The Sea Surface Bounce Channel: Bubble-Mediated Energy Loss and Time/Angle Spreading

Transcription

1 The Sea Surface Bounce Channel: Bule-Mediated Enery Loss and Time/Anle Spreadin Peter H. Dahl Applied Physics Laoratory, University of Washinton 1013 NE 40 th St., Seattle, WA , USA Astract. A model is presented for the enery loss in the sea surface forward ounce channel due to attenuation from wind-speed-dependent ules; the model is compared to data from ASAEX and other archival data sets. At hih wind speeds the model predicts an enery loss ound, i.e., no further attenuation with increasin wind speed. Prior to reachin this ound and while there is attenuation, time and anle spreadin in the forward ounce path remain larely controlled y the spectral properties of the air-sea interface, i.e., they remain unchaned y the ules. Once oundin of enery loss occurs, initiated y the dominance of ule scatterin over air-sea interface scatterin, time and anle spreadin of the arrival chane profoundly. NTRODUCTON The process of sound enery arrivin via the sea surface forward ounce path, or channel, is loosely classified usin the parameter χ = 2kH sinθ, where k is acoustic wavenumer, H is rms waveheiht, and θ is the nominal razin anle correspondin to specular reflection. Reflection is either important or dominant when χ is less than aout 1.5, and scatterin dominates when χ is larer than 1.5. For natural sea surfaces and typical conditions, a transition from a coherent reflection to an incoherent scatterin process occurs for frequencies etween aout 1 and 10 khz. Thus, forward scatterin is operative for frequencies of order 10 khz and aove ut also at lower frequencies iven sufficiently lare kh ; here, the coherent intensity loss is typically very lare and intensity is for the most part incoherent. n this lare- χ reime an overall reduction in received incoherent intensity can also happen owin to anular spreadin (and time spreadin) eyond that which can e measured y the receive aperture (or processin time window), or from use of hihly directional sources. Yet in some propaation modelin schemes, losses associated with coherent intensity reduction, or with time and anle spreadin of incoherent intensity, have the potential of ein mistaken for real enery losses. n contrast, for eam widths and receive time windows sufficiently lare to capture this time and anular spreadin, a zero-deciel enery loss for sound arrivin via the sea surface ounce path can e readily oserved in field data (in a transmission ensemle-averaed sense). For example, this has een shown in measurements taken in the O(10)-kHz frequency

2 rane [1] and measurements taken etween 400 Hz and 1500 Hz [2], ut under waveheiht conditions such that χ spanned the rane O(1-10). For air-sea conditions that enerate sufficiently hih concentrations of near-surface ules (often requirin wind speeds in excess of 5 m/s) a true enery loss has een oserved in surface duct [3] and shallow water [4] propaation measurements at frequencies in the O(1-10)-kHz rane. This loss is the result of attenuation from nearsurface ules. n this paper a model for enery loss in forward scatterin from the sea surface due to such attenuation is introduced and compared to recent field measurements from the East China Sea and other archival data. The model and field data reveal that ules impact forward scatterin from the sea surface in three phases. The first occurs under mild conditions (wind speed less than 5 to 7 m/s); here the pulse forward scattered from the sea surface is extended in time, ut only at levels some 30 db elow the peak level, which itself is not attenuated. The second occurs under more viorous conditions (wind speed 7 to 12 m/s); here a sinificant enery loss is oserved, ut time and anle spreadin (dominated y rouh surface scatterin) remain relatively unchaned. The third occurs under still more viorous conditions (wind speed reater than 12 to 15 m/s). Here, there is near total occlusion of the sea surface, time and anle spreadin are manifestly altered, and ule-mediated enery loss ecomes ounded y scatterin from ules. ENERGY CONSERVATON N FORWARD SCATTERNG AND MODEL FOR ENERGY LOSS DUE TO BUBBLES Fiure 1 shows the asic eometry for forward scatterin from the sea surface for an acoustic source at position P 1 and receiver at position P 2. Scatterin is descried y the distriution of the istatic cross-section over the sea surface as a function of position s, with position s SP correspondin to the specular point. These positions are taken to e on the plane associated with the mean sea surface heiht. The istatic cross section associated with sea surface rouhness σ r () s is a function of frequency, eometry (source depth, receiver depth, and rane), and environment (sea-surface rouhness correlation function and χ ). We construct σ r () s usin a comination of surface wave measurements and modelin [1, 5]. The property of enery conservation is assumed to apply as: σ () sbsda ( ) 1 =, (1) ( )( ) [( ) ( )] r s Ps 1 Ps 2 Ps 1 SP + Ps 2 SP where Bs () is the comined transmit and receive eam pattern weihtin, and the interal on the left side over the area of sea surface is computed as a Riemann sum with area interval da. This equality holds for transmit and receive eam patterns S

