Low-Frequency Sound Attenuation in the Deep Ocean R. J. Urick
Citation: The Journal of the Acoustical Society of America 35, 1413 (1963); doi: 10.1121/1.1918705 View online: https://doi.org/10.1121/1.1918705 View Table of Contents: http://asa.scitation.org/toc/jas/35/9 Published by the Acoustical Society of America
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Low-Frequency Sound Attenuation in the Deep Ocean
R. J. URICK U.S. Naval OrdnanceLaboratory, White Oak, Silver Spring, Maryland (Received24 May 1963)
Signalsreceived from Sofar bombsdropped from an aircraft eastwardfrom Bermuda have beenstudied quantitatively. The energydensity of the signalsreceived at Bermuda, measuredin variousbands between 20 and 1600cps, can be accountedfor by cylindricalspreading beyond a "transitionrange" predicted approxi- mately by simpleconsiderations, plus an attenuationcoefficient in dB per megayardgiven by the linear expression1.5+8.2 f, wheref is the frequencyin kc/sec.At frequenciesbelow 1 kc/sec,this attenuationis far in excessof that which would be producedby absorptionalone. At very low frequenciesthe excessat- tenuation is postulatedto be due to the failure of the Sofar soundchannel to act as an acoustictrap. At frequenciesfrom about 50 to 500 cps, quantitative evidenceis presentedto indicate that the dominant attenuationprocess is scatteringby index-of-refractioninhomogeneities deep in the sea.Other characteristics of Sofar-transmitted signalsare described.
INTRODUCTION tention.4.* However, the amplitude, duration, and spectralcharacteristics of Sofar signalshave not been Nsurfaces,the deep the ocean, attenuation farfrom of soundeffects at of frequenciesthe bounding be- studied extensively from a quantitativeviewpoint, even low 1 kc/sec is known to be of the order of only a small though these characteristicsare of dominant interest fractionof a decibelper mile. For example,the formula for long-rangeacoustic communication in the deep sea. This paperdescribes the resultsof a seriesof measure- a=0.033f• (a in dB per kiloyard,f in kc/sec)proposed ments made across the Atlantic Ocean between by Sheehyand Halley,• as a fit to their measurements, wouldindicate a coefficientof only 0.033dB per kiloyard Bermudaand the United Kingdom. The spreadinglaw and attenuation coefficient for this series of shots and at 1 kc/sec, with smaller values at lower frequencies. Measurementsof valuesas low as theserequire propa- the lossproduced by the Mid-Atlantic Ridge are de- gation paths that are measuredin hundredsof miles, scribed,and processesare postulatedto accountfor under conditionswhere reflection and scattering from the excessattenuation over that due to absorptionat the sea surface and sea bed are not involved. This low frequencies. implies,in turn, the useof the Sofarchannel for long- MEASUREMENT PROCEDURE distancepropagation, since the requiredpath lengths and freedom from boundaries cannot otherwise be ob- StandardNavy Sofarsignals, containing the equiva- tained.In addition,the useof explosivesis dictatedby lent of 4 pounds of TNT, were dropped on a pre- the needfor high acousticsource levels. assignedtime scheduleby an aircraft as it flew between The existenceof a soundchannel in the deep seawas Bermuda and Great Britain via the Azores during predicted and demonstratedby Ewing and Worzel2 June1962. The locationof the dropsis shownin Fig. 1. about 20 yearsago. Named for its usefor soundfixing The maximumrange, from Bermudato the furthermost and ranging,it has receivedattention as a meansof drop,was 2516 miles. At eachlocation a pair of signals location of downed aviators and, more recently, of set to detonate at depths of 1500 and 3500 ft was missileimpacts? In consequence,the travel times for droppedalong with a sonobuoyfor observingthe Sofarchannel propagation have receivedabundant at- instant of detonation aboard the aircraft. At the Bermudaend, recordingswere made with hydrophones •M. J. Sheehyand R. Halley, J. Acoust.Soc. Am. 29, 464 4 R. A. Frosch,M. Klerer, and L. Tyson,J. Acoust.Soc. Am. (1957). 33, 1804 (1961). 2 M. Ewing and J. L. Worzel, Geol. Soc.Am. Mem. 27 (1948). 5 G. M. Bryan, M. Truchan,and J. Ewing,J. Acoust.Soc. Am. 3H. H. Baker, Bell Lab. Record39, No. 6, 195 (June 1961). 35, 273 (1963). 1413 1414 R. J. URICK
Fro. 1. Location of Sofar bomb drops.
