J'OURNAL OF GEOPHYSIC^L RESEARCH

VOL. 73, NO. 18, SE•'TEMBER 15, 1968

The Effect of Temperatureand Partial Melting on Velocity and Attenuation in a Simple Binary System I-IARTMUT SPETZLER AND DON L. ANDERSON

California Institute o/Technology, SeismologicalLaboratory Pasadena, California 91105

A possibleexplanation of the low-velocity, low-Q zone in the upper mantle is partial melting, but laboratory data are not available to test this conjecture.As a first step in obtaining an idea of the role that partial melting plays in affectingseismicvariables, we have measured the longitudinal and shear velocities and attenuations in a simple binary system that is corn= pletely solid at low temperatures and involves 17% melt at the highest experimental temperature. The system investigated was NaC1 ß H•O. At temperatures below the eutectic the material is a solid mixture of H•O (ice) and NaC1 ß 2 H•O. At higher temperaturesthe system is a mixture oœice and NaC1 brine. In the completely solid regime the velocities and Q change slowly with temperature. There is a marked drop in the velocities and Q at the onset of melt= ing. For ice containing 1% NaC1, the longitudinal and shearvelocitieschangediscontinuously at this temperatureby 9.5 and 13.5%, respectively.The corresponding Q's drop by 48 and 37%. The melt content of the mixture at temperatures on the warm side of the eutectic

for this compositionis about 3.3%. The abrupt drop in velocitiesat the onset of partial melting is about three times as much for the ice containing2% NaC1; for this composition, the longitudinal and shear Q's drop at the eutectic temperature by 71 and 73%, respectively. If theseresultscan be usedas a guidein understanding the effectof melting on seismicproperties in the mantle, we should expect sharp discontinuitiesin velocity and Q where the geothermcrossesthe solidus.The phenomenaassociatedwith the onset of melting are more dramatic than those associatedwith œurthermelting. INTRODUCTION

have sharply defined melting temperatures

Knowledgeof the mechanicalpropertiesof multicomponent systemsin the vicinity of their meltingpointsis requiredin variousgeophysical problems.In particular, the behavior of seismicvelocityand attenuationnear the melting pointis pertinentto discussions of the upper mantle low-velocityzone.In this study we have measuredthe velocity and attenuationof longitudinal and shear waves in the vicinity of the eutectic temperature in a simple dilute binary system.By varying the composition, we have been able to study the effects of temperature and partial melting. We chosedilute solutions so that we couldinvestigatethe regioninvolving partial melting. In the system studied, NaCI-I-I•O, the amount of melt could be changedsimplyby varying either the tempera-

rather than a melting interval. Mizutani and

Kanamori [1964] measuredthe compressional and shearvelocitiesand the compressional wave Q for an alloyconsisting of Pb, Bi, Sn, and Cd. The velocitiesvaried approximatelylinearly with temperature until T/T,• wasabout0.97,at whichpoint they decreased rapidly. The P velocity dropped 20% upon melting, and the quality factor Q droppedby about an order of magnitude.The Q decreased very rapidlyas the melting point was approached.Similar results

wereobtained by Polco•'ny [1965],whoobtained a velocitydrop of about 15% and a Q drop of an order of magnitudeas melting progressed. Again the mechanicalpropertiesstartedto anticipate the melting point at a T/T,• of about 0.97.

Both of the precedingstudiesused an ultra-

ture or the initial concentration of NaC1.

Previous studies of this sort have used pure

materials or eutectic mixtures, both of which • Contribution 1528, Division of Geological Sciences, California Institute of Technology, Pasadena

sonicpulsemethodwith frequencies in the high kilocycleor megacyclerange, i.e., very short wavelengths.The actual amount of melt as a

functionof temperatureand the configuration of the molten zones was not described.

91105.