3 FGURE 1. Geometry for study of forward scatterin from the sea surface; source is at P 1, receiver at P 2, S SP is specular point on the plane correspondin to mean sea surface and S is aritrary point, with variale shadin depictin the hypothetical sea surface istatic cross section. Path connectin P 1, S SP, and P 2 has razin anle θ. sufficiently wide to oth illuminate the sea surface and receive scattered intensity from areas away from the specular point [6]. As a rouh uideline [5] the necessary horizontal anular width for the case of equal source and receiver depths oes as SLsinθ and the vertical anular width oes as SLcosθ, where S L is the root-meansquare lare-scale slope of the sea surface [7]. Takin S L ~0.15 as a nominal value, the necessary one-way intensity eam width for transmit and receive is ~20. For a more eneral conditions we take the left side of Eq. (1) as the enery conservation measure to e used susequently. Scatterin and attenuation from susurface ules contriutes to, and modifies, the total istatic cross section σ as: σ = σα r + σ, where α (dimensionless) is an attenuation factor and σ is the istatic scatterin cross section per unit area sea surface due to ules [1]. Both α and σ depend on the dimensionless parameter β, equal to the depth-interated extinction cross section per unit volume, withβ enterin into α as: α = exp( β /sin θ β /sin θ ), (2) i s where θ i and θs are incident and scattered razin anles, respectively. The parameter β succinctly descries an acoustically relevant measure of the concentration of near-surface (wind-enerated) ules; however, an expression for β as function of environmental conditions must necessarily e determined empirically. One such expression derived from low-anle ackscatterin measurements made in the O(10 100) khz frequency rane, that are exceedinly sensitive to the concentration of near-surface ules, is: lo10 β = U lo10 f, (3)

4 where U10 is 10-m heiht wind speed in m/s and f is frequency in khz [8]. The aove concepts lead to a model for ule- mediated enery loss in hihfrequency ( χ >> 1) forward scatterin from the sea surface, which is the followin ratio expressed in db: σ () s α ( sbsda ) ( ) σ ( sbsda ) ( ) + r s s ( Ps 1 )( Ps 2 ) ( Ps 1 )( Ps 2 ) σ ( sbsda ) ( ) ( )( ) r s 2 2 Ps 1 Ps 2. (4) n the numerator, the left-hand (attenuation) term determines enery loss as a function wind speed (i.e., ule concentration), and this term dominates at low to moderate wind speeds; in the asence of ules α 1, σ 0, and the ratio oes to unity. At hih wind speeds, the left-hand term vanishes and the riht-hand (scatterin) term ecomes sinificant and estalishes an enery loss ound. This ound is inherently a result of scatterin from a two-dimensional surface. When the enery loss reaches the ound determined y ule scatterin, there is in effect total occlusion of the sea surface. n reards to the attenuation term, we note that α() s α( ssp ), and thus Eq.(4) ehaves very nearly as Eq. (2) evaluated at θ i and θ s, oth set equal to the specular razin anle θ, with implication that enery loss scales with the inverse of θ. A typical value for β is ~ 0.1 for wind speeds of 8 10 m/s and frequencies near 20 khz; settinθ to 10 puts α = 0.32, or an enery loss of aout 5 db per interaction with the sea surface. t is important to keep in mind that ecause the model applies only to the χ >> 1 reime, surface decouplin (Lloyds mirror) effects [3, 9] are not operative. For the same example, when the wind speed exceeds aout 12 m/s, β ~ O(1), and the left side of the numerator in Eq.(4) vanishes. Given sufficiently wide eam patterns (as per aove), the enery loss ound is 17 db, with narrower eams resultin in a hiher ound. FELD MEAUREMENTS FROM ASAEX AND EARLER STUDES Measurements of forward scatterin from the sea surface were made in the East China Sea as part of the ASAEX field proram [5]. Fiure 2 shows the sound speed profile and correspondin ray diarams for two sets of measurements made simultaneously at frequency 20 khz. The wind speed durin these measurements ( UTC 31 May 2001) was 7 m/s ± 0.5 m/s and the rms sea surface waveheiht was 0.3 m ± 0.1 m. Based on the sound speed profile (Fi. 2a) the razin anle associated with the specular path (dashed lines in Fi. 2) for the upper () and lower (c) receivers is 6.1 and 10.9, respectively. Fiure 3 shows received multi-path arrival structure for the mean intensity (ased on an ensemle averae of 20 transmissions) for the 26-m (upper plot) and 52-m (lower plot) receiver depths and model curves correspondin to