at variousdepths; however, only the data from a As a result,Sofar signals received at a greatdistance hydrophoneat 3900ft, in water14 000 ft deep,are havea typicalenvelope that showsa gradualbuildup describedin thispaper. The taperecordings were later and reaches a sudden climax at the instant that the analyzedin theconventional way by playingback into axiallytraveling energy arrives. This abruptending is bandpassfilters, squaring, and integrating to obtainthe the characteristicthat makes them useful for triangu- energydensity of the receivedsignals in the various lation purposes. filter bands. Alongthe path of the dropsshown in Fig. 1, the transmission of sound in the Sofar channel is inter- SOFAR CHANNEL AND SIGNAL ENVELOPES ruptedby the Mid-AtlanticRidge, which forms an The Sofar soundchannel is an internal acousticduct acousticbarrier for deeppropagation across the Atlantic havingits axis, or depth of minimum velocity, at depths Ocean.Bathymetric charts ø shownumerous places in rangingfrom about 5000 ft in thetropics to nearthe thevicinity of theacoustic path where the crestsof the surfacein highlatitudes. Its existencedepends upon Ridgepierce the depthof the Sofaraxis and thuscut the fact that the velocityof soundincreases with both off near-axialrays carrying the principalportion of the transmittedenergy. The attenuatingeffect of theRidge temperatureand pressure; at shallow depths, where the will be evident in the results to follow; in spite of it, temperaturedecreases with depth, the temperature effect is dominant and the velocity decreases;at great signalswere received 5 to 10 dB abovenoise at the depthswhere the sea is nearlyisothermal, the pressure maximum range (Drop 29), althoughthe dropsjust effectcauses the velocityto increaseagain. Figure 2, beyondthe Ridge(Drops 20, 21) appearto havebeen taken from the now-classicpaper on the subjectby cut off by the shadowingeffect of the crestsand were not received at Bermuda. Ewingand Worzel, •'shows a typicalvelocity profile in The sound-velocitystructure along the line of drops midlatit.udes•together with a ray diagramfor a source on theaais. Ray pathsnear the axis carry most of the 6Charts BC 0307N, BC 0308N, publishedby the U.S. Navy .energy•.n,.• .a.r,e •oc[ated with the longest travel time. OceanographicOffice. SOUND ATTENUATION IN THE DEEP OCEAN 1415
DO0
FIG. 2. Ray diagramof the Sofar soundchannel. [Reproduced from Ewing and Worzel.2-] was estimated from velocity data provided by the been done by Brekhovskikh,7 that for both sourceand National OceanographicData Center. Figure 3 is a receiver on the axis of a sound channel the difference in velocity contour cross section drawn from N.O.D.C. travel times along the axial ray and along the ray hydrographicdata for the month of Juneat stationsin leavingthe sourceat an angle00 is tOo2/6,where t is the the vicinity of the drop path. The feature most worthy axial travel time. The straightline in Fig. 5 showsthis of note is the decreasingvelocity at shallow depths calculatedduration for 00-12.2 ø for the ray of maxi- toward the right, reflectingthe lower surfacetempera- mum inclination propagating without reflection at tures toward the northeast along the drop path. How- either the seasurface or seabed. The agreementis sur- ever, the depth of the Sofar axis is approximatelycon- prising, consideringthat the Sofar channelhas by no stant, although at the northeasterlyend its depth is means the linear gradient on either side of its axis re- made uncertainby the occurrenceof nearly isovelocity quired for this approximation.The absenceof a clear conditions. beginningto the receivedsignal