00

1, NUSC Technlcil Report 7923 ",l. FiLE COPY00 14 May 1S37

Global Model for SoundAbsorption in Sea Water

R. H. MellonPSI. Marine Sciences

P. M. ScheifeleCombat Systems Analysis Staff

D. G. BrowningSurface Ship Snnar Department

S0

Naval Underwater Systems CenterNewport, Rhode Island/ New London, Connecticut DTIC

S.-ELEC TE

Z) UN2 3 11987UApproved for public release; distribution is unlimited. E

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Preface

This report was prepared for the Naval Ltrerwater Systems Ceter, Jr.nctrpaInvestigator LT P. M. Scheifele (Code 61M). The report wan prepar•nd alarge paxt by Dr. R. H. Yellen, Pl-anning System Incorporated - lSciences and co-aut•ored by LZ P. M. Sc-5eifele. and D. G. Brow••ng =fthe Naval Ltnderwater Systems Cet , New London Laboratory.

The authors wish to acknowlede T. Bell, B. Fisch, G. &uth, Dr. D. :Klinbeiel,3. Hanrahan, C. DeVoe, J. Dobler, ýnd J. Diubac for tbheir guidande- andassistance with the direction and format of the reports.

Reviewed and Approved. 14 May 1987

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11. TITLE (include Socunrty Classifiavorn

GLOBAL MODEL FOR SOUND ABSORPTION IN SEA WATER

12. PERSONAL AUTHOR(S)R. H. Mellen (PSI). P. M. Scheifele and fl. G. Brow nina (NUSC)

I Is. TYPE OF REPORT 13b. TIME COVERED 114. DATE OF REPORT (Year, &Eoerth, Day) jS. PAGE COUNT

PROM TO. 1987 May 14,6. SUPPLEMENTARY NOTATIjON

17 COSAri coots 18. SUBJECT TERMS (Continuo on 'evens it necessary arid identify by block n~umber)

FIELD GROUP SUS-GROUP

19 ABSTRACT (Cantinuit on reverse of necesuey and identlify by block numbter)

The attenuation term in the sonar equation for propagation loss can betaken to include all losses tooat are proportional to range. Absorption in themedium is usually the dominant mechanism- however, interface scattering,volume scattering and diffraction con also become important componentsunder certain conditions.

Sound absorption in sea water is on order of magnitude greater than infresh water at sonar frequencies. Resonator experiments in the 1950'sidentified the mechanism as an ionic relaxation of magnesium sulfate inthe 100 kHz range. Sea experiments In the 1960's sh-,wed another anomalyin the I kHz range. T-jump measurements in the 1970's showed that boric

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P. M. Scheifele (203 r ;ý IPM

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19. ABSTRACT (Cont'd.)/.. acid is Involved. Details of the mechanism were investigated using the

resonator method in the 1980's. Other relaxations were also discovered

but the only one of these that plays a significant role in sea water is themagnesium-carbonate relaxation.

A three-relaxation model of sea water absorptionthasv been developedbased on both laboratory and sea experiments. The main feature of the newmodel is the pH dependence of two components: boric acid and magnesiumcarbonate. In the nominal sea-water pH range 7.7-8.3, the low-frequency

absorption changes by nearly a factor of 4. Model tests, using available seadata and archival pH values, show good agreement.

Error analysis Indicates that predictions can be expected to be accurate, to within •i 5%, providing that local pH is known to within ±0.05 units.

Variability of pH with depth Is usually much larger than this.1Jntegrationof loss over ray paths for typical depth profiles indicates that adequateaccuracy can be attained byusing axial values for sound channels and 2 kmdepth values for convergence zones. A global model with contour charts forestimating these values throughout the World Ocean is presented.

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Table of contents page

Introduction ...................................................................................................... I

Background .......................................................................................................... 2

Low -Frequency Anom aly ........................................ .............................. 7

T-Jum p Measurem ents ........................................................................ 10

Sea-Data Analysis ........................................................................... ............ 12

Resonator Measurem ents ........................................................................... 15

Boric-Acid Mechanism ........................................................................ 19

Other Relaxations ................................................................................. 20

Absorption Model .................................................................................. 21

Absorption Model and Data ................................................................ . 22

Diffraction Effects ........................... 26

Lake Experim ents .................................................................................. 28

Scattering Effects ..................................... ......................................... 29

Absorption Model Sum m ary ............................................................... 34

PH Model ............................................................................................................. 38

Global Model ............................................................................................... 45

Conclusions and Recom m endations ............................................... . 49

References ......................................................................................................... 50

"-4-

6

Introduction

Acoustic propagation loss is a critical factor in the design, performanceand effectiveness of all submarine and surface-ship sonar systems. Theattenuation term in the sonar equation for propagation loss is taken hereto include all the mechanisms for which the loss is proportional to range.Absorption in the medium is generally the dominant mechanism.

70PL(dB) Mediterranean-Ionian basin

80

90 Hz100

100 250400

500120 2000 000

1001; 640

0 100 200 300 400 500 600Range(km)

Figure 1: Mediterranean propagation loss data.

Absorption tends to Increase os the square of the frequency and thislimits the maximum useable frequency for any given range. The situationIs Illustrated by the rLsults of a recent sound-channel experiment In theMediterranean Sea I.Il The curves of propagation loss In dB//Im shown InFigure I clearly demonstrate the Increasing effects of absorption withIncreasing signal frequency.

In order to deal quantitatively with limitations Imposed by attenuation,* the other loss mechanisms can not be neglected. Internal scattering and

diffraction loss are Important in some of the experiments to be discussed.However, they are Incidental to the main purpose of the report, which is to

* develop a predictive global model for sound absorption in sea water thatIncludes the dependence on environmental factors.

"- I-"

Background

The 1935 Naval Research Laboratory report by Stephenson [21 appears tobe the first to recognize that sound absorption in sea water is veruy muchgreater than in fresh water. However, it was not until after WWII, afterthe anomaly had been clearly established by extensive 'i.ald measurements,that efforts were undertaken to determine the cause.

Laboratory studies in the MHz range had shown that pure wdter followedthe classical law of absorption proportional to frequency-squared, but themagnitude was four times greater than that predicted by shear viscosityalone. This anomaly was eventually attributed to the additional effects ofbulk viscosity. When extrapolated to the 10-100 kHz range, the predictedcoefficients were still lower than the sea data by an order of magnitude.

100A (dB/km) LIEBERMANN 9A48

100-

10

SEA WATERFRESH WATER.4

.,.1

10 100 1000Frequency (kHz)

Figure 2: Liebermann's experiment.

In 1948, Liebermann 131 reported experiments comparing fresh and sea-I water absorption in the band 10 kHz to I MHz. Data obtaineu in a fresh-water reservoir agreed with high-frequency laboratory measurements.Below 100 kHz the sea data were also in agreement with reported oceanresults; however, they fell off at higher frequencies, approaching thefresh-water values near I MHz as shown in Figure 2. Liebermann proposed

•- tonic relaxation of NaCI as a candidate mechanism.

-2-I

Rela:aCtunal absorption can occur in aqueous solutions as the result ofpressure-dependent chkmical equilibria. Density of the medium chcngesaccording to LeChttelier's principle; i.e. if cne species is smaller than theother, increasing pressure will drive the reaction in the direction of thesm.!ler species and the compressibility is thereby altered. The rate of theprocess is governpd oy the time constant of the rPction. Therefore, thesound speed c becomes complex and acoustic wave3 d,•,; with range.Better in-,ight is gained from the complex wbvenumber 1•-211f/c. Since

dispersion is very small (<<1 m/s), It can be neglecttd futd the wavenumbercan be approximated as kz 21f /c. +'A where cO is constunt. Then we have

Azjrfr f2 /(!2 + f r2) where A is the loss per unit distance arid fr anri i. are

the relaxation-frequenr-g and amplitude parameters.It -an shown that Anmx =r fr = V>ZI AV? pc /2R(T+273) wvherv kV is the

forward rate constant, 1-7.1 is the concentratior. of the species Z, AV is tkLvolume change of the equilibrium involved, P is the 'gas constant" and T isthe temperature in °C. The equilibrium constant for the reaction is givenby K=k'/ k where kV is the r,.ve.-s rote constant.

Various types of e',4uilibria may be involved and each one has a specificformula for relaxation frequency and volume change. The examples listedbelow are typical and can easi!y be extended to other cases.

The simplest type is the single-step equilibrium:Z " Z, fr = ( V * k' )/21l K =[Z]/[Z*].