6051

Water and NaC1form a simplebinarysystem

6052

SPETZLER

AND ANDERSON

that can easily be studiedin the vicinity of the eutectie temperature. Both the phase diagram and the geometry of the componentsare well known. The melt phase (brine) occursat the grain boundariesin cylindricalchannelsor thin layers, depending on the temperature. In polycrystalline specimensthe melt occurs in irregularly shapedpocketsbetweencrystal and subcrystalboundaries.We useda resonancetechnique and large samplesto assurethat the wavelengthswere alwayslarge comparedwith crystal

slightconcentration of salt towardthe centerof the rod and away from the ends. The total

variation, however,was less than ñ0.15% of salt concentration.

Photomicrographsof thin sectionscut from the ice rods were taken in order to study the size and orientationof the ice plateletsand the distribution of the brine. From the photomicrographsit was possibleto determinethe size and orientation of the ice platelets. Most plateletswere oriented such that their c axes or melt zone dimensions. Ice rods were frozen were in planesparallelto the surfaceof the rod. from dilute NaC1 solutions,and the resonant Figure 1 showsa radial cut closeto one end of frequencieswere measuredto obtain longitudi- a 2%NaC1 ice rod. The view is parallel to the c nal and shearvelocities.The quality factors,Q's, axis of the platelets. The temperature was --5.3øC. The hexagonalplatelets have an averwere obtained by measuringthe width, and in some casesthe decay, of the resonancepeaks. age diameterof 0.5 mm, and their diameter4oThe measurementswere performed on pure thicknessratio is about 8 to 1. Photographsof H•O ice and on NaCl-ice mixtures as a function 1% ice NaC1 show platelet diameters of apof NaC1 concentrationand temperature for the proximately 1 mm. fundamental mode and several overtones. A solenoid arrangement was used to excite longitudinalmodesin the ice. A small bar magEXPERIMENTAL 1)ROCEDURE net was frozen into each end of the ice rod, The experimentswere performedin a So-Low and the external transducer coils were enclosed EnvironmentalEquipment Co. refrigerator. To in aluminum boxes that were covered with /• assuretemperaturestability the refrigeratorwas metal to avoid electromagneticcouplingbetween packedwith ice, and the experimentwas placed the driving and receiving transducers.The transducers at each end of the ice rod were insidea styrofoaminsulatingbox. A carefully measured amount of distilled identicaland arrangedsymmetrically.The shear water was heatedcloseto its boiling point, and transducers consisted of small flat coils which the appropriate quantity of NaC1 was added. were frozen into the ice at both ends. To reduce couplingbetweenthe coils,they To remove entrappeal air, the solution was electromagnetic placed in an airtight container and a vacuum were oriented 90 ø to each other. Permanent (10 torr) was pumped until the solution was magnetswere used at the driver and receiver boilingslowly.The solutionwas pumpedunder end to completethe motor and dynamo action, vacuum into a Teflon tube 2.54 cm ID and respectively.The ice rods were supported by 30.5 cm long. The ultrasonic transducerswere two narrow copper-band slings at the nodal supportedwith Teflon plugs at each end of the points of the second harmonic. Various other tube. To avoid separation of the ice crystals supportswere tried, includingthree slingsand from the brine during the freezingprocess,the foam rubber pads, but the best reproducibility and the highest Q values were obtained with samples were frozen quickly at about --30øC and were rotated at 1 rpm while in a horizontal the two-sling arrangement, which was mainposition. The Teflon tubes were removed when the freezing was complete.After the resonance experimentswere performed, the ice rods were melted and the salinity of the solution was remeasured.The salt content of the rod was approximately 10% lessthan the starting solution owing to concentrationof salt at the surface of the rod during the early stages of freezing. Salinity was measuredon one ice rod as a function of position within the rod. There was a

tained throughout all measurements. To monitor the temperatureof the specimen, a separateice rod was prepared under identical conditions to the one used for the velocity measurements.