is perhapsdue to the Figure 4 showssignal envelopes in the band 50-150 contributionby rays which leave the sourcebeyond cpsfor a shotat 3500 ft as receivedby the hydrophone 12.2ø and which sufferrepeated reflection at either or at 3900 ft at Bermuda. The vertical scale shows the both seaboundaries. Beyond the Ridgeat abouta range band level in decibelsrelative to the intensity of a plane of 1800 miles, the durations based on the above cri- wave of 1 dyn/cm2 rms pressure.The envelopesexhibit terionare muchshorter because the early portion of the the expectedlengthening and weakening with increasing signalsare buried in noise,and becausethe near-axial range.Signals from dropson the far (eastern)side of rays are cut off by the Ridge. In the South Atlantic, the Mid-Atlantic Ridge were weaker and shorter than where the Ridge crestsdo not pierce the Sofar axis, those on the near side, presumablybecause of the the effect of the Ridge on signal duration is not as removal of near-axial rays by the Ridge. In no case great.* If, however, one measuresfrom a point on the beyondDrop 3 (93 miles)did the signalsexhibit a clear envelope1 Np (8.7 dB) belowthe peak intensityto the beginning. cessationof the signal,a steadyincrease along the whole Figure 5 is a plot of signal duration against range, path is found, as indicated in the right-hand portion of usingtwo criteria for measurementof duration. If the Fig. 5. If the envelopebe assumedexponential, the con- signalduration is taken to be the interval from a point venienceof this criterion is that the energylevel E can on the envelope3 dB above the ambient noiseback- easilybe shownto be related to the peak intensity level groundto the suddentermination, the durationshows a steadyincrease with rangeout to the Ridge.By simple • L. M. Brekhovskikh, Waves in Layered Media (Academic ray theoryfor a linear gradient,it can be shown,as has Press Inc., New York, 1960), Eq. 39.14. 1416 R.J. URICK
A 5olo B C D E F G H I J K L M 1_22_.98 ---117'"'"''92•.-- •" _.97•101------'102-"'82'66 '68 •.'85'•..-""---78..-•82...,•.60 •'54 '60 '65 '44 w•-• •-'56-'34' •'" '20 '`32 '19•50 113 4990 IOOO
85 '86 '72'63 •'6 .'29"'--'-'33'" '48..-'18 '18 '19 '25 12 2000 - 4970 _._....----' --' '" • • "• ., •" • • ...... •;;_-./ ...... 3ooo ,7 ------..4910.____.12 ..... I I'"'--• O•_lB .-12 '-7 '1 ..(9j15 --2 '22 27
4000
5000 ()-I0 0 2 8 9 7 7 0 3 12•010 II
6000- ...... 49,o • '""'' ...... 6 .-I ß16 '17 ßi5 13 7000 - 4930
8OOO ,40 9000
!o, ooo
0 •. 4I 6! 8! I0I 12I 14I, , 16I 18I , 20! ?-21 24! DISTANCEFROM BERMUDA(HUNDREDS OF MILES)
Fro. 3. Velocity structurealong a profileapproximating the path flown.Velocity data at selectedoceano- graphicstations during the monthof June,as compiledand computed by the NationalOceanographic Data Centerfrom measuredtemperature and salinitydata, using the Kuwaharaformula. Velocity values in ft/sec relativeto 4900ft/sec (i.e., 4900ft/sec=0). Minimumvalues (circled), shown at tabulateddepths for the various observationstations, determine the depth of the Sofar axis. Locationsof various stationsA to M are: A' 32.ø1N,64.ø5W; B: 38.5N, 56.7W; C: 38.0N, 50.2W; D' 37.2N, 48.5W; E: 36.1N, 44.0W; F: 37.1N, 38.1W; G' 39.5N, 33.7W; H: 39.9N, 31.1W; I: 41.1N, 29.8W; K: 43.1N, 18.1W; L: 45.0N, 16.0W; J i 48.1N,43.0N, 12.7W.24.1W;
I and the above interval T2 in secondsby the simple againstrange for shots at 3500-and 1500-ft depths. The relationshipE=Iq-10 logT2--3, whereE is in decibels shots at 1500 ft were about 10 dB weaker than those referred to the unit of intensity, taken for a period of near the axis of the Sofar channel. The dashed curves 1 sec.