In ionic solutions like sea water, equilibria can be of the type:SZ +- X+ 4 Y" f r = (V• + k'([X*l 4 [Y-]))/2yl K=IZI/[X*]IY-]

Generally, the single-step equilibria are diffusion-controlled and toofast to cause sound absorption in the sonar frequency range. Slower ionicrelaxations ih sea water can usually be modeled as two-step equilibria,which have two distinct relaxation frequencies. The second step is rapidand the associated high-frequency relaxation does not contribute to theabsorption at sonar frequencies and the slow f'rst step controls therelaxation frequency in question. This type can be represented as:

Z 0Z'" X* 4y"

Then fr = (k',+ k~jq/(i~q))/211 and AV = AV, * VI. /(I-q)

where q= K2 (IX1 4 WD'), K,--ZJ/iZ'] and K2 = [ZI/[X+IIY"]

Another type that will be encountered Is the exchange equilibrium.S.....XY" 4-) YX° Ir = (k'(lX]41Y'])+ k'(IYl+IX'i)/2v K=IXIIY-I/[x'IIYI

The formula for A.. remains the same for all equilibria except that the

concentration factor IZI becomes IXI[Y' for the exchange type.

-3-

Vacuum Chamber

Owill"OscpeRelaU Resonator

Signal Generator <xducer

Figure 3: Resonator apparatus.

In 1949, Leonard et. al. 141 reported initial results of a laboratory studyto determine what equilibrium is involved in sea-water absorption. Theirapparatus consisted of a spherical resonator as illustrated in Figure 3. Theresonator Was suspended in a vacuum chamber by wires to minimize anyresidual losses caused by acoustic radiation. The useable frequency rangewas 25-500 kHz and values of Q> I05 were realized in pure water at lowerfrequencies.

In the resonator method, the transducer can serve as both transmitterand receiver. The sphere is excited specific resonant frequencies. Radialresonances usually give the lowest residual losses and they can usually bylocated by calculation. However, because the resonator is not perfectlyspherical, the resonances are hardly ever simple. The resonant frequenciesshift with changes in sound speed caused by variation of temperature orthe addition of chemicals. Interference effects among adjacent modes canresult in rapid changes in residual loss and this limits the accuracy of themeasurements.

Losses are determined by switching the transducer from the transmit tothe receive mode and measuring the rate of decay in dB/s. The system isfirst calibrated using distilled water. The excess losses of the variouschemical constituents are then determined by subtracting the calibrationvalues from the measured values. The losses in dB/km are calculated budividing by the sound speed.

The exoeriments of Leonard et. al. showed no effects for NaCI alone. Thesalt responsible for the excess absorption In sea water was determined tobe magnesium sulfate (MgSO 4).

A (dMA/kn) WILSON & LEONARDt1954

100-0 00

00

000100

10 0

SEA WATER MgSO4 RELAXAT ION

1 ... p I 11 i I I p p p p ma I

10 100 1000Frequency (kHz)

Figure 4: Resonator measurements of Wilson and Leonard.

Results of a more detailed study of magnesium sulfate by Wilson andLeonard 151 appeared In 1954 and are Illustrated In Figure 4. The earlierconclusions were confirmed and dependence on concentration was alsoInvestigated. It was found that Interactive effects of NaCI actually causesa reduction In sea water absorption.

In 1953, Kurtze and Tamm [61 also reported resu;ts of sililar resonatorexperiments confirming Leonard's findings. Several pc3sible mechanismswere proposed; however, It was not until 1962 that a definitive analysisby Elgen and Tamm 171 disclosed the details of the multistep equilibriumInvolved. Two or more steps were Indicated by the fact that the relaxationfrequency Increases with concentration up to a limiting value.

The essential acoustic properties oa the relaxation can be modeled In amore simplified form as the two-step equilibrium:

(MgSO4)I 4 (MgSO 4)Ii --) Mg2+ + S042-

The slower first step involves only a structural change and this controlsthe relaxation frequency of the absorption process in question. The secondrelaxation is very rapid and its contribution is negligible. The reductioneffect of NaCI can be attributed to the coupling effects of another rapidequilibrium involving the ion-pair NaS0 4-.

-5-

In 1962, Schulkin and Marsh [81 introduced the first practical formulafor sound absorption in sea water. The approximation was based on thelaboratory resonator experiments and extensive sea measurements in thefrequency range 2-25 kHz.

The parameters involved in the S&M formula are temperature, salinityand pressure. The pressure factor of magnesium sulfate was assumed to bethe same as the pure water value obtained by laboratory measurements athigh pressures and is given by (0-6.54x 10- 4P) where P is the ambientpressure In atmospheres. An alternative appro:ximation is 10 -D013 where Dis the depth in km. The S&M formula can then be written:

A40.02 S fr f2 /( fr2+ f 2 ) + 0.03 f2 /frx O1-D/5 dB/kmfr =59X I 0T/ 49 kHz

where fr is the relaxation frequency of1 moyviesium sulfhke, S is salinity inparts per thousand (ppt) and I is temperature In °C. The first term is the

magnesium sulfate component and the second is the pure water component.The temperature depend'nrj e of pure water has been approximated by usingthe relaxation frequency as a parameter, which makes both coefficientsequal.

For the parameter values S=35, 1=49C and D=O, the formula becomes:Az 50 f2/( (71)2 + f2) + 0.0043 f2 dB/km

which reduces to Az.01 f2 dB/krn for f<< frz7I kHz.

The S&M formula was adequate for the sonar problemrsof that period;however, attention in underwater acoustics subsequently shifted to longerranges and lower frequencies and the accuracy of extrapolating beyond thedatabase was questioned.,A number of sea FI'-periment$ were then carriedout which indicated anomalous behavior 3t much lower frequencies.

-6-

44

Lo-Freyuencg Anomalg

A (dB/km) North Atlantic 40C

Anomaly M Formula

.1Thorp 1965.01 . .-

.1 10Frequency (kHz)

Figure 5: Thorp's data and 2-component model.

In 1965, Thorp 191 carried out a sound-channel propagation experiment Inthe Bermuda-Eleuthera area over a 500 km track. Measurements were madeat 1200 m near the sound-channel axis using explosive sources. Resultsshowed a clear anomaly below 3 kHz as seen in Figure 5. Comparison withother earlier data confirmed his conclusion that the values were an orderof magnitude greater than that predicted by the Schulkin-Marsh formula. Ina later paper, Thorp and Browning I101 modeled the anomaly, adding a I kHzrelaxation component to the absorption formula. The formula used in thedata-fIt of Figure 5 Is given by:

A= 0.009 f2 + 0. II f f21/( fr2 + 12) dB/km (fr= I kHz).

The first term is the magnesium sulfate component approximated forfrequencies well below the relaxation frequency 71 kHz. The second termis the anomalous component. The pure water component is negligible inthis frequency range and has been omitted.

"-7-

II

A (dB/km) MediterraneanProvencal basin 130C

anomnaly lgS04

.1Leroy-1963

Frequency (kHz)

Figure 6: Leroy's data and 2-component model.

Another propagation experiment was carried out in the Provengal Basinof the Mediterranean Sea by Leroy II I]. Ir Lhis case, propagation loss wasmeasured over a single refraction path and not in the sound channel. Therange was therefore limited to 40 km.

Leroy's results also showed a similar anomaly of roughly the samemagnitude as Thorp but with a significantly higher relaxation frequency.

The formula used by Leroy for the data-fit is given by:A: 0.006 f2 + 0.155 fr f2/( fr2 + f2 ) dB/km (fr: 1.7 kHz)

The first term is the magnesium sulfate component and the coefficient IsIn reasonable agreement with the S&M formula for the 130C temperature.The coefficient of the anomaly is also significantly greater than Thorp'svalue.

Under the assumption that the anomaly is truly a relaxation process, the9 difference between the two relaxation frequencies can be attributed to the

difference in temperatures. However, the difference in coefficients issomewhat greater than the estimated experimental error. Despite thisdisagreement, a second relaxation still seemed to bethe most promisingexplanation of the anomaly.

j-6

A (dB/km) Red Sea22°C

<anomaly 1gS04

Browning 1969

.01

Frequency (kHz)

Figure 7: Red Sea data and 2-component model.

Browning et. al. carried out a number of sound-channel experimentstest the relaxation hypothesis. In the Red Sea experiment of 1969 1121, thetrack was 300 km long and the water depth was 750 m or greater. Sound-velocity profiles showed a strong sound channel with axis near 200 m. Theambient temperature was 22°C on the axis and 301C at the surface.Measurements were made axis-to-axis using SUS charges at 200 m depth.

..elaxation frequency can be expected to Increase exponentially withtemperature over the limited range of temperatures encountered In thesea. Based on extrapolation of the Thorp and Leroy values, the expectedrelaxation frequency In the Red Sea experiment was approximately 2 kHz.However, the curve fit of Figure 7, Indicated a significantly lower value.