5 the mean intensity for the sea surface ounce path. (The overlap etween the direct and surface ounce paths for the upper receiver is not addressed y these model curves.) Note that for modelin purposes oth the source and receiver are effectively omni-directional. (There were in fact four such receivers separated y 13 cm, 30 cm, and 60 cm at each receive depth to measure vertical spatial coherence [5].) The model curves are the result of convolvin a model for the intensity impulse response [7] with the envelope of the transmit pulse (a 3-ms lenth oxcar function). The intensity impulse response is set y istatic cross section σ. The solid curves are ased on σ = σr for which an estimate of the 2-D autocorrelation function of sea surface waveheiht variation is required (see [5] for additional details on this function), and the dashed curves incorporate ules via σ = σα r + σ, for which a wind speed of 7.4 m/s is used, puttin β = Clearly, incorporatin ules via α, σ as a uniform distriution over the sea surface is a very simplified representation of the distriution of near-surface ules. Yet the two dashed model curves reproduce well ule scatterin phenomena oserved fully 20 to 30 db elow peak scatterin level and a few db aove the noise. (Model curves are made consistent with the data y addin noise, the level of which is shown in Fi. 3.) Attenuation from ules results in a predicted enery loss of 1.14 db for the shallow receiver and 0.77 db for the deep receiver; the difference is due to the different nominal razin anles. The data are consistent with these loss estimates; however, the small difference etween the two losses is difficult to verify statistically ased on 20 pins. An estimate of the time spread in forward scatterin from the sea surface is made y formin the time-delay scatterin function, which is a scaled version of the intensity impulse function. nteral measures of the time spread, defined as the characteristic time spread L [7], are noted in Fi. 3 for the cases with and without ules; they show that althouh the pulse extension due to ules (seen est with the upper receiver in Fi. 3) appears sinificant, the overall chane in characteristic FGURE 2. (a) Averae sound-speed profile correspondin to time of acoustic measurements taken durin ASAEX, East China Sea () Ray diaram for 26-m depth receiver and (c) for 52-m depth receiver. Dashed lines in () and (c) show rays interactin once with the sea surface.

6 FGURE 3. (a) Averaed received intensity (ray line) in db plotted on relative scale (0 db corresponds to approximately 126 db re µpa) for the direct, surface-ounce, and ottom-ounce paths correspondin to the eometry in Fi. 2. Solid, lack line is model for mean intensity in the surface ounce path ased on a 3-ms lenth, CW pulse with center frequency 20 khz. Dashed, lack line is same model ut includes the effects of ules; () corresponds to eometry in Fi. 2c. The noise level for each eometry is shown y the dotted, lack line. time spread due to ules is small. There is, however, a sinificant difference in L associated with the different receiver depths, and a model for L [7] predicts results in Fi. 3 reasonaly well, ivin L = 0.67 ms and 0.83 ms for the upper and lower eometries, respectively. A somewhat analoous, yet different, situation exists for anular spreadin in the sea surface ounce path. n ASAEX, anular spreadin was determined via 1/2 measurements of vertical spatial coherence [5]. The ( e ) vertical coherence lenth d at 20 khz for the 1-m VLA at the 26-m depth is 3.4 wavelenths, whereas this value is 4.0 wavelenths for the VLA located at 52 m. Anular spreadin oes as * 1/kd, thus vertical anular spreadin for the upper receiver is slihtly reater than that for the lower receiver. This result is opposite that for time spreadin, ut consistent with the models for the eometric dependence for oth time and anle spreadin iven in [7]. The analoy is that ules also have little influence on anular spreadin. Spatial coherence estimates can e modeled well usin an approach involvin the istatic cross section and the van Cittert-Zernike theorem [5]. Model results with and without ules show no difference, consistent with time and anle spreadin in the sea surface ounce path ein larely set y properties of rouh surface scatterin. Measurements made at 30 khz displayin more sustantial loss (3 db) also suest that characteristic time and anle spreadin in forward scatterin from the sea surface are altered little due to scatterin from ules [7]. We show