28 PREDICTED MAXIMUM RANGE 24 Figure 6 is a plot of the peak-signalintensities read from the signal envelopesin the 50- to 150-cpsband 2O
4O
z //•,o•7 / • g 20 494 O8
2 O4
o o 4 8 12 16 20 24 •u•-I0 / 24.30 RANGE (HUNDREDS OF MILES) - / -I0 ,-9 i , -8i -7i -6i -õi -4[ -3i -2! -i I 0i iI 2 Fro.5. Signaldurations in the50- to 150-cpsbands from a point TIME (SECONDS FROM PEAK) on the rectifiedenvelope 3 dB aboveambient noise to the end of thesignal (crosses) (T•), andfrom a point8.7 dB belowthe peak Fro. 4. Rectifiedenvelope of receivedsignals at variousranges. signalto the end (circles)(T•). The vertical dashedline is at the The signalat 2430 miles came from a shot on the east side of the locationof the Mid-AtlanticRidge. The slopingline is the pre- Mid-AtlanticRidge. The tracesshown are from Drops 4, 7, 12, 17, dictionbased on a linear velocitygradient. Different scalesare and 28 (Fig. 1). used for Tt and T•.. SOUND ATTENUATION IN THE DEEP OCEAN 1417
DROP NUMBER • 4 6 8 I0 12 14 16 18 20 22 2426 28
• 3ø1 I '1'./ I /1'I44 SP.ER•CALSPREAO•NG I1 I I I I I I I , I i I I II II I I I I • I I x] dlll'Io.oPLUS ,•oATTENUATIONLoG r, 80• • + •+•-J'-'- 20-40 I z 20 75 •-•-7-+ -•---•+-I 4o-8o I + ++ 45 •rn S 85 • - -:F'" * [ 40 •tn I0 80i" +"'7'-'•'•++ •-L.•+ I .... (-• >-0 • + 55 • • 0 X I I •11 + •• •I 5o • Z7 Xø , • • + 8o-•6o I z -I0 MEANOBSERVEDI I I I III •1 • • • • '1 I/IX • BACKGROUND LEVEL j + • ,, 55 • I + 5o • •- 95 • + J • •• + •o-,•c I ]11 ,,, 90 • Z I00 I000 I0 000 RANGE (MILES) >- 85 •+1 Fro. 6. Pe•k Sof•r signMintensities in the 50- to 150-cpsb•nd J 60 m for shots•t 1500 •nd 3500 ft. The dashedcurves show spherical 95 •+ I + ++ spreadingplus attenuationat 4.0 dB per kilomile. The extrapo- lated peak level equMsthe mean •mbient level at 6000 miles for • 90 • '•• • +•0-•40 JI + 55 4-lb charge •s used in the experiment. The signal from • 300-lb 85 + •x I depth chargewould equal ambient •t 10 000 miles. +••1 ' I J + + 50 showspherical spreading 8 plus attenuation fitted to the 45 measureddata and (for the 3500-ft shots)extrapolated 0 4 8 12 16 20 24 28 in rangeuntil the measuredaverage level of the ambient RANGE (HUNDREDS OF MILES) backgroundis reached.If this can be taken as the limit Fro. 7. Energydensity levels plus 101ogr, in unitsof dB relative of detectability, then a 4-lb charge should be received to the energydensity of a 1-dyn/cm•-plane wave for a periodof 1 sec (dB re 1 dyn/cm•') in octave bands. The vertical dashedline out to a range of 6000 miles, and a 300-lb chargeto showslocation of Mid-Atlantic Ridge. Different level scalesare about 10 000 miles, in the absenceof attenuation caused usedfor the data on eachside of the ridge. by a major path obstructionsuch as the Mid-Atlantic Ridge in the vicinity of the Azores.The latter distance may be compared with the observationmade by the dricalspreading. The fit of thedata to thestraight lines Lamont GeologicalObservatory ø that a depth charge drawnby eye throughthe plottedpoints indicates that detonated off the coast of Australia was heard at the decreasein energydensity with rangemay be de- Bermuda 12 000 miles away. scribedin termsof cylindricalspreading (10 logr) plus an