This

control

rod contained one

thermocouplein the center and one on the outside. By connectingthe constantan of the two iron-constantan couples, it was possible to record the absolutetemperature and the difference temperature between the outside and the

VELOCITY

AND

ATTENUATION

IN A BINARY

SYSTEM

6,053

Fig. 1. A view parallelto the c-axisorientation of the ice plateletsin ice containing 2% NaC1.

inside of the rod. The resistance between the

of the various modes of the ice rods. A Scho-

top and the center and the center and the

mandle ND30M frequency synthesizer was driven by a synchronous motor to sweep

bottom

of the rod was also measured. This

measurement wasperformedto checkfor a possible•brine drainagein the regionwarmer than the eutectic.No settling of brine was recorded on the time scaleof the experiment.The absolute temperaturewas measuredwith the aid of a Leeds and Northrup potentiometer.Small temperatureincrements werereadwith a digital voltmeter. Periodic cross calibration between the

throughthe appropriatefrequencyrange. To excite the longitudinalmodes,the output of the synthesizerwas amplifiedand applied directly to the driving solenoid. The shear transducerarrangement,shownin

Figure 2, is somewhatmore complicated.An arrangementof resistorsbetween synthesizer and amplifier served to select amplitudesfor

voltmeter,the potentiometer, and variousther- various frequency ranges. This arrangement toocouplessuggestsan absoluteaccuracyin enabled the operator to perform all measuretemperatureof --0.15øC anda relativeaccuracy mentswithout disturbingthe output 1.evelof between measurements of --+0.05øC. The referthe synthesizer.The output of the receiving transducerwas amplifiedin two stagesand then detected. The detected signal was recorded on a strip chart recorder and on a digital voltINSTRUMENTATION meter. Both the driving signal and the output Figure 2 showsthe circuitryusedto measure signalwere displayedon an oscilloscope. and record the resonantfrequenciesand the Q's A typical record of a frequency sweep is

ence ice bath was aerated and carefully main-

tained by usingdistilledwater and shavedice.

6054

SPETZLER

AND

ANDERSON

51 12

(Motor Driven Sweep) • Frequency Synthesizer I ['"• • o

....

, •,

I pøwer AmP"r'er_ I

½3612

,

Input Output

4 XMagnet/ ___•__ ql• XMagne,/••

J• ,, I /oo•ooJ •' Io[ Pre- mp'fief I

&;;•

Io.o•T••

/

Fig. 2. Schematicillus[ra[ion of the shearresonanceexperimenL

shown in Figure 3. The frequency at the peak of the resonancewas read from the synthesizer. The widths of the symmetric resonancepeaks were measuredby changing the frequency to the valueswhere the digital voltmeter was 0.707 of the peak value, thus giving the half-energy points. In casesof high noise level the resonancewidth wasmeasuredfrom the graph. Many data points for Q were checkedby measuring Q from the decayof the rod oscillationsafter the power was turned off. The results were compatible. A few data points were obtained on rods that were frozen under identical

conditions in order

to check reproducibility. These Q and velocity

and receiver.To cancelthe coupling,a second driver and receivercoil were placedoutsidethe refrigerator and adjusted so that the electromagnetic couplingwas the same as that for the coils embedded in the ice. The two receiver

coilswere connectedto a centertrapped transformer. By tuning off the resonanceand adjusting the couplingof the compensating coils, the output of the two receiver coils could be made to be 180ø out of phase and thus cancel. The transformer

served also to match the low

impedanceof the coils to the high input impedanceof the amplifier.On the driver side,a transformerwas used to match the impedance betweenthe amplifier and the transducercoil.

data fell within the scatter of the data shown.

The perpendicular orientation of the sheartransducer coils did not completely eliminate the electromagneticcoupling between driver

%

RESULTS

Measurementsof resonant frequency and peak width were made for the fundamental and

_••rtone Second damental •_vertone Temp-72 øC

I

EXPERIMENTAL

A First

Third

Fourth

c••Overtone

F•fth

•e LONGITUDINAL

MODES,

Overtone PURE

ICE

Fig. 3. Tracing of strip chart recordingof a typical frequencysweep.