The Red Sea formula used In the data-fit is given by:A= 0.000 f2 + 0. 148 fr f2 /( fr 2 + f2 ) dB/km (fr= 1.5 kHz)

The anomaly coefficient Is clearly in better agreement with Leroy's valuethan that of Thorp and the magnesium sulfate coefficient is significantlygreater that predicted by the S&M formula.

The relaxation hypothesis remained promising despite inconsistencies;however, it was not until 1973 that it ,was firmly established by anentirely different experimental technique, I.e. the T-jump method.

"-9-

T-Jumo Measurements

lcapecltor _.

F

Switch

Ipe ScorLight 1 LTlPU

Source PfOtOCell Ogcllocco

Figure 8: Temperature-jump apparatus.

In 1973 Yeager et. al. 1131 reported results of T-jump experiments withboth synthetic and actual sea-water. In this method, a very rapid rise intemperature is produced by discharge of the capacitor through electrodesIn the cell containing the solution, as shown in Figure 8. A chemical pHIndicator was used. Light transmission to the photocell measures the pHchange produced by the temperature jump and the relaxation frequency isdetermined from the rate of change as measured by the oscilloscope.

Sea water showed the I kHz relaxation, proving that the equilibrium isthe acid/base type. Synthetic sea water (SSW) was tested by addition ofchemicals to distilled water according to the formula:

Cgonstituent Concentration (mM)Sodium Chloride (NaCl) 400Magnesium Sulfate (MgSO 4) 35

Magnesium Chloride (MgCl 2) 20

Calcium Chloride (CaCl 2) 10Sodium Bicarbonate (NaHC0 3) 2.5

Boric Acid (B(OH) 3) 0.5

where concentrations are in millimoles per literr(mM). The constituentresponsible was Identified as boric acid. The relaxation rate was found toIncrease with concentration and temperature but pH had negligible effect.

In aqueous boric acid, the ionization mechanism Is believed to be:B(OH) 3 + OH" -- B(OH) 4"

where OH" is the hydroxyl ion and B(OH) 4" is the borate ion. However, theSt concentration of the carbonate Ion is much greater in sea water and an

exchange reaction was proposed as the more likely mechanism.

-10-

C Concentration (mM)

" ~CO3

B(OW)3 B(OH)4

PH 1

Figure 9: B(OH) 3 and CO2 specie concentrations vs pH.

The proposed ionization equilibrium In sea water is given by:B(OH) 3 + C032- + H20 4- B(OH) 4" + HCO37

For chemical purposes, the individual equilibria can be written:HCO" +-) W + C032- Kc=1 H1+1 C•02'/IHC03"1

B(OH)3 + H20 4 HW + B(OH)4" K0=1 H+IIB(OH) 4 "1/iB(OH)31

where I H+] is the hydrogen ion concentration jnd pH=-log(I Hi). Theequilibrium constants In these terms are pK9=9.2 and PKc=9.8.

Concentration of the carbonate ion, for example, Is given by the formula:I Co32 IC02) 1 OX/( 1+ 10 x ) x=pH-pKc

where [C0 2] is the total carbon dioxide concentration.

Possible effects of Ion-pairing of carbonate with metallic ions werealso pointed out. Carbonate has a strong affinity with sodium, magnesiumand calcium ions. Bicarbonate affinities are much smaller and can beIgnored. The principal equilibria to be considered are therefore:

, Na+ + CO32- -- NaC3" K- 1.6/M

"Mg2+ + C032"ý4) MgCO3 Kz53/MCa2+ + CO32 - *4 CaCO3 K- 125/M

In sea water, most of the carbonate exists In assoch0,"d form and theCO. curve of Figure 9 represents the total of the four carbon.,:e species.

Borate ion formulae are similar but the affinities are much smaller.Boric acid and bicarbonate affinities are negligible.

-I1-

ii

Sea-Data Analusis

2Fr (kHz)

Med

S~Red See

S Atlantic

subArctlc

.5 L0 5 10 15 20 25

. Temperature °C

Figure 10: B(OH)3 relaxation frequency data.

In order to estimate the relaxation frequency of boric acid with thetwo-component model, the measured absorption spectra had to be fitted bya curve with two other parameters; namely, the magnesium sulfate andboric acid coefficients. Because of limited accuracy of the low-frequencydate, the boric acid relaxation frequency often tends to be difficult todetermine with the required accuracy.

Figure 10 Includes only those experiments for which reasonably goodestimates of relaxation frequency could be obtained from analysis of theexperimental data. The Atlantic and Red Sea experiments were believed tobe the most accurate and were heavily weighted. The solid line is given byfr=O.9xl O/l°° (kHz), which intersects both points. In the analysis of theother data, this formula was taken to be the best estimate of relaxationfrequency vs temperature at that time.

Except for Leroy's Mediterranean point, there Is reasonable agreementwithin the limits of estimated experimental error. Further Investigationshave resolved all of the discrepencies, as will be seen In the latersections of this paper.

-12-

10a(B () hop

c Sea Water>

7.5 8.5 9 9.5 10

Figure II: Boric a,;id coefficient a(B)//Thorp vs pH.

For the exchange mechanism proposed by Yeager et. al., the boric acidcodficient a(B) Is proportional to the product of the two reactants oneither side of the equilibrium as Indicated earlier. Taking boric acid andcarbonat8 as the reactants we have:

lO(OH) 311C 32"1 z IDJIlC021 I VA( 1+ 1 x)( I+ 1 0 )where 161 Is total boric acid concentration and x=pH-pKc, y=pH-PKB

The coefficient should therefore Increase exponentially and then decayafter reaching a maximum value near pH,9.5. In the curve Figure 1 1, thecoefficient Is expressed relative to Thorp's value. In the sea-water pHrange, the coefficient Increases approximately as I0PH. In practice, pH>8.5Is not possible In sea water because calciurn carbonate will precipitateout of solution.

The pH dependence of the experimental sea-data was investigated 1141.Analysis was based on the assumption that the rate constant, whichcontrols the relaxation frequency, Is the main temperature-dependentfactor. The relaxation amplttud, parameter, a(B), is easily determinedwhen the relaxation frequercy is calculated from the data-fit of Figure 10.The value should also be nearly Independent of temperature because therate censtant then cancels out of the equation.

-13-

I'

a( (//Thorp)

51, . L• N.Alatc(To

S9

6 Me7Lry

S5S34

l ~2 Indian .3 S. Pacific4 Tasrman See5 N. Atlantic (Thorp)6 Med MLeroy)7 Red Sea8 Davis Strait9 Surf ace Ducts

.1 i i I i I a a 2 a

7.5 pH 8 8.5

Figure 12: B(OH)3 parameter a(B)//Thorp vs pH

All sea data were fitted by the two-relaxation model 1141. Values forthe magnesium sulfate component were obtained by matching the spectraat the higher frequencies. Other components of low-frequency loss werealso added when Indicated. (see the later sections on diffraction andscattering loss). The parameters of the boric acid spectrum were thendetermined by adjusting the amplitude and relaxation-frequencyparameters for "best-fit'.

When the relaxation frequency could not be estimated with sufficientaccuracy, the boric acid coefficient Amax=a(B) fr was measured The value

of a(B) was then obtained by dividing Amax by the appropriate relaxationfrequency from the data-fit of Figure 10. The values shown in Figure 12are relative to Thorp's value a(B)=O. 11, which is still believed to be thebest approximation for the two-relaxation model.

The standard deviation of the data vs pH shows a correlation of betterthan 90X and no temperature trend Is evident, supporting the assumptionthat relaxation frequency Is the only temperature-dependent parameter.Using Thorp's pH=8 as the standard, the approximation for the absorptionparameter becomes a(B)=O. I I x I 0(P-e)

-14-

Resonator MeasurementsPlH Wete Pump

Filter RelayResonator.

Synthesizer

Yecuum Chamber

Figure 13: Resonator apparatus (ref. 16)

The temperature-jump measurements showed that only boric acid canproduce a relaxation in the I kHz range. However, since the method permitsmeasurement of relaxation frequency and not absorption, it was not yetclear what part it played in the actual absorption mechanism.

Resonator measurements in the I kHz range are not feasible because ofsize limitations. Subsequent investigations by Simmons 1151, using theresonator method at higher frequencies and the temperature-jump method,proved that boric acid Is essential to the low-frequency sound-absorptionprocess. However, since aqueous boric acid showed comparable relaxationfrequency as well as absorption, the mechanism remained uncertain.

From 1979-1983, resonator measurements of synthetic sea water (SSW)were carried out at NUSC by Mellen et. al. 1161. The apparatus is shown inFigure 13. The useable frequency band was limited to 10-100 kHz and theerrors were estimated to increase from tO.2 to I1 dB/km in this range.