attenuationloss proportional to range.Thus, the ENERGY ANALYSIS energydensity level E, at ranger in yardscan therefore The signals-whose envelopes have just been described be related to the energydensity level E0 at the unit were filtered in octave and third-octave bands and rangeof 1 yard by the expression integrated soas to obtain energydensity. In the follow- E,= E0-- 20 logr0--10 log(r/ro)--arX 10-• ing, the unit of energy density is the energy density of a plane wave of rms pressure1 dyn/cm2 taken for a = (E0-- 10logr0)-- 10 logr-arX 10-• , period of 1 sec; in decibel units, this reference is abbreviatedsimply as 1 dyn/cm2, in analogywith the wherer0 is a transitionrange separating the regionsof practicefor intensity. Figures7 and 8 showmeasured sphericaland cylindrical spreading, and a is an attenua- valuesof a singledrop in variousbands of the quantity tion coefficientmeasured in dB per megayard(10 • F,-+-10logr, where E is the band energydensity in dB yards).In Figs.7 and8, theintercept at zerorange is relativeto 1 dyn/cms and r is the rangein yards.Thus, the quantityE0--10 logr0,while the slopeis the coeffi- thesevalues are energy-density"corrected" for cylin- cienta. TableI listsmeasured values for (E0--10 logr0), a, and the energyloss produced by the Mid-Atlantic 8Although energy spreads cylindrically in a channel,intensity must decreaseas the inverse square of the distance in the Sofar Ridgefor the variousanalysis bands. channelbecause of the travel time dispersiondiscussed above. In the recently reported work of Bryan, Truchan, and Ewing,5 an inverse third power, instead of inverse square, is said to fit the EXPLOSIVE SOURCE LEVELS measured peak intensities. However, attenuation, in the un- specifiedfilter band used,was neglected;inverse-cube spreading may well be sensiblyequivalent to inverse-squarespreading plus Furtheranalysis requires a determinationof E0, the attenuation. sourceenergy density level at 1 yard. In orderto obtain 0 Note, Trans. Am. Geophys.Union 41, 670 (1960). this quantity, 4-lb Sofar bombs similar to thoseused 1418 R.J. URICK
DROP NUMBER pulse,occurring at the expectedTM interval of 7 msecafter 2 4 6 8 I0 12 14 16 18 II I I ! I I I I I I I I II the shockwavefor the particular charge weight and depth used, were found to make an appreciablecon- __ I tribution to the total energy. Figure 9 showsenergy • 355-446 •..!-F spectrumlevels at the measurementdistance of 3700ft, obtained by digital analysis at frequency intervals of 50 cps. The right-hand scalegives theselevels reduced to oneyard on the assumptionthat sphericalspreading appliesto the shockwaveas well as to the bubble-pulse 5dõ contribution. This assumptionyields one-yard levels different from those which would be actually measured at 1 yard, inasmuchas the scalinglaws for shockwaves '• 710-901 are ignored;the correctionsrequired would lie between 0 and 5 dB, dependingon frequency. The measured •+•+ ++ data agreewell with the spectrareported by Weston.TM + From this spectrum, octave and third-octave band levelswere computed,and are given in Table I.
T•m•.• I. Transition range, attenuation coefficient,and Mid-Atlantic Ridge lossin various frequency bands.