VELOCITY

AND ATTENUATION

several harmonicsas a function of temperature. The temperaturewas varied slowly so that the difference temperature between the center of

IN A BINARY

SYSTEM

6055

alwaysgreaterthan 0.94 of the eutectictemperature.

The normalized temperature derivatives of the velocities -- (l/V) dV/dT are 0.6 X 10-', This required a coolingor heating rate between 0.9 X 10-8, and 1.4 X 10-8 øC-• for longitudinal i and 2 degreesper hour, slowerin the eutectic waves in pure ice and 1% NaC1 and 2% NaC1 region.A typical data run from --35 ø to --8øC ice, respectively, for temperatures colder than and back through the eutectic took approxi- the eutectic. The correspondingshear velocity mately 100 hours.The velocitieswere calculated derivatives are 0.8 X 10-8, 1.4 X 10-8, and from the fundamental resonancefrequenciesof 2.8 X 10-8 øC-•, significantlylarger than the the longitudinaland shearmodesof the ice rods longitudinalderivatives.The drop in longitudinal V = 21)•/nwhere )• is the fundamental frequency velocity acrossthe eutectic for the ice containof the appropriatemode,n is the modenumber, ing I and 2% NaC1 was 9.5 and 28%, respecand l is the length of the ice rod. No correction tively. The correspondingdrops for the shear was applied for the temperature dependenceof velocities were 13.5 and 40%. These velocity 1. Accordingto estimatesof Weeks [1961], the decreases occur within 0.1øC but over a time maximum length change in the temperature span of several hours when the ice is warming from --30 ø to --10øC for the 2% NaC1 ice up. When the ice is cooledthrough the eutectic would be approximately 0.3%. point, the systemis able to supercoolby 1.5ø to Velocity data from the fundamentalmode of 2.5øC. In this casethe cuteeric region is spread the I and 2% salt-ice-rodsare presentedin Figover a larger temperature range but occursin a ure 4 as a function of temperature. The cuteeric shorter time interval. While the ice warms up, temperature for the NaC1. H20 system is the velocitiesincreasefor several degreesimme--21.3øC. Figure 5 gives the same data as a diately after the eutectichas been passed.When function of brine content. At temperatures the temperature is reversed, the velocities do colder than the eutectic, the velocity decreases not show this dip. approximately linearly as the temperature inFigure 5 gives the velocity as a function of creasesand at a faster rate than pure ice. In brine content and salinity. To achieve a given theseexperimentsthe absolutetemperaturewas brine content, the ice containing 1% NaC1 the rod and the outside never exceeded 0.1øC.

VL Pure Ice

3.0

_

VL I% NoCI

2.5

-

J •,2.0

VL 2.% NoCI

'

o

VsPure Ice

Vs 2 % NoCI

: -• : Incteas,rig Temperature

o--o--o -8

-12

-16

-20

Temperature,

-24

Decreasing -28

-52

øC

Fig. 4. Longitudinal VL and shear Vs velocities in pure ice, ice containing 1% NaC1, and ice containing 2% NaC1. Note the large drop in velocity at the cuteerie temperature and the hysteresisbetween the warming and cooling cycles.

6056

SPETZLER

--

,5 E

AND ANDERSON

VL 1% NaCI

•

: Increasing -- 1.7 ----o--- Decreasing Temperature _

,

•1.6•

.2.5 --

•

--

E

vs IO/oNoC•

_o

"',e,,

--1.4•

.•_ 3 2.0-

--•.3

•

o

o

-J

--

• 2 %

--I.2

NoCI

--

--I.I

•.50 I I I I 5I I

I0

I I I 15I I I I I

20

Per cent Bnne by volume

Fig. 5. V•. and Vs as g function of brine volume .The ice crystalsin the 1% NaC]-ice system hgve linear dimensionsapproximatelytwice as large as in the 2% NaC]-ice system.