In order to measure the relaxation parameters, the reactions had to bemaneuvered into the measurement window by Increasing concentrations.Sea-water relaxation parameters were obtained by extrapolating back tonormal concentrations. Sulfate was omitted in order to eliminate themagnesium sulfate relaxation and thereby improve the accuracy. Otherrelaxations involving magnesium were also discovered; however, of these,only the magnesium carbonate relaxation plays any significant role in seawater 1161. All relaxations were measured separately and in combinationto determine interaction effects between them.

-15-

A (dB/km) O(OH-)3 (raM) 4

u,, InS ,b. - -, ' • ',w~' ':r .L'W ~VI100

Frequencg (kl-z)

10

1100 2

Frequency (kHz)

Figure 14: Boric acid absorption spectra at pHz9.Magnesium chloride has negligible effect on the boric acid relaxationand was omitted in the experiments of Figure 14 In order to elim'nate theundesired relaxations. In the top spectra, calcium chloride was included at10 mM and the sodium bicarbonate concentration was reduced to 1 mM inorder to prevent precipitation of calcium carbonate. Relaxation frequencyIncrt. es linearly with boric acid concentration to nearly :35 kHz. Thelower spectra (calcium chloride omitted) show the same effects when thesodium bicarbonate concentration is increased and the concentration of

boric acid is held constant (2 maM), conflrmirg the exchange mechanism.

- 16-

S......... i 'UU rWNI(W ' .• -- '•" l ,-d• •... . .... .. ... .F..,• • . -

I00Amex (dB/km)

CaCl2 10mMNaHCO3lrnM

10

(CaCl2 0mM1(OH)3 2mM

10 100

Concentration Factor (mM)l2

Figure 15: Boric acid Amex data vs concentration.

In figure 15, the maximum volues of each spectrum of Figure 14 areplotted vs the relative concentration of the varied constituent.

Amax Is proportional to the product of the reactants. The concentrationfactors (aM)2 for the two cases are given by:

IB(OH)31 x [C0 3 totkcmt.

lC0 321 x IB(OH)4c]¢6t.

Wt*h pH=9 held constant, the concentration of the varied reactant issimply a constant factor times its total concentration. The calciumcarbonate Ion-pair concentration is Included In the first case. Calciumchloride was omitted in the second case.

Both data sets are proportOnal to the concentration factor; however, theabsorption Increases dramatically when calcium Is Included, which clearlyIndicates a large contribution to &V. The other metallic Ions do not showany significant effects.

Extrapolated to sea-water concentrations and pH, the deta with calciumare In good agreement with sea measurements. Without calcium, the valuesare too low by almost an order of magnitude.

-17-

a(B) Boric Acid Coefficient

.,

@ See datac' Sea Water > o Resonator data

7.5 8 8.5 9 9.5 10

PH

Figure 16: Comparison of resonator and sea date vs pH.

Figure 16 shows a comparison of the boric acid resonator data with thesea data of Figure 12. The resonator data were obtained at elevated boricacid concentrations and were corrected to sea-water concentration byextrapolation.

The resonator experiments confirm, In detail, that the boric/carbonateexchange Is the dominant mechanism and that all assumptions are valid.

As the result of this work,. It is believed that the boric acid absorptionmechanism is now understood to almost the same degree es that ofmagnesium sulfate. However,*to construct an practical absorption modelbased solely on relaxation chemistry would be far too complex and theaccuracy would be limited to that of the supporting measurements as well.Therefore, the combined results of resonator, T-Jump and sea experimentshave been taken Into consideration in the development of a simplifiedmodel for the boric-acid mechanism.

There are la number of possible models for the boric acid/carbonateequillbriumitn sea water. One that Is both tractable and consistent withthe experimental data is preferred as a matter of convenience and may notrepresent all the essential chemical details involved.

-I1-

Boric Acid Mechanism

B(OH) 3+ CaCO 3 +H20 --* B(OH)4+ HCO• +Ca2+1

principal exchange reaction

2- 2+ 24D(OH) 3+C0 3 +Ca +H2 0 ---) (OH)4 +HCO 3 +Ca

B(OH) 3 +CoCO 3 H20 +- CaD(OH) 4 *HCO 3

coupled exchange reaction

fr k-- ([B(OH)3]+[HCO3]/Ki) (Hz)

Amox(o lAk) [B(OH)31 [CO3t.t 1.C 2 (Np/sec)

2R(T+273)

absorption formula parameters

AV s-22m]/mole

k' . 4xi 06+T/7°/mol*secR=gas constant T=temp Cp =density c=sound speedKI= KB/K 2c x 4

Figure 17: Boric acid relaxation equilibria.

The top box of Figure 17 shows the principal equilibrium describing theessential chemical factors involved. However, the relaxation frequency forthis model depends on calcium concentration, which is not observedexperimentally.

The second box shows deta!ls of the proposed ion-pair equilibria. In thiscase, the two sides are separated by equally slow steps and relaxationfrequency Is quite Independent of calcium concentration. This model isused as the basis of the present analysis.

Simplified formulae for the absorption parameters for the model aregiven in the third box. Species having negligible effect on relaxationfrequency are omitted in the formula.

The bottom box shows the estimated values of the relaxation parameters&Y, 0C and K1.

-19 -

v•%

Other Reloxotions10A - (dB/km) pH8.5

SM~qCI 2 50rnM' CeC12 l0mM

'NaHClI03 2.5rnM

/1

10 20 so t100

Frequency (kHz)

Figure 18. Absorption spectra of B(OH) 3/CO2 /Mg/Ca system.

The contributions of two other relaxatiors Involving magnesium areshown in Figure 16. The mechanisms of both appear to be similar tomagnesium sulfate and are modeled by two-step equilibria:

(MgCO 3 )1 *- (MgCO,) I I - Mg2+ + C032-

(MgB(OH) 4+)I - (MgB(OH) 4 +)1 l -) Mg2 ¼ + B(OH)4 "

Both relaxations have been studied independentlq. In the magnesiumcarbonate experiments, boric acid was omitted. In the magnesium borateexperiments, sodium bicarbonate was omitted. /ithout carbonate, boricacid absorption is so small that it can be ignored.

Temperature, concentration and pH dependencies of both relaxationswere determined from the relaxation spectra.

With the parameters of the two relaxations known, the two systemswere then combined to determine any interaction effects. The results

4 shown in Figure 18 indicate that interactions are negligibib and that allthree components are simply additive.

For normal sea-water boric acid concentration, the magnesium boratecomponent becomes negligible. The magnesium carbonate component, whilesmall, can become significant at high pH values 1171.

-20-

Absorption Model

A=A, (MgSO 4 )+A 2 (B(OH) 3 )+A 3 (MgCO 3 )2 f/ 2 2

An= Onf fn/(f +fn)

S= 0.5xOd(km)/ fl = 50xo0=O (pH-8) f 2 0.9xlTIO

3= o~o3xo(PH-8) T/30a = 0.3X 10f 3 =4.5xl0

Atlantic. 40C pH8.0

A=O.007f2 +0.1 f2/(1 f2)+O. 18 f2/(62,f 2)

N.Pacific 4"C pH 7.7

A=0.007f2 +0.05f2/(,+ f2)O0.09 f2/(62+f2)

Mlediterranean 14"[ pH 8.3

A= 0.006f 2+0.26f 2 /(1.42+.1 2 )+0.78 f2/(122+f2)

Red Sea 22"C pH 8.22 22(.0

A=0.004f +0.27f2/(. 2+f 2) +I. /f2/(24 +f )

sub-Arctic -IC pH 8.3I2+. 21.5 2) 2+ 22

A=:0.Of 2 +0.17 + /(0.85 +f2) 0.24 f 2/(4 'f )

Figure 19: Simplified absorption formulae.

The simplified formula for the 3-relaxation model is shown at the top of

Figure 19 where A is the absorption coefficient (dB/km), f is frequency(kHz), T is temperature (OC) and pH=8.0 is the reference value. The pure-water term is omitted, making the formula valid for frequencies less thanroughly 100 kHz. The pressure factor in the magnesium sulfate formula of

Fisher and Simmons 1181 for has been modified as the depth term D(km) inthis model. Depth dependencies of the other relaxations are not yet known;however, measurements in both deep and shallow channels indicate that

the effect on boric acid must be very small. Magnesium carbonate effectsmay be greater but can be neglected because its contribution is so small.

Salinity dependence is neglected temporarily but will be considered in alater section.Specific values for several experimental locations are also shown in the

bottom box. Note that the magnesium sulfate terms Al are approximationsvalid orly for f<<f.