Energy loss across Freq. Mid- • 1400-1810 band, Mid- Atlantic r0 cps freq. (E0--101ogr0) a Ridge E0 101ogr0 yards
20-40 28 78 dB 1.7 25 dB 113 dB 35 3000 40--80 56 86 2.2 21 120 34 2500 80-160 110 90 2.8 22 126 36 4000 160-320 220 97 3.7 20 129 32 1600 320-640 450 98 5.0 25 132 34 2500 355-446 400 .-. 4.5 ...... 710-901 790 ... 7.8 ...... 0 2 4 6 8 I0 12 14 16 18 1400-1810 1590 ... 15.6 ...... RANGE (HUNDREDS OF MILES)
FiG. 8. Energy density levelsplus 101ogrin third-octavebands. Relative scaleonly. TRANSITION RANGE
Correspondingvalues for the transitionrange r0 for aboard the aircraft were droppedfrom a surfaceship, various filter bands are also given in Table I. They and the detonationwas recordedwith a hydrophoneat rangefrom 1600 to 4000 yards. Althoughthese ranges a depth of 300 ft. The tape-recordersignal was later may be thoughtto be surprisinglysmall when compared analyzeddigitally. Only the shockwaveand first bubble with the scaleof the ray diagram of Fig. 2, it shouldbe rememberedthat most of the energy is carriedby rays that remain relatively near the channelaxis and cross it at relatively short-rangeintervals. A theoreticalestimate of the transition range can be made by assumingthat the energywithin a small ray bundle becomes,at a sufficientlylong range, distrib- uted uniformly over the channelwidth that it occupies. •>%•o Thus, in Fig. 10, the energyemitted by the source within the small angleA0 is assumedto be spreadover its track width H at a sufficiently long-range r. As shown in the Appendix, this leads to the simple • so io I00 I000 I0000 expression FREQUENCY (CPS) (r0)k=tt/AO cos0 FxG.9. Energy-densityspectrum of a 4-lb Sofarbomb detonated at 4000 ft and measuredat 300 ft, as obtainedby digital analyses for the transition range of the kth bundle, so that the of the pressure-timecurve. The scaleat right showsreduced levels at 1 yard obtained by assumingspherical spreading (20 log z0R. H. Cole, UnderwaterExplosions (Princeton University 3700/3). The meanspectrum was used for computingoctave and Press,Princeton, New Jersey,1948), Sec.8.3. third-octave band levels. n D. E. Weston,Proc. Phys. Soc.76, 233 (1960). SOUND ATTENUATION IN THE DEEP OCEAN 1419 transitionrange r0 for all the trappedenergy is givenby ioo 1/r0=•k 1/(r0)k, where the summation is taken over all bundles that are trapped in the channel. This summationprocess was carried out for the ve- io locity profile at Bermuda (Location A, Fig. 3), ex- trapolateddownward at the rate of 0.0164 ft/sec/ft accordingto Wilson'sformula? The profilewas divided into incrementsof 10 ft/sec, H was measured,and the correspondingvalues of 0 werecomputed by Snell'slaw for a sourceon the axis. The resulting value for the transition range was 5900 yards. This agreeswith the measuredvalues as well as couldbe expected,consider- ing the crudenessof the basicassumption and the above- mentioneduncertainty in sourcelevel. 0'il i00 I000 5000 ATTENUATION FREQUENCY (CPS)
The attenuation coefficientsof Table I are plotted Fro. 11. Measuredattenuation in units of dB per megayard againstfrequency in Fig. 11, and can be fitted within (=500 miles),plotted over the bandwidthsused. The valuesare the limits of accuracy of their determination by the fitted approximatelyby the linear expressiona=1.5-•8.2 f, wheref is in kc/sec.The slopinglines are for a= 33f• asreported by Sheehyand Halley, • andfor a= 8.5f•' expectedfrom absorption alone.