must be much warmer than the ice containing 2% NaC1. For example, a 7% brine content occurs at --8.4øC for the ice containing 1% NaC1 and at --19øC for the ice containing2% NaC1. Brine content was computed from the phase diagram in Figure 6 and Weeks [1961]. Contrary to our initial expectations,the velocity is not a unique function of the melt fraction. In the 1% NaC1 systemthe velocitiesdecreaseby about 1.2 to 1.4% for each 1% increment in brine content. In the 2% NaC1 system, the correspondingdecreasein velocity is about 2%. The Q measurements(Figures 7 through 12) were taken simultaneouslywith the velocity measurements.The Q decreasesslowly with temperature to about --30øC and then begins to rise gradually.There is an abrupt decreasein Q at the eutectictemperature,which in all cases recoversslightly as the temperature is further raised. A peak in anelasticityis often observed at critical points in gas or fluid mixtures. In our case, this phenomenonis complicatedby the large changein mechanicalpropertieswhich occurs when the systemgoesfrom a solid-solidto

the temperatureis reversed,i.e. when the sample is cooled,the ability to supercool(which is related to the difficulty of nucleation)permits nonequilibriumconditionsto maintain during the passageof a stresswave, and there is no loss associatedwith thermodynamicrelaxation

a solid-fluid mixture. It is this mechanical effect -14 -18 that we are primarily interestedin. The elastic Temperature, øC wave upsetsthe local thermodynamicequilibFig. 6. Volume per cent of brine versus temrium in a mixed phase region, in this case a salt-water-ice system. This effect is superim- perature and composition in the system studied. Insert showsthe phase diagram of the NaC1 sysposed on the grain boundary looseningasso- tem [Weeks, 1961]. Dashed lines are the com-

ciatedwith the onsetof partial melting.When

positions studied.

VELOCITY

AND ATTENUATION

IN A BINARY

SYSTEM

6057

IOO

50

Fundamental

I- irsf

Overlone

becond

Overtone

I -8

-12

-16

-20

Temperature,

I

-28

-24

-32

øC

Fig. 7. Q for the first three longitudinal modes or the heating cycle for 1% NaC1.

IOO

--

50 o

-8

-12

I

I

I

I

Temperature,

Fig. 8.

-2

o

Fundamental

•'

First

ß

Second

!4 I

-28

Overtone

I

Overtone

]

I

-32

I

øC

for the first three shear or torsional modes or the heating cycle for 2% NaC1.

ioo

50

o ß

-8

-12

-16

-20

Temperature,

-24

o

Fundamental First

Overtone

-28

-32

"C

Fig. 9. Q for the first two harmonics, the shear or torsional modes for 1% NaC1. Arrows

indicate whether the data were taken on the warming or coolingcycle. effects. In this case the losses are associated with nal Q's for the 1 and 2% NaC1 ice. The corremechanical,presumably grain-boundary effects spondingvalues for the shear Q's were 37 and alone. On the warming cycle,the drop in Q at 73%. the eutectic point amounted to 48 and 71% A further increasein temperatureleads to a for the fundamental frequency of the longitudi- small increasein Q for the longitudinalmodes.

6058

SPETZLER

AND ANDERSON

IOO

5o

0

-12

-16

-20

o

F'•rst

©

Sacand

-24

Temperature,

Fundamental

&

_

Overtone

Overtone

-28

-•2

øC

Fig. 10. Q in shear for the first three harmonicsfor 2% NaC1. Arrows pointing to the left indicate that the data were taken on the warming cycle. Arrows pointing to the right indicate that the data were taken on the cooling cycle; note the supercoolingin the secondcase.

For the shear modes, especiallyfor the 1% NaC1 mixture, the increase was very pronounced.At warmer temperatures as the brine content further increases,the Q's begin to decrease. For comparison, the longitudinal and shear Q's for pure ice are shown in Figures 11 and 12. For pure ice, and for salt ice below --35øC, Q increaseswith frequencyfor the first few harmonics.For higher temperaturesin the salt ice, Q decreasesas the frequencyincreases. Above the eutectictemperature this generalization does not hold.