-21 -

/

Model and Data

IA :(dB/km) Atlantic pH8 40C

.Al

" i• (A2/ •3

, I .Thorp 1965

.01 . .A -.1 1 10

Frequency (kHz)

Figure 20: Thorp's data end model.

Figure 20 shows Thorp's data compared to the 3-component relaxationmodel. Note that the magnesium sulfate (A1) coefficient Is 0.007 ratherthan the earlier value 0.009 used in the 2-component model. The new valueIs based on a very careful laboratory re-evaluation of magnesium sulfateabsorption in sea water by Fisher and Simmons I181.

Note also, that the boric acid (A2) coeffIciene, is 0. 1 compared to 0. I1 inthe 2-component model The magnesium carbonate (A3) component makesup for both differences and the fit to the data is somewhat better.

The possible existence of a third relaxation in sea water was proposedearlier by Fisher 1191. He observed a pers'stent bump in the data around3-4 kHz that could not be removed by any consistent readjustment of theparameters of the 2-component model. The discoverL; of the magnesiumcarbonate relaxation in Lake Tanganyika and subsequait study of themechanism put the hypothesis on very fun ground. In facW, resonatormeasurements of sea water at 1H=8.5 revealed, beyond all doubt, thedeficiencies of the 2-component model. Regardless of eny reasonablereadjustment of the parameters, measured values were much too highwithout the third component 1 171.

-22-

°|.1

A (dB/km) N. PacificpH7.7 40C

.01

2AAl> A3

.001L. 1 10

Frequency (kHz)

Figure 21: North Pacific data and model.

In the North Pacific model, the lower value pHz7.7 reduces both the boricacid (A2) and the magnesium carbonate (A3) coefficients by a factor oftwo compared to TIorp. Relaxation frequency depends only on temperatureand remains the same. Note that the dB/km scale has been reduced by thefactor 10 In Figure 21.

Sea water Is highly alkeline. Values of pH In the World Ocean range fromabout 7.7 to 8.3 Whereas the neutral value is 7. Surface values averagearound 8.1 and tend to have a much narrower range. Evidently, circulationand contact with the atmosphere are Involved in controlling pH. The lowestvalues are found in deep waters where the circulation times are thelongest, which would account for the very low absorption observed in theNorth Pacific sound-channel.

At the higher latitudes, the sound-channel axis comes to the surface asthe thermoclir.e diminishes and the absorption increases because the pH Ishigher. The very low-absorption phenomenon Is t erefore probably limitedonly to the central North Pacific Ocean.

- 23 -

4

IA .(dB/km) Red Sea pHO.2 220C

.1 b2

.011 10

Frequency (kHz)

Figure 22: Red See data and model.

The Red See data were originally fitted with a 2-relaxation model andthe results Indicated a low-frequency relaxation at 1.5 kHz compared tothe formula value 1.8 kHz. Figure 22 shows that an even better fIt Isachieved with the 3-relaxation model using the latter value.

The major remaining anomaly appears to be the 1.7 kHz relaxationfrequency of Leroy's Mediterranean experiment. Since the method ofmeasurement is different, other sources of error must be considered.

Experiments reported here made use of explosive sources. A possiblesource of error is nonlinearity wherein the overtaking effect regeneratessome of the lost high-frequency energy at the expense of low. Earlier, anattempt was made to explain the entire attenuation anomaly by such amechanism. However, propagstion In a sound chanael Involves phase shiftsat caustics, which reverses nonlinear effects so that there Is negligibleaccumulation at long ranges. Leroy's ranges were limited to the firstconvergence; I.e.z40 km. If the wavefront remains coherent over the entirepropagation path, effects can be significant.

The recent Mediterranean sound-channel experiment appears to supportthis argument because the range extended to more then 600 km and resultsare consistent with the model.

- 24-

I

A :(dB/kn) Mediterranean pH8.3 140C

.1 A2

AlA3

.011

Frequency (kHz)

Figure 23: Mediterranean data and model.

The Mediterranean experiment was carried out in the deep Ionian basinbetween Sicily and Crete In July 1902 by SACLANTCEN 1I1. Sound velocityprofiles Indicated a strong sound channel with a rather broad minimum at100-200 m depth. Temperature, salinity and sound-speed profiles wereuniform over the 640 km path. Effects of the rising bottom were notedonly at extreme ranges and these points were omitted In the analysis.

Measurements of pH and boric acid concentrations also showed littlevariability with range or depth ovcr the track. The high pH value is typicalof surface values In other regions. Both the boric acid and carbon dioxideconcentrations were found to be normal. The salinity (Sz38) Is slightlyhigher than normal.

At pH=8.3, the boric acid coefficient Is a factor of 2 greater than thatfor the North Atlantic. However, the much higher temperature increasesthe relaxation frequency so that the absorption spectrum is not Increasedby such a large factor at the lower frequencies.

The 3-component relaxations calculated for the experimental conditionsare shown in Figure 23 and the fit to the data Is clearly excellent.

-25-

Diffraction Effects

A (dB/krn) 3ismark See pH8.3 30Csurface duct &z=90m

.1

diffraction>• A2 Al A3

/,

.010.01 .10Frequency (kHz)

Figure 24: Bismark Sea surface-duct data and model.

An experiment In the Bismark Sea by Wylie 1201 indicates the need forIncluding diffraction loss in surface-duct calculations. In this case, theduct depth was approximately 90m. Diffraction effects become significantwhen the acoustic wavelength becomes tuo large for total refractivetrapping. The consequence is an additional component of attenuation thatincreases rapidly with decreasing frequency.

Acoustic trapping is the result of an Isothermal mixed-layer at thesurface overlying the thermocline. The sound-speed gradient in the layercan be approximated as that In deeper Isothermal water. The diffractionloss in Figure 24 was calculated for a bilinear gradient with the normalpositive gradient dcvwn to the duct depth an. a negative gradient of largermagnitude below. Note that trapping is never total; however, the lossdecreases exponentially with increasing frequency and rapidly becomesnegligible. The only effect of diffraction, In this case, appears to be theabsence of data at frequencies below effective cutoff.

The absorption model was calculated for the ambient temperature 301Cand the pH=8.3 was estimated from archival data. Agreement with the dataabove I kHz Indicates that surface scattering was negligible as expectedfor the low sea state.

- 26 -

A :(dB/km):Gulf of AdenpH82 3WCsurface duct I"Az-30m difffraction\,

A2 A A

I

.01.

. :10Frequency (kHz)

4' Figure 25: Gulf of Aden surface-duct data and model.

In the Gulf of Aden experiment 1121, the duct depth was only 30m and thecalculated diffraction effect remains strong to well above I kHz. However,the date shows Increasing attenuation over only a limited range and thetrend reverses as frequency decreases. This is the result of the leakysurface-duct signals returning from the deep channel.

The absorption model was calculated for the ambient temperature 300Cand the pH value estimated from archival data. Agreement with the dataabove I kHz indicates plausibility of both the absorption And diffractionmodels.

See states In both experiments were very low and the absence of surfaceloss was not unexpected. In most sound-channel experiments, refractivetrapping by the thermocline tends to make effects of surface scatteringnegligible. However, If the thermocline is weak or absent, the excess lossshould certainly become appreciable at moderate sea states. In such cases,a marked frequency-dependence is expected, particularly at the lowerfrequencies. For acoustic wavelengths large compared to the surfacewavelength, the excess loss should fall off very rapidly.

- 27 -

V.

I-

a /

Lake Experiments

I

A (dB/km) a Superioro Tengenyike

.,i, , , 4 4I

4gIXJ3 Pure Water>

.01I Frequency (kHz) 10

"Figure 26: Lake experiments.

The experimental program of Browning et. al. 1121 included two lakeexperiments for comparison purposes. Both gave surprisingly anomalousresults compared to pure water as seen in Figure 26.

Attenuation in Lake Tanganyika was found comparable to the magnesiumsulfate relaxation in sea water. Analysis of the constituents showed thatthe concentration was too low by a factor of 30 to account for the result;however, both the carbon dioxide content and pHzB.5 were abnormally high.Chemical synthesis of artificial lake water in other resonator experimentsshowed the mechanism to be the magnesium carbonate relaxation.

'Attenuation in Lake Superior of was found to be comparable to that ofboric acid in sea water. In this case, the anomaly has been attributed toInternal scattering. Frequency-independent attenuation is apparently theresult of multiple-scattering by large-scale temperature inhomogeneitieswithin the thermocline. Energy gradually diffuses out of the channel by a"random-walk" process and is absorbed in the bottom. This mechanismseems to be common to all sound-channel experiments; however, It isusually observed only at very low frequencies 1211. Much of the spread inscattering loss can be attributed to differences in channel strength;however, no reliable method of prediction has yet been found.