7 susequently that this conclusion chanes when ule concentration is sufficiently hih such that total occlusion of the sea surface is in effect. Fiure 4 shows estimates of enery loss due to attenuation from near-surface ules (i.e., in excess of spreadin and sea-water asorption) for the entire ASAEX measurement set taken at 20 khz and similar archived data. The ASAEX measurements, taken over two continuous 24-h periods (separated y 6 days), represent the larest data set of this kind. There is considerale eoraphic variety represented in Fi. 4: ASAEX measurements were taken in the western Pacific littoral; FLP measurements [7] were taken in the Pacific pelaic zone; Quinault measurements [10] were taken in eastern Pacific littoral; and Whidey measurements [11] were taken in inland waters of Puet Sound althouh with an extended fetch to the west. Each measurement represents a careful accountin of losses due to spreadin and sea water asorption, for a sinle interaction with the sea surface. The error ars (not availale for the data from [11]) take into account oth caliration uncertainty and statistical fluctuations (ivin a neative loss in some instances) that depend on the numer of transmissions; e.., uncertainty in the ASAEX estimates is due larely to the 20 transmissions that enter into the averae. FGURE 4. Estimates of enery loss in the sinle surface ounce channel due to attenuation from near-surface ules as a function of wind speed. Frequency is 20 khz and nominal razin anle is 9. Results from four experiments (year of experiment identified in leend) are shown. Whidey measurements were taken etween 15 khz and 25 khz; see text for further explanation on the razinanle-scalin of some of these data points. The solid curve is the ule enery loss model ased on Eqs. (3) and (4) computed at 20 khz, with source, receiver, and rane eometry such that nominal razin anle θ equals 9, correspondin to the majority of the ASAEX data; further Bs () = 1 ecause all measurements in Fi. 4 were made with omni-directional sources and receivers. Note, however, that some measurements from the other experiments were taken at razin anles different from 9, e.., the FLP measurements represent the

8 rane θ = Therefore, these data have een scaled y the factor sin θ /sin 9 whereθ is the particular razin anle of the measurements. The data and model suest three phases of impact of ules on forward scatterin from the sea surface: no attenuation, increasin attenuation with increasin wind speed, and an attenuation ound phase (occlusion) at very hih wind speeds. Sinificantly, the data in Fi. 4 also demonstrate that it is very difficult to oserve a loss-versus-wind-speed sinature in the field measurements of forward scatterin until the wind speed exceeds aout 7 m/s. This contrasts with low-anle ackscatterin, which is exceedinly sensitive to wind speed [8], ut is also consistent with the model iven here, that puts the loss at only 0.45 db at 7 m/s wind speed. With addition of the larer set of ASAEX measurements, a transition to the attenuation phase (wind speeds etween 6 m/s and 8 m/s) now appears to e displayed y the comined data set. Althouh the comined data set in Fi. 4 is reasonaly consistent with the model, there are, unfortunately, fewer measurements made in the attenuation phase that are also ased on a sinle interaction with the sea surface, such as the measurements in Fi. 4. The measurements of Wille and Geyer [4] show convincinly, however, how an excess total transmission loss in shallow water involvin oth sea surface and seaed interaction, increases and ecomes stronly dependent on wind speed, when in their case the wind speed exceeds aout 10 m/s, and thus are somewhat consistent with Fi. 4. (n this case, one component of excess transmission loss is due to scatterin into hiher razin anles with enery susequently lost to the seaed.) The field measurements reported in McConnell [11] represent intriuin oservations apparently made under conditions of total occlusion, for which an enery loss ound is oserved. These measurements (plotted on the far riht side of Fi. 4) were also interleaved with measurements of vertical and horizontal spatial coherence, the results of which were first iven in a 1990 report [12] and re-visited here. Fiure 5 shows the estimates of horizontal and vertical coherence compared with model-ands for spatial coherence, computed usin the method from [5]. The three versions of model-ands are ased on rouh-surface scatterin equivalent to a wind speed of 17 m/s and fetch of 40 km, plus scatterin and attenuation from ules for three cases: no ules, ule concentration from Eq. (3) for wind speed of 10 m/s, and for wind speed of 17 m/s representin total occlusion. The model-ands incorporate uncertainties (the ands) in the six receivin eams involved in the measurements, three distriuted horizontally and three vertically, and appear nominally consistent with the coherence estimates. (Here the apparent insensitivity of the models for vertical coherence to ule concentration, is due to the individual eam patterns that compose the vertical receivin array.) Most sinificant, however, is that horizontal coherence must always exceed vertical coherence for sea surface forward scatterin with this acquisition eometry, yet it can e seen in Fi. 5 that horizontal coherence has een knocked down to levels predicted y istatic scatterin from near-surface ules and susequent total occlusion of the sea surface.