The shear Q data of pure ice show minima for the first three harmonicsat --28 ø, --16 ø, and --12øC, respectively.Figure 12 showsthe relation of these minima to temperature and relaxation time. The activation energy correspondingto this frequencyresponseis approximately 7.5 kcal/mole.

SIZE OF ICE PLATELETSAND VELOCITY

The spacingbetweenthe centersof adjacent ice platelets is a linear function of salt concentration and is directlyproportionalto the square root of the freezing time [Rohatgi and Adams, 1967]. The freezing times for the I and 2% ice rods in this experiment are of the order of 100 to several hundred seconds.This freezing time corresponds approximatelyto that usedin Figure 14 of the abovementionedreference.The spacingbetweenthe centersof the platelets of

the 1 and 2% ice is thereforequite similar,and this is confirmedby the photographsdescribed earlier. The other dimensionsof the crystals are, however,approximatelytwice as large for the 1% ice as for the 2% ice. It is clear from Figure 5 that the mechanical properties depend on more than just the brine or melt content. Since most of the brine is con-

IOO0

Q 5OO

--

LONGITUDINAL O

•x•,...•

--- ---o-PURE ICE Fundamental -- I I --

First Overtone

•

•,--"•

I •'•-'•'-• •,.•••_.• ' '•'• •._•_•.•_.__+---

•

FouF•h

0veF•one

I00

5O

-0

I

I -4

I

I -8

I -•2

• . I -16

--+-I -20

Seventh I -24

-28

TempeFotuFe,

Fig. 11. Q as a function of temperature and frequency for pure ice; longitudinal modes.

VELOCITY

AND ATTENUATION

IN A BINARY

SYSTEM

6059

of more than passing interest. This dip was observedon all the samplesbut was most pronouncedin the shear data for ice containing1% T, sec NaC1. A multicomponent, multiphase system that is in equilibrium will be disturbed by an acoustical signal. The degree to which the equilibrium is disturbed is a function of the frequencyand amplitude of the signal.The rate at which the chemical equilibrium can follow temperature and pressurefluctuations(chemical kinetics) controls the frequency dependenceof Ixl(• 4 --this part of the ultrasonicabsorption.At a given frequency, the absorption is a function of the :300 I i I concentrationgradientsassociatedwith the temShear Q perature and pressurefluctuationscausedby the Q "'816 cps stress wave. Energy is absorbed from the (Flexural) • I0,500 acoustic signal and converted into chemical 200 -energy.Someof this chemicalenergyis released in the form of heat as the system attempts to return to equilibrium. The slopesof the curves 7000 cps in Figure 5 give a measure of the extent to which the equilibrium may be disturbed by a •3500 small change in temperature. At the eutectic I00 -where the slopeis discontinuous, the absorption -I0 -20 -30 -40 shouldbe a maximum, as is observed.The above Temperature, øC described absorption mechanism is well known and has been used to study reaction kinetics in Fig. 12. g as a function of temperature and harmonic for shear modes in pure ice. Also shown liquids (see,for example,Tabuchi [1956, 1957]; are the results in flexure obtained by Kuroiwa Yasunagae• al. [1965]; Tatsumoto [1966]) in [1985]. the megacycles-per-second range. The precedingargumentssuggestthat a sharp rained in layers between subcrystal platelets, dip in Q will be associatedwith the onset of the function of the liquid (brine) seemsto be partial melting in the mantle. Solid-solidphase one of decouplingat the grain boundaries.The changesmay showsimilar dips.The low-velocity number of grain boundariesper unit volume, zonesof the upper mantle has been interpreted an important parameter, is inversely propor- in terms of (a) proximity to the melting point tional to the surface area of a grain, and the [Press, 1959], (b) high temperature gradients velocity is a function of the brine contenttimes [Gutenberg, 1959; Birch, 1952; Valle, 1956], the surface area of the grains. and (c) chemical inhomogeneityin the mantle [Ringwood, 1962a and b]. The data of the presCONCLUSTONS ent investigation indicate that the seismic veThere are a number of generalizationsthat locities and Q values will drop abruptly if the can be made from the data of this investigation. solidus crossesthe geotherm. If due to partial A small volume fraction of liquid has a large melting,the boundariesof the low-velocityzone effect on the velocity and attenuation of shear will be abrupt. This is consistent with recent and longitudinalwaves. As expected,the effect tectonic and oceanic mantle models. The lowon the shear velocity is considerablymore than velocity zonewill alsobe a zoneof high attenuathe effect on the longitudinal velocity. Because tion and this also seems to be the case. of the anisotropyof the ice rods,no direct comAcknowledgments. It is a pleasure to acknowlparisoncan be made betweenthe velocitiesand edge the help of David F. Newbigging who asQ's of the shearand the longitudinalmodes. sisted in all phases of the experiment. We are The sharp dip in Q at the eutectic point is grateful for helpful discussions with Thomas 3.8