-28-

Scattering Effects

IA b(B/m) HusonBay

sascatering ho s n r(•A2. Ai> A3

Frequency (kHz)

Figure 27: Hudson Bay data and model.

Hudson Say 1121 was the first see experiment to show excess frequency-Independent loss and served to put the scattering hypothesis on more firm

footing. The puzzling result of the earlier Lake Superior experiment, Inparticular, was clearly attributable to the same mechanism.

Since the loss Is independent of frequency, ray-diffusion theory will beapplicable and losses can be calculated from the diffusion equation 1211.Diffusion loss depends inversely on the strength of the channel. In order toreach the bottom, axial rays must overcome a potential barrier AC, whichIs the difference In sound-speed between the bottom anq channel axis. Forsmall angles, loss is Inversely proportional to the square of the criticalangle of the bottom-grazing ray.

In Figure 27, the dashed line Is the estimated total absorption, and theexcess scattering-loss Is taken as 0.04 dD/km independent of frequency.Water depth In Hudson Bay Is only lOOm and trapping Is weak. Although theLake Superior depth is nearly the same, a slight negative temperature-gradient reduces the channel strength, making the loss approximately fourtimes greater.

- 29 -

A :(dB/km) Gulf of AdenpH7.9 130C

.01

.1 10Frequency (kHz)

Figure 28: Gulf of Aden data and model.

In the Gulf of Aden experiment 112J, there was a strong Intermediate° sound channel caused by outflow of water from the Red Sea. This Is in

"addition to a deeper channel and the surface duct discussed earlier. Sourceand receiver were located In the Intermediate channel. The experimentaltrack was 500 km In length and the total water depth was roughly I km.Absorption parameters are estimated for the ambient temperature 130Cand archival value pH=7.9 at axis depth.

Despite the relatively strong trapping In the Intermediate channel, thereIs marked evidence of scattering loss. Th!s may be the result of InstabilityIn the upper part of the thermocline where the temperature falls from300C at the surface to 209C at 100 m. Sound-speed profiles Indicated agreat deal of fluctuating flne-structure and this could account for thereverse scattering back into the surface duct as noted In Figure 25. Inaddition, scattering Into the deeper channel may also be a significantfactor.

In Figure 28, an additional component of 0.02 dB/km has been added tofit the data.

- 30 -

/

A :(dB/km) Baltic Sea46C pHB SO

.00

.10

6',,

.,'A2 A3

10Frequency (kHz)

Figure 29: Baltic Sea data and model.

Interpretation of attenuation measurements In the Baltic Sea 1221Indicates need for estimating sound absorption In low-salinity waters.

4 While the magnesium sulfate component depends simply on the firstpower of concentration, the low-frequency boric acid relaxation is morecomplex. The mechanism Involves exchange with carbonate in which theIon-pair calcium carbonate governs the absorption magnitude.

Measurements of absorption by the resonator method show roughly 1/2power dependence on calcium concentration In the range of Interest.

The Baltic Sea salinity of 8 Is about 25% normal while the carbonate andacidity are both normal. Since loss Is multiplicative, SI15 dependence isIndicated. This would yield a reduction in magnitude by the factor 8.However, a more exact calculation, taking Into account the coupled-Ioneffects, shows somewhat less reduction. In addition, relaxation frequencyIs lower. T-Jump measurements of Baltic water samples by Candau 1231(unpublished) show that It Is only 0.6 kHz, which agrees with theory. Allfactors have been Included In the calculations.

Comparison of the measured data In Figure 29 shows that attenuation Isstill anomalously high by a large factor. The relative weckness of thelower part of the channel due to the small water-depth (zI1O0 m), is againIndicatatlve of loss by Internbl scattering.

-31 -

A -(dBirm) Tasnen SeapH7.9 4'C

.01

.001 ,//

l A2 A

.01 F1. :' Frequency (kHz)

Figure 30: Tasman Sea data and mudel.

In the deep ocean, the sound-channel is much stronger and scatteringloss ranges from negligible to only a few dO per thousand kilometers. Themeasurements In the Tasman Sea by Bannister et. a1. 1241 in Figure 30 aretypical. In both experiments shown, measurements were made In the deepchannel and the maximum range was roughly 3000 km. The absorptionspectrum was calculated for pH-7.9, a value estimated from archival data.

In the lower curve, a scattering loss of 3ýj04 dB/km has been added inthe data-fit. This amounts to only I dO total over the path and Is probablyinsignificant. In the upper data, the scattering loss is taken as 2x 10-3

dB/km and amounts to roughly 6 dB total, which Is considered well beyondthe limits of experimental error.

In the top experiment, the track encountered the Sub-Antarctic Frontwhere the channel axis rises close to the surface. Range dependence of thesound-speed profile may account for some of the anomaly; however, theabsence of frequency dependence of suggests that Internal scattering Isagain the principal mechanism.

Regional dependence of scattering loss has also been Investigated in theNorth Pacific by Kibblewhlte et. al. (25). Their results Indicate a similarIncrease at higher latitudes that the range dependence of the sound-speedprofile does not account for.

- 32-

,i I' . . -, .

A :(dB/km) SubArcticpH8.2 -1.5°C

.01

•t /

o Davis Straita Baffin Bay

A2 A3 AAI.0011

.01 .1Frequency (kHz)

Figure 3 1: Sub-Arctic data and model.

Figure 31 shows results from two experiments by DREA in ice-freewaters west of Greenland. Both of the tracks analyzed were In excess of300 km In length with water depths of 1-2 km. The sound-speed profilesshowed a distinct channel with axis depth near 100 m and any surf ace-scattering effects are therefore believed to be negligible. Absorption hasbeen calculated for pH=8.2, which is consistent with archival data.

The southern track in the Davis Strait shows clear evidence of an excessscattering-loss component despite the strong channel. The data are fittedby adding the value Ox 10-3 dB/km, which is comparable to the highestvalues reported in any of the experiments 1251.

The northern track In Baffin Bay also shows a simi~ar excess loss butonly at the higher frequencies. At 100 Hz It becomes negligible. A possibleexplanation is that the bottom absorption at lower frequencies may besmaller In that area, causing energy to be reflected back Into the channel.Alternatively, the Inhomogenelties may be smaller In scale. Scatteringloss can be expected to decay rapidly when the dime.-.ions become smallcompared to the acoustic wavelength.

-33-

Model Summary

A/F dB/lkn *kHz

E Mediterranpan 14*C pIH8.3

/t Atlantic 4°C pH1.0

N,/ • Pacif ic 40C p17.7

.01.I1 10 100

Frequency (kHz)

Figure 32: Experimental absorption spectra comparison.

The absorption spectra for the North Atlantic, North Pacific and EasternMediterranean experiments are compared In Figure 32. The coefficientshave been divided by frequency in kHz In order to compress the scale.

The North Atlantic and North Pacific are apparently the extreme casesfor deep (> km) waters of the World Ocean. For latitudes less than 45, theaxis depth of the deep sound-channel is roughly I km; therefore, the twocases represent the limits of variability expected for sound-channelpropagation In this latitude range. For the pH range 7.7-8.0, the max/mmnratio Increases uniformly with decreasing frequency, approaching a factorof two.

The Eastern Mediterranean is the highest pH so far; however, since thetemperature Is also high, the curve Is displaced upward In frequency andthe max/mmn ratio Is slightly less than a factor of two compared to theNorth Atlantic.

From all the experimental evidence, it appears that the North Pacific andEastern Mediterranean absorption spectra encompass nearly all the rangeof expected variability.

- 34 -

A/F (dBkrOWk2) pH47.7-6.3 40C

.1 '

.01 / . .. . . ., . . . .1 10 100

Frequency (k0z)

Figure 33: Absorption spectra A/F vs pH for T-4°C.

The principal results of the 3-relaxation model, are summarized InFigures 33 and 34. The absorption coefficient A has again been divided bythe frequency In kHz In order to compress the range. The predicted spectraYs pH for 4°C and normal salinity (S=35) are shown in Figure 33 and coverthe approximate sea-water range of pH 7.7-8.3 In steps of 0. 1.

The effect of pH on the absorption spectrum below 10 kHz is mainly dueto the coefficient of the boric acid component. Below I kHz, the max/minratio approaches the factor four.

From the present analysis of the experimental data, the overall error ofthe absorption model Is estimated to be roughly of the order of t-15%. Inother words, the RMS error of an estimated coefficient in dB/km at anygiven frequency Is not expected to be greater than this amount If notlimited by the accuracy of the environmental factors. Since a change of0.05 pH units corresponds to a 12% change In the boric acid coefficient,the pH errors must be within these limits In order to realize the modelaccuracy. The major limiting factor therefore appears to be the accuracyand availablility of of the pH data-base.