9 FGURE 5. Estimates of the manitude of vertical (a) and horizontal () spatial coherence plotted as a function of receiver separation normalized y 15-kHz wavelenth. Model-ands are derived usin rouh-surface istatic cross section at wind speed 17 m/s and three cases for ules: no ules, ule concentration at 10 m/s, and 17 m/s. For vertical coherence the case of no ules and ule concentration at a wind speed of 10 m/s are indis tinuishale. SUMMARY A model for enery loss in the sea surface ounce path due to attenuation from near-surface ules has een presented; it applies to the nominal frequency rane O(10 100) khz and assumes the parameter χ is >> 1. The model compares reasonaly well with measurements from the recent ASAEX experiment and archival data sets. Three phases of impact of ules on forward scatterin from the sea surface are illustrated: the first is no discernale attenuation, which occurs under mild conditions (wind speed < 5 7 m/s), wherein ules extend the pulse forward scattered from the sea surface, ut only at levels 30 db elow the peak level, which itself is not attenuated. The second occurs under more viorous conditions (wind speed 7 12 m/s); here a real enery loss is oserved, ut time and anle spreadin (dominated y rouh surface scatterin) remain relatively unchaned. The third occurs under still more viorous conditions (wind speed > m/s); here there is near total occlusion of the sea surface, time and anle spreadin are manifestly altered, and ule-mediated enery loss ecomes ounded y scatterin from ules. Althouh two major effects of total occlusion, the reduction in horizontal spatial coherence and the oundin of attenuation, were demonstrated with field data, additional field measurements of this phenomenon are needed to verify the model presented here.

10 ACKNOWLEDGMENTS This work was funded y the Office of Naval Research, Ocean Acoustics Proram. REFERENCES 1. Dahl, P.H., On Bistatic Sea Surface Scatterin: Field Measurements and Modelin, J. Acoust. Soc. Am., 105, (1999). 2. Nichols, R.H., and Senko, A., Amplitude Fluctuations of Low-Frequency Underwater Acoustic Pulses Reflected from the Ocean Surface, J. Acoust. Soc. Am., 55, (1974). 3. Weston, D. E., On Losses due to Storm Bules in Ocean Sound Transmission, J. Acoust. Soc. Am., 86, (1989). 4. Wille, P.C. and D. Geyer, Simultaneous Measurements of Surface Generated Noise and Attenuation at the Fixed Shallow Water Rane NORDSEE, in: Proceedins Advanced Research Workshop on Natural Mechanisms of Surface Generated Noise in the Ocean, June 1987, Lerici, taly, pp Dahl, P.H. The van Cittert-Zernike Theorem and Forward Scatterin from the Sea Surface, J. Acoust. Soc. Am., 115, (2004). 6. McDonald, J. F. and Spindel, R.C., mplications of Fresnel Corrections in a non-gaussian Surface Scatter Channel, J. Acoust. Soc. Am., 50, (1971). 7. Dahl, P.H. Hih-frequency Forward Scatterin from the Sea Surface: The Characteristic Scales of Time and Anle Spreadin, EEE J. Ocean. En., 26, (2001). 8. Dahl, P.H. The Contriution of Bules to Hih-Frequency Sea Surface Backscatter: A 24-h Time Series of Field Measurements, J. Acoust. Soc. Am., 113, (2003). 9. Tappert, F. D., nhomoeneous Asorption and Geometric Acoustics, J. Acoust. Soc. Am., 103, (1998). 10. Thorsos, E.., Hih Frequency Surface Forward Scatterin Measurements, presented at the 108 th meetin of the Acoustical Society of America, Octoer McConnell, S. O. Acoustic Measurements of Bule Densities at khz, in: Proceedins Advanced Research Workshop on Natural Mechanisms of Surface Generated Noise in the Ocean, June 1987, Lerici, taly, pp Dahl, P.H. and McConnell, S. O. Measurements of Acoustic Spatial Coherence in a Near-Shore Environment, APL-UW TR 9016, Auust 1990.