JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 89, NO. C1, PAGES 637-640, JANUARY 20, 1984
Winter Mixed Layer Entrainment of Weddell Deep Water
A. L. GORDON
Lamont-DohertyGeolo•7ical
Observatoryof ColumbiaUniversity
C. T. A. ellEN
Ore,ton State University
W. G. METCALF
Lamont-DohertyGeolo•ticalObservatoryof ColumbiaUniversity
Observationsfrom the Somovduring the US-USSR Weddell Polynya expeditionshow that the mixed
layer below the sea ice just prior to the austral spring retreat in the 60øSGreenwich meridian region has
an oxygen content of 7.4 ml/1. This is 86% of full oxygen saturation, representingan oxygen deficit,
relative to full saturation, of 1.1 ml/l. The source of this deficit is believed to be a consequenceof
oxygen-poor(4.5 ml/1) Weddell Deep Water (WDW) entrainment by the winter mixed layer. Assuming
effectivecutoff of ocean-atmosphere
oxygenexchangeby the nearly completesnow and seaice cover with
no net impact of oxygen content as a result of biological factors, a mixing ratio of 1:3 for WDW to
"beginningof winter" surfacewater is requiredto explain the end-of-wintermixed-layeroxygencontent.
Accompanying
theWDW transferinto themixedlayeris heattransferof approximately
7 x 103 cal/cm'•
(2.9 x 108J/m2) duringthe fivewintermonthsof seaicecoverage
as wellas salttransfer,whichrequires
34 cm of fresh water to produce typical mixed-layer salinity. During the sevenice-free months when
entrainmentis expectedto be minor, diffusiveheat and salt flux continues.A mean annual heat flux of 12
W/m2 is suggested,
with an annual demandfor freshwaterof 46 cm/yr. Considerationof the winter
period salinity budget indicates net sea ice melting of 20 cm, which can be attributed to regional
convergenceof sea ice. The remaining freshwateris derived from excessprecipitation and possibly
icebergmelt. Oxygenundersaturation
of the winter surfacewater suggests
slightlylesspotentialfor
abyssalwaterventilationthanmightbeexpected
froma fullysaturatedcondition.
1.
warmer and occur over anomalouslywarm WDW cells
INTRODUCTION
The joint US-USSRWeddellPolynyaexpeditionaboard
the Sovietship Mikhail Sotnovof the Arctic-AntarcticResearchInstituteof Leningrad[GordonandSarukhanyan,
1982;
Gordon,1982] permitted,for the first time, detailedobservationsbelowthe SouthernOceanseaice for investigationof the
cumulative winter effects. The CTD (conductivity, temper-
[Gordonand Huber,this issue].The slightbut meaningful
temperature
excess
relativeto thefreezing
pointis believed
to
be a consequence
of introductionof WDW heat into the
mixed layer.
Summerstratificationdiffersprimarilyby the presenceof a
seasonally
warmedandslightlyfreshersurface
layeroverlying
the remnant of the winter mixed layer marked by a temper-
ature,depth)hydrographic
stations[Huberet al., 1983]were
taken in nearlyfull ice coverconditions[Ackleyand Smith, ature minimum [Toole, 1981; Gordonand Molinelli, 1982,
of vertical
sections
andplates196-199].Comparison
of
1983]in the vicinityof 60øS,just eastof the Greenwichmeri- plates
Sotnovstation21 [Huberet al., 1983] with the summerIslas
dian (seestationmap and hydrographic
sectionsin Gordon
Orcadasstation102 [Huber et al., 1981]--the stationsbeing
and Huber [this issue]).
separated
by 64 km (Sotnov
station21 wasobtainedon NoIn this study we presentevidenceof significantwinter
vember3, 1981,at 62ø20'Sand 3ø07'E;the Islas Orcadasstaperiodtransfer
of deepwaterto thesurface
watermixedlayer
tion 102 was obtainedFebruary 2, 1977, at 62ø02'Sand
and estimatethe associated
rate of upwardheat and saltflux.
4ø10'E)--shows
the summertemperature
minimumto be
2.
about 0.5øCwarmer,with little salinitychangerelativeto the
WINTER VERSUS SUMMER STRATIFICATION
wintermixed-layer
base.Abovethetemperature
minimum,the
seasonally
warmedsurfacewater represents
storageof 2.4
two-layerstructureof a homogeneous
cold, relativelyfresh, x 104cal/cm
2 (1.0x 109 J/m2)relativeto thefreezing
point.
The thermohaline stratification below the sea ice is a simple
mixed layer separatedfrom the nearly homogeneouswarmer,
more saline,Weddell Deep Water (WDW) with an abrupt but
weak pycnocline(Gordonand Huber [this issue]; Figure 1).
The mixed layer variesin thicknessfrom 50 to 135 m, averaging 108 m, with a meantemperatureand salinityof -1.844øC
and 34.287%0,
respectively,
whichis 0.035øCabovethe freezing
point at 1 atm. The thinner mixed layers are somewhat
Copyright 1984by the American GeophysicalUnion.
Paper number 3C 1478.
0148-0227/84/003 C- 1478505.00
637
The Islas Orcadassummerwater salinity is lower than the
Sotnov
station21 by 0.063%0,whichrequiresstorageof 20 cm
of freshwaterrelative to the winter mixed layer. Two other
Sotnov-IslasOrcadas station pairs, composedof stations
within 100 km of each other (9-101; 2-99), indicate the same
heatstorage
asthe21-192pair,but somewhat
different
freshwaterstorage(16 and37 cm,respectively).
Seasonal
freshwater
storage
in therangeof 16to 37cmseems
smallin viewof the
approximately
1 m of seaiceandsnowcovercharacteristic
of
theregionasobserved
fromSotnov
[Ackleyet al., 1982]prior
to the springmelt.A possible
solutionis that someof the
s13ring
seaicemelt,ratherthandilutingresident
surface
water,
638
GORDONET AL.' MIXED-LAYERENTRAINMENT
IN WEDDELLWATER
PotentialTemperature(øC)
-2.0
i
-I.0
0.0
1.0
i
i
i
30
,.
40
ß
50
;
2.0
i
Oxygen(ml/I)
20
ß
60
ß
7,0
•+
80
ß
90
.
+
ml/1 lower than our measuredvalue, while the temperature
and salinityare only 0.01øCand 0.07 %0higher,respectively.
The excellentagreementin oxygenconcentrationcollectedin
different seasonsagain suggestsa low rate of oxygenproduction and consumption.Additionally, Somovoxygen,pH,