- 35 -

/t

A/F (dB/krn*kHz) pH8.0 0-300C

.1

OOC> <30C

.01.1 1 10 100

Frequency (kHz)

Figure 34: Absorption spectra A/F vs temperature for pH8.0.

Figure 34 shows the predicted spectral dependence on temperature forpH=8.0 and normal salinity (S=35) and cover the nominal sea-water range0-30°C In 5°C steps.

The temperature effect in the model comes only through the relaxationfrequency coefficients of all three terms. Increasing temperature shiftsthe curves upward In frequency.

Model errors involving temperature coefficient are also estimated to beof the order of ± 15%. Since the temperature sensitivity Is rather low, the

* value need only be known only to within roughly _2°C to realize the sameestimated accuracy.

Salinity corrections have been omitted In the simplified model. Errorsare probably within the accuracy limits for the normal sea-water range32-38 ppt. Salinity variations are evidently the result of evaporation anddilution by fresh water. Therefore, the concentrations of all constituents,except carbon dioxide, tend to remain in constant ratio. A multiplyingfactor S/35 for all three components may be Justified over a limited"range, say 30-40 ppt. Beyond this range, corrections must be made forchanges In the boric acid relaxation frequency. In more extreme cases likethe Baltic Sea, chemical analysis of the constituents may be required.

- 36 -

------ --------------------. ....

A/Ao pa.3 4*C

1.5

0.00

Frequency (kHz)

2.0

AiAo 3 pet8.O

0. 5

300C

In Figure 35, the spectra of Figures 33 and 34 are expressed as the ratioA/Ao where the Ao is calculated for the North Atlantic parameter valuesPH=8.0 and T=40C. The range of pH is 7.7-8.3 in steps of 0. 1 and the rangeof temperature is 0-30C in steps of 5C. The curves indicate theaccuracies required to realize the desired error limits.

-337-

PH Model0

Depth (kin)

2

North Atlantico 31 ON 390W

3 * 270N 54oWA2IN 540W* 15ON 54OWx2N 1414 W

4 1 __ __ __ __ I_

p1 "7.6 7.8 8.0 8.2 8.4

0Depth (kmn)

2

South Atlantic0 20S 14W

3 ,126S 20EA 200S 20E

x460S 14°E4 1

pH 7.6 7.8 8.0 0.2 8.4

Figure 36: Atlantic Ocean pH profiles.

PH data for many regions of the World Ocean are included in the data ofthe GEOSECS oceanographic expedition report 1261. Figure 36 shows plotsof typical profiles for a range of latitudes in the Atlantic Ocean.

- 38 -

0\• ' Depth (kmn)

2

North Pecf ico 45ON 1770W

3 * .38O1N 125OWA 28N 1220W* 160N 1230 Wx 8ON 167OW

pH 7.6 7.8 8.0 8.2 8.4

0Depth (km)

2

South Pecif ico SOS 12S°W

3 , 90S ! 2SOW

A I8SOS 1650Et O* 300SJ 1760E

' Nx 5709G 1700E.4

pH 7.6 7.8 8.0 8.2 8.4

Figure 37: Pacific Ocean pH profiles.

Figure 37 shows plots of typical pH profiles for a range of latitudes inthe Pacific Ocean from GEOSECS data [26).

- 39 -

I0Depth (kim)

2

Indiano 200N 650E

3 e 60N 640EA 69S 5 1E0 19"S 1O1*Ex 38*S 58*E

4pH 7.6 7.8 8.0 8.2 8.4

Figure 38: Indian Ocean pH profiles.

Figure 38 shows plots of typical pH profiles for a range of latitudes Inthe Indian Ocean from GEOSECS data [261.

A striking feature of all the pH profiles Is the relative constancy of thevalues at the surface and at great depths. The greatest variability occursIn the thermocline region around I km. depth.

For surface-duct propagation, depth variability should be small becauseboth the pH and temperature obviously are quite constant In the surfacemixed-layer.

For convergence-zone propagation, most of the travel time Is in the deepwater where the pH Is relatively constant. In the Southern Ocean, the valueIs 7.9. In the North Pacific, pH decreases to 7.8. In the North Atlantic, itincreases to 8.1 at high latitudes. Variability with latitude can thereforebe expected to be relatively easy to estimate.

The sound-channel axis depth Is roughly 1 km at mid-latitudes andrises to the surface at high latitudes. The net result Is that the pH valueon the axis will tend to Increase at the higher latitudes. The axial pH rangeIs approximately 7.7-8.3 and values tend to vary rapidly and unpredictablywith latitude. Sound-channel absorption should therefore be the mostdifficult to estimate with acceptable accuracy.

- 40 -

aJ

0Depth (kin)

SV H0 <H* I "

2

3

-4

5SV(krn/) 1.0 t

2H 7.'. .

0

2

3

4

50 10 20 30 40 50 60 70

Range (kmn)

Figure 39: PH test profiles and ray paths.

In order to estimate the effects of the pH profiles at mid-latitudes, thetwo typical cases illustrated at the top of Figure 39 will be examined. Thesound-velocity profile (SVP) is typical of latitudes less than 450. ProfilepHO I is the simple exponential decay and pH*2 is the case where there isa sharp minimum above the axis as in the North Pacific. Effective values ofA for the two profiles are calculated by numerical integration of the lossover single cycles of the sound-channel and convergence-zone (CZ) raypaths shown at the bottom.

-41 -

Sound ChennelA/A*

1.1

1.0

•09 1 1

.1 tFrequenCY (kHz)

A----Convergence Zone

1.1

.1 FreqUenCg

Figure 40: Absorption ratio A/A*.

I.

F r40 shows the effective values of A relative to where A* is the

value calculated using the axial temperature and pH for thesonChne

case and 2 km depth values f or the CZ case, The results Show the' the neft

errors are far less than the estimated uncertainty in absolute pH values,

which is taken to be ±0.05 units and corresponds to ± .12% OFange in AIA*.

- 42 -

* tr

0Depth, (kM)•'17

I

2

3

4

GV.k'At /e) 1.50 1.55

pH 7.5 8.0 8.5

0

2

4

0 10 20 30 40 50 60 70Range (kni)

Figure 41: High latitude test profiles and ray paths.

In order to estimate effects of the pH profiles at higher latitudes, thetwo cases shown at the top of Figure 41 will be examined. The SVP istypical of latitudes around 600. Profiles pHr3 and pHr4 represent currentestimates for the North Atlantic and North Pacific, respectively. The raypaths used in the numerical integration of loss are shown below. Note therelative lack of distinction between sound-channel and convergence modesfor shallow ray-angles. At higher angles, surface reflection is involved.

-43 -

A/A* North Atlantic pH*3

1.0

S 1.0

Frequency (kHz)

A/A* North Pacific pH*4

1.0

1.0.

0.9. ... . . . , , •. . .

Frequency (kHz)

Figure 42: Absorption ratio A/A*.

Figure 42 shows the effective values of A/A* where A'is calculated for

ýhe 2 km depth values of temperature and pH. In this case, errors diminish

0s ray angles increase while the opposite occurs if axial values are used.

At high latitudes in the Southern Ocean, profile pH*I Is the appropriate

model and errors for this case are roughly doubled compared to the case of

profile pH*3. Interpolation between the 2 km and axial values in the ray

"nalysis would clearly help to keep the errors within acceptable limits.

- 44 -

,o. ., f . ... A. . ..-

I ~ . - .

GIlobal Model

A=A, (MgS04)+A 2 (B(OH) 3 )+A 3(MgCO 3 )A n =(S/35)anf 2 fn/( f 2 +f)

a I =o. 5sXO-D(km)/20 fI = 5 0 x1oTI 6 0

0 2 :0.1 K f2 =0-gxIoOT/30

03= 0.03 K f3 =4.5xo10

Figure 43: Global model absorption formula.

Variability of pH is clearly the major limiting factor in the accuracy ofthe absorption formula. In Figure 43, the pH parameter K= 10(p"e8) has beensubstituted in the simplified absorption formula. Salinity dependence hasbeen taken as S/35 with the caveats noted. An interim model is proposedfor estimating effective K values for specific propagation modes.

Based on the analysis of the previous section, the recommended methodIs to use axial values of K and temperature T (°C) for the sound-channelmode and the 2 km depth values for the CZ mode. Errors at higher latitudescan be reduced by interpolating between the two values, depending on theray paths involved. Temperature is not a problem since it can be easily bederived from the SVP if not directly available from XBT data.

Contours of pH for the surface and for the 0.5 km and I km depths areshown in the World Ocean Atlas of Gorshkov 1271. Contours for 2 km depthare also included in Vol. 2. Since the contour intervals are 0.1 pH unit,interpolation is required. Correction to in-sfiu pressure is also necessary.