3.9

I

I

I/T(OK)

I

4.0xlO-3

.,•

_

_

_

_

6060

SPETZLER

AND ANDERSON

Ahrens, Charles Archambeau, and Samuel Epstein.

This research was partially supported by National Science Foundation grant GA 1003. l•EFERENCES

Birch, F., Elasticity and constitution of the earth's interior, J. Geophys. Res., 57, 227-286, 1952. Gutenberg, B., The asthenosphere low-velocity layer, Annali di Geo/•sica,12, 439-460, 1959. Kuroiwa, D., Internal friction of H20, D20, and

natural glacier ice, U. $. Army Material Command Res. Rept. 131, Cold Regions Research and Engineering Laboratory, New Hampshire, 1965.

Mizutani, It., and H. Kanamori, Variation of elastic wave velocity and attenuative property near the melting temperature, J. Phys. Earth, 12(2), 43-49, 1964. Porkorny, M., Variation of velocity and attenuation of longitudinal waves during the solidliquid transition in Wood's alloy, $tudia Geophys. Geodaet. Cestcoslov.Atcad. Ved, 9, 1965. Press, F., Some implications on mantle and crustal structure from G waves and Love waves, J. Geophys. Res., 64, 565-568, 1959. Ringwood, A. E., A model for the upper mantle, J. Geophys. Res., 67, 857-867, 1962a.

Ringwood, A. E., A model for the upper mantle, 2, J. Geophys. Res., 67, 4473-4477, 1962b. Rohatgi, P. K., and C. M. Adams, Jr., Ice-brine dendritic aggregate formed on freezing of aqueous solutions, J. Glaciol., 6, 47, 1967. Tabuchi, D., Dispersion and absorption of sound in liquids in general chemical equilibrium and its application to chemical kinetics, J. Chem. Phys., 26(5), 993-1001, 1956. Tabuchi, D., Dispersion and absorption of sound in ethyl formate and study of the rotational isomers,J. Chem. Phys., 28(6), 1014-1021, 1957. Tatsumoto, N., Ultrasonic absorption in propionic acid, J. Chem. Phys., 47(11), 4561-4570, 1966.

Valle, P. E., On the temperature gradient necessary for the formation of a low velocity layer, Ann. Geofis. Rome, 9, 371-377, 1956. Weeks, W. F., Studies of salt ice, 1, The tensile strength of NaC1 ice, U. $. Army Material Command Research Report 80, U.S. Army Cold Regions Research and Engineering Laboratory, New Hampshire, 1961. Yasunaga, T., N. Tatsumoto, and M. Miura, Ultrasonic absorption in sodium metaborate solution, J. Chem. Phys., 43(8), 2735-2738, 1965.

(Received April 8, 1968; revised June 7, 1968.)