor subsurface scattering, high-frequency Ak-acoustic sensing yields an absolute measure of the\norbital velocity of the wave, without requiring knowledge of a modulation transfer coefficient, as\nis necessary with Ak-radar, and Ak-lidar sensing. This conclusion was supported by the analysis\nof a data set of coherent high-frequency returns from bubble clouds modulated by ocean surface\nwaves.\nThe results of an open-ocean experiment attempting to demonstrate the appearance of a\ndelta-k resonance line were reported. No resonance line was seen, and this result was shown to\nbe consistent with theoretical estimates for the signal-to-clutter ratio for the conditions of the\nexperiment. An unfavorable wind direction relative to the transducer look direction was\nidentified as a likely cause for not seeing the delta-k resonance line.\n7. ACKNOWLEDGMENT\nSupport for some of this work was given by the DOD Advanced Sensor Application\nProgram.\n8","8. REFERENCES\n1.\nM. V. Trevorrow, and D. M. Farmer, \"The use of Barker codes in Doppler sonar.\nmeasurements\" J. of Atmos. Oceanic Technol. 9,(5), 699-704 (1992).\n2.\nR. Pinkel and J. A. Smith, \"Open ocean surface wave measurement using Doppler sonar\"\nJ. Geophys. Res., 92, 12,967-12,973 (1987).\n3.\nD. M. Farmer and J. D. Smith, \"Tidal interaction of stratified flow with a sill in Knight Inlet\"\nDeep Sea Research 27A, 239-254 (1980).\n4.\nL. Zedel and D.M. Farmer, \"Organized structures in subsurface bubble clouds; Langmuir\ncirculation in the open ocean\", J. Geophys. Res., 96 (C5), 8889-8900.\n5.\nW. J. Plant and D. L. Schuler, \"Remote sensing of the sea surface using one-and two-\nfrequency microwave techniques,\" Radio Sci., 15, 605-615 (1980).\n6.\nW. J. Plant, \"Studies of Backscattered Sea Return with a CW, Dual-Frequency, X-Band\nRadar\" IEEE Trans. Ant. & Prop., AP25, 28-36 1977).\n7.\nR.E. McIntosh, C.T. Swift, R.S. Rughavan, and A.W. Baldwin, \"Measurements of ocean\nsurface currents from space with multifrequency microwave radars-a systems analysis,\"\nIEEE Trans. Geosci. Remote Sens., GE-23, 2-12 (1984).\n8.\nA.J. Palmer, \"Ak-lidar sensing of the ocean surface\" Applied Optics 31, 4275-4279\n(1992).\n9.\nChurnside, J.H., and A.J. Palmer, 1993, \"Delta-k lidar sensing of surface waves in a wave\ntank\" Applied Optics 32, 339-342 (Jan. 1993).\n10. D. Gjessing, Private communication; A. S. Frisch and S. F. Clifford, NOAA Environmental\nTechnology Laboratory Patent Disclosure.\n11. A. J. Palmer, \"Surface current mapping performance of bistatic and monostatic Ak-radars\"\nIEEE Trans. on Geoscience and Remote Sensing, 29, 1014-1016 (1991).\n12. J. H. Churnside and S. G. Hanson, \"Effect of penetration depth and swell-generated tilt on\ndelta-k lidar performance\" Applied Optics 33, 2363-2368 (1994).\n13. M. Trevorrow and R. Teichrob, \"Self-contained acoustics platforms for probing ocean\nsurface processes\", IEEE J. Oceanic Eng. 19 (3), 483-492 (1994).\n9","Ocean Surface\nBubbles and\n0\nParticulate Tracers\nAk Bragg Condition:\nKsurface-wave = 2 AK COS 0\nCoherent Dual Frequency Acoustic Source\nP16 ei[k1°r-wit] + P2eilki+ak) or - (w1+Aw)t]\n(a)\n*\n2\n*\nP\n2\nP\n-\nw\nsurface wave\nT\nClutter\nBackground\nW\nW\n(Aw+ w surface-wave)\n(Aw+2Ak V current )\n(b)\n(c)\nFigure 1. Basic elements of Ak acoustic sensing of surface waves: (a) physical configuration,\n(b) standard Ak cross-product power spectrum, (c) phase coherent Ak cross-product spectrum\nfrom subsurface scatterers.\n10","3 Pings averaged\nSusy IV Sonar Display\n120 kHz Channel\n20log(N):\n<38\n0-\n41\n1-\n45\n2-\n48\n3-\n52\n4-\n55\n5-\n58\n6-\n62\n7-\n65\n8-\n69\n72\n9-\n75\n10-\n79\n11-\n82\n12-\n>=82\n13:50:41\n13:55:09\n13:38:05\n13:42:07\n13:46:27\n13:34:23\nDate: 11/24/91\nFigure 2. Raw 88 kHz sonar intensity vs. depth and time from the Susy acoustics platform,\nNovember 24, 1991 in Georgia Strait, British Columbia.\n11","NOAA\nMiami\n4301\nRickenbacker\nCauseway\n102\nVertical Ranging Sonar\nSidescan Doppler Sonar\n101\n10°\n10-1\n10-2\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\nFrequency (Hz)\nFigure 3. Surface waveheight spectrum measured in Georgia Strait with sidescan Doppler sonar\nand vertical ranging sonar.\n12","RV FLIP\nNominal water line\n45'\nAcoustic sidelobes\nSonar beam (+4° )\n10° Elevation angle\nTransducers\n(10° grazing angle @ surface,\nintersection ~75m range)\nFigure 4. Depiction of the open ocean, delta-k acoustic experiment.\n13","Ping - to - ping spectrum,\nping rate = 3.2 Hz\n0.263 Hz\nLow-pass of Af mixdown\n1.0\n0.825 Hz\nof signal squared\n-0.4 Hz\n0.8\n-0.838 Hz\n0.6\n0.4\n0.2\nk resonance @ 0.915 Hz\n0.0\n0.8\n1.6\n1.2\n0.0\n-1.0\n-0.8\n-0.4\n-1.6\n-1.2\nFrequency (Hz)\nFigure 5. A typical, observed delta-k acoustic power spectrum from the open-ocean experiment.\n14\n*U.S. GOVERNMENT PRINTING OFFICE 1997-0-573-018/40057"]}