Pressure-corrected pH data from the GEOSECS report have also been usedIn the analysis, allowing estimation of the 2 km contours in regions of thePacific Ocean not covered by the Russian work. Discrepencies between thedata sets in other regions have been arbitrarily resolved by adjustment ofthe contours so as to minimize effects on estimation error. Considerablesubjectivity is obviously involved.

The K contours on the sound-channel axis in Figure 44 are based on ananalysis of the Russian pH contours by Lovett 1281. The 2 km depth andsurface contours derived from the Russian report are shown in Figures 45and 46, respectively. All have been modified in taking the GEOSECS datainto account.

- 45 -

40

3AV

40.

I0.

3003D6 2

60 A .7 _ _ _ _ _ _ _ _ _ _ _ _

Fiue4:Sudchne otus

q0-8

3D k

. . ......

ao

1 47-

30 /

doa 1.6

605 0 120 90 12

Fiur 4 11ur.c6 Kcntus

12.0

il.

Conclusions and Recommendations

The three-component absorption model appears to be firmly establishedby NUSC laboratory and sea experiments. In addition, independent studiesat the Academia Sineca laboratory confirm the results in detail [29,301.

The proposed simplified model has been shown t give very satisfactoryfield predictions within the error limits imposed by the environmentaldata. Future refinements may require slight adjustment of the parameters;however, .ne overall accuracy seems to be adequate for current purposes.

The main limitation of the global model is the accuracy of the pH values.Depth-dependence does not appear to be the critical factor. The simplifiedmodel uses axial values for the sound-channel mode and 2 km depth valuesforthe other mode•. Approximation errors are evidently smaller than theuncqertainty in the 4ppolute values except at the higher latitudes whereinterpolation betw ten 2 km and axial values will help improve accuracy.

The K contours provided in this report should give reasonably accurateapproximations for absolute pH effects in most of the World Ocean. Thepossible exceptions are regions where significant discrepencies betweenRussian 3nd GEOSECS values have been noted.The Russian data representlocal averages of archival data and tend to be lower and more variable.Errors involved in interpolating the data can also be significant.

The scippe of this report has been limited to development of a suitableabsorption model, a method of predicting the pH effects, and a rationalefor incorporation intb existing propagation models. Analysis has shownthat the estimated overall accuracy ± I5X of the absorption model can onlybe realized if the pH error is ±0.05 units or less and this remains thecrucial factor. Portions of the GEOSECS pH data have been used to analyzeprofile effects, to ýupplement the missing Pussian 2 km contours and tomodify the others where indicated. Significant disagreements with theRussian data have been noted. It is therefore recommended that the ent:.,eGEOSECS data set be analyzed for the purpose of either refining the Kcontours or devising a more accurate data-base format.

At sea, the simplest solution is to measure surface pH. Measurement ofthe pH profile along with the normal XBT would, of course, help to resolveall the uncertainties. Since no suitable apparatus seems to be available forthis purpose, development of an expendible pH prob4 may be indicated.

Surface scattering is another loss mechanism that can be important insurface-duct and other RSR propagation modes. Previous estimates ofscattering loss vs waveheight have been based largely on surface-ductexperiments. Inaccurate absorption models may cause the effects to beseriously overestimrated and reassessment using the improved absorptionmodel is also recommended.

-49-

'k J

References

1. R. H. Mellen, T. Akal, E. H. Hug and D. G. Browning, Low-frequency soundattenuation in the Mediterranean Sea", J. Acoust. Soc. Am. 78 S70 (1985)

2. E. B.:Stephenson, "Transmission of sound in sea water: Absorption andreflection coefficients and temperature gradients",

NRL Report S 1024 (1935)3. L. N. Liebermann, "Origin of sound absorption in water and in sea water",

J. Acoust. Soc. Am. 20 868-873 (1948)4. R. W. Leonard, P. C. Combs and L. R. Skidmore, "Attenuation of sound in

synthetic sea water", J. Acoust. Soc. Am. 21 63 (1949)5. 0. B. Wilson and R. W. Leonard, "Measurements of sound absorption in

aqueous salt solutions by a resonator method",J. Acoust. Soc. Am. 26 223-228 (1954)

6. G. Kurtze and K. Tamm, "Measurement of sound absorption in water andaqueous solutions of electrolytes", Acustica 3 33-48 (1953)

7. M. Eigen and K. Tamm, "Sound absorption in electrolytic solutiuns due tochemical relaxation", Z. Electrochem. 66 93-121 (1962)

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10. W. H. Thorp, "Analltic description of the low-frequency attenuationcoef' icient" J. Acoust. Soc. Am. 42 270-271(1967)

11. C. C. Leroy, "Sound propagation in the Mediterranean Sea", inUnderwater Acoustics, ed. V. M. Albers (Plenum, 1967) Vol. 2, pp. 203-241.12. Attenuation of Low Frequency Sound in the Sea,

NUSC Scientific and Engineering Studies, Volumes I & IIPublished by the Naval Underwater Systems Center (1981)

13. E. Yeager, F. H. Fisher, J. Miceli and R. Bressel,"Origin of low-frequency sound absorption in sea water',

J. Acoust. Soc. Am. 53, 1705-1707 (1973)14. R. H. Me len and D. G. Browning, "Variability of low-frequency sound

absorption: pH dependence', J. Acoust. Soc. Am. 6_1 . 704-706 (1977)15. V. P. Simmons,

"Investigation of the 1 kHz sound absorption anomaly in sea water",Ph.D. thesis, University of California, San Diego, CA (1975)

16. R. H. Mellen, D. G. Browning and V. P. Simmons, "Investigation ofchemical sound absorption in sea water by the resonator method',

J. Acoust. Soc Am. Part I, 668 246-257 (1980); Part II, 69, 1660-1662(1981); Part I11, 70,143-148 (1981); Part IV, 74, 987-993 (1983)

- 50 -

17. R. H. Mellen, V. P. Simmons and D. G. Browning, "Sound absorption in seawater: a third chemical relaxation',

J. Acoust. Soc. Am. 6 923-925 (1974)18. F. H. Fisher and V. P. Simmons, "Sound absorption in sea water",

J. Acoust. Soc. Am. 6 558-564 (1977)19. F. H. Fisher, "Sound absorption in sea water by a third chemical

relaxation', J. Acoust. Soc. Am. 61, 704-706 (1977)20. D. V. Wylie, "Losses in surface duct propagation", Weapons Research

Establishment (Australia) Technical Memorandum 1250, (1974)21. R. H. Mellen, D. G. Browning and J. M. Ross, "Attenuation in randomly

Inhomogenecus sound channels', J. Acoust. Soc. Am. 56, 80-82 (1974)22. H. G. Schneider, R. Thiele and P. C. Willt, "Measurement of sound

absorption in low salinity water of the Baltic Sea",J. Acoust. Soc. Am. 77 1409-1412 (1985)

23. S. J. Candau, Laboratoire de Spectronomie et d'lmagerie Ultrasonores,Universite Loui.s Pasteur, 67070 Strasbourg Cedex, France.

24. R. W. Bannister, R. N. Denham, K. M. Guthrie and D. G. Browning, "ProjectTasman Two: Low-frequency propagation measurements in the

South Tasman Sea", J. Acoust. Soc. Am. 62 647-859 (1977)25. A. C. Kibblewhite, N. R. Bedford and S. K. Mitchell, "Regional dependence

of low-frequency attenuation in the North Pacific Ocean",J. Acoust. Soc. Am. 61 1169-1177 (1977)

26. GEOSECS Atlas, International Decade of Ocean Exploration (NSF),Superintendent of Documents, U. S. Government Printing Office,Washington DC 20402, Stock Number 038-000-00491-3

Vol. I, Atlantic Expediton 1972-1973Vol. 3, Pacific Expedition 1973-1974Vol. 5, Indian Ocean Expedition 1977-1978

27. World Ocean Atlas, edited bu S. G. Gorshkov (Pergamon Press, New York)Vol. I, Pacific Ocean, pp.234-235 (1974),Vol. 2, Atlantic and Indian Oceans, pp234-235 (1978)

28. J. R. Lovett, "Geographic variation of low-frequency sound absorptionin the Atlantic, Indian and Pacific Oceans",

J. Acoust. Soc. Am. 67"338-340 (1980)29. Qiu Xinfang, Jiang Jiliang and Wan Shimin, "Sound absorption in sea

water due to low frequency chemical relaxations",Chinese J. Acoust. 2 71-80 (1983)

30. Qiu Xinfang, Jiang Jiliang and Wan Shimin, "Investigation of themechanism of sound absorption by the boric acid relaxation in sea water",

Chinese J. Acoust._3 51-63 (1984)

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