for the coefficient.The expressionjust cited fitted the measured data when zero attenuation was assumed at 40 cps; the presentdetermination yields a value of 1.8 dB/megayardat thisfrequency. In Fig. 12 are plotted the Sheehy-Halleycoefficients adjusted to 1.8 dB/ Fro. 10. The energywithin a small ray bundle A0 is assumed megayardat 40 cps.The excellentagreement between to be distributed uniformly over the channel thicknessH at a sufficientlylong-range r. This assumptionenables the transition the presentdata and the Sheehy-Halleycoefficients range r0, separating the regions of spherical and cylindrical adjustedin this way indicatesa closecompatibility spreading,to be computed. betweentwo experimentalresults, one of which was obtained in the Pacific and the other in the Atlantic linear expression Ocean Basin. Figure 11 showsthat the coefficientsob- tainedin the presentexperiment are much higherat a= 1.5+8.2f, frequenciesbelow 100 cpsthan thosepredicted by the wherea is expressedin dB per megayard,and f is the Sheehy-Halley formula. frequencyin kilocyclesper second.It shouldbe pointed out, in passing,that the measuredattenuation coeffi- cientsdo not dependon the absolutecalibration of the measurementsystem, the sourcelevel, or the transition 7 range, sincethey are merely the slopesof energylevel vs rangeplots when adjustedfor spreading. The measuredcoefficients are seen to be higher by an order of magnitude than the attenuation that would be producedby absorptionalone23 An excessattenua- tion in deep-seatransmission over what would be pro- duced by absorption was also found by Sheehy and Halley,1 as is evidenced by their empirical formula v a= 33f• (a in dB/megayard,f in kc/sec). The Sheehy- + Halley method of determiningattenuation, however, IOO IOOO was a differential method yielding only relative values FREQUENCY (CPS)
Fro. 12. Comparisonwith Sheehy-I-Ialleyresults when the latter •2W. D. Wilson, J. Acoust. Soc. Am. 32, 641 (1960). are adjustedto a value of 1.8 dB/my at 40 cps (insteadof zero). •3M. Schulkinand H. W. Marsh, J. Acoust. Soc. Am. 34, 864 Crosses:present data; dotsand circles:Sheehy-Halley data from (1962). hydrophonesat Kaneoheand Point Sur,respectively. 1420 R.J. URICK
CAUSES OF THE EXCESS ATTENUATION I00• • • • , • •
[ I I I IIII. I I IIIII I /I I I Illl A numberof processesmay be imaginedto account for the excessattenuation over that due to absorption alone. Losses at the sea surface and sea bottom must I I Ill I IIIIIII be ruled out when both sources and receiver are near the axis sincethe bulk of the transmitted energymust ,olI IIIIII travel at depthsnear the channelaxis.
• L. Lieberman, J. Acoust. Soc. Am. 23, 563 (1951). • R. J. Urick and C. W. Searfoss,"The Microstructure of the Fro. 13. Scatteringat a patch of inhomogeneityof the ray Oceannear Key West, Florida, Part II--Analysis," Naval Res. bundle AA'-BB' into anglesthat are not trapped in the Sofar Lab. Rept. S-3444 (April 1949). channel. •* A. DeFant, Physical Oceanography(Pergamon Press, Inc., New York, 1961),Vol. 1, pp. 393-398. •a C. C. Lin, TurbulentFlows and Heat Transfer (Princeton •4L. A. Chernov, Wave Propagation in a Random Medium UniversityPress, Princeton, New Jersey,1959), pp. 223-225. (McGraw-Hill Book Company, Inc., New York, 1960), Eqs. 65 • D.C. Whitmarsh,E. Skudrzyk,and R. J. Urick, J. Acous.t. and 66. Soc.Am. 29, 1124 (!957). SOUND ATTENUATION IN THE DEEP OCEAN 1421 the ratio (g2)/al abouttwo ordersof magnitudesmaller where A V is the changein soundvelocity between the than thosebelow the layer. axisand the surface,and V is the axial velocity.Using At the low end of the spectral range, the Sofar valuesfor AV, V, and d from Fig. 3, we find X•= = 2000 channelfails to trap soundof longwavelength, and the and 1400 ft at Bermudaand at the Azores.Thus, fre- ocean beginsto act as a couplingfluid between the quenciesof the order of 2.3 and 3.5 cps are predicted soundsource and the earth, rather than as an effective to be the lowest frequenciestrapped in the Sofar acoustictrap. Thus, at very low frequencies,the at- channel; at such frequencies,where the first mode tenuationshould begin to increasewith decreasingfre- beginsto be leaky, a relatively high attenuation should quencyas fewer and fewermodes remain trapped.A exist. suggestionthat this is happeningmay be seenin the Sheehy-Halleydata below40 cps (Fig. 12). An expressionfor the lowesttrapped frequencyfor CONCLUSIONS radio waves in atmosphericducts may be taken over In summary, three processesfor the attenuation in bodily for the correspondingunderwater analog. When Sofar propagation,when both sourceand receiver lie the axis of the duct lies at a depth d, the longestwave- length trappedis that which just "fits" in the duct near the channel axis, may be postulated (Fig. 15). betweenthe axis and the surface,and can be shownto Below 10 cps the dominant source of attenuation is be approximately2ø probably leakage out of the Sofar channel so that low frequenciesfail to be trapped in the channel;between d about 10 and 1000 cps,the attenuationis probably due to scatteringby inhomogeneitieslying near the channel X....x=8/3(2)•f0 [3:(d)--N(z)]•dz, axis; above 1000 cps,the dominantattenuation process is the conversion of acoustic energy to heat by where N(z) is the index of refractionat depth z, and absorption. •\?(d) is the indexof refractionon the duct axis. If for simplicity we assumea linear gradient g for the index of refractionabove the axis, suchthat for z < d ACKNOWLEDGMENTS The author is indebted to many groups and indi- N(d)--N(z)=g(d--z), viduals for assistance in the work just described. Specialthanks are due to A. E. Adamsand the flight and carry out the integration,the result is personnelof the Naval Air Test Center, Patuxent, Maryland, and to Dr. W. A. VonWinkle and othersof X.... x= (16/9) (2)«(gd)«.d the Trident Laboratory, Bermuda, for obtaining the = (16/9)(2)•(AV/V)l.d, fielddata; to R. Richter of Daystrom,Inc., for obtaining and analyzing the explosivesource level data; to G. Lund of NOL for assistancein analysis; and to IOO T. F. Johnstonand C. B. Brown of NOL for many I II •LEAKAGE _- SCATTERING I I III_ABSO LL,I. helpful discussions. "'--REGION APPENDIX .-- IO MEASURED .I/11/11 111 ATTENUATION 'tl J'11 I 11 Referringto Fig. 10, considera pair of rays having inclinationangles of 0--(A0/2) and 0+(A0/2) at the ABSORPIION source.At a distance of 1 yard from the source,this pair of rays subtendsan area 2•rZX0cos0. If the energy ii ...... Ill densityof the sourceat one yard is E0, the acoustic / Ill energyradiated into A0becomes 2•rEoAO cos0. At a long ranger, this energyis postulatedto be evenly dis-
O.I ._ I IO IOO IOOO IO OOO tributedthroughout the channelthickness H, and thus FREQUENCY (CPS) will be spreadover an area 2•-rtt. Hence,the energy Fro. 15. Attenuation regions for Sofar transmission.Three densityzXE• at r, contributedby the energyradiated regionsare postulated,in whichthe attenuation-producingproc- into A0,is then2•-EoAO(cosO)/2•rrH, or essesare thoseof leakage,scattering, and absorption. AE•= (EoAOcosO)/rH a0D. E. Kerr, Propagationof ShortRadio Waves (McGraw-Hill Book Company,Inc., New York, 1951),pp. 18-21. = Eo/rro', 1422 R.J. URICK if we write density is r0'=////x0 cos0 Eo 1 Eo 1 for the transitionrange ro' for the ray bundle/x0.At a Er = • kAEr = • k' point on the axisof the channel,the total energydensity is the sum of all the contributions/x0 out to the limit of 0 set by the channel.If the transition range of the kth wherero is the effectivetransition range for the channel contributionbe denotedas (r0)k,then the total energy as a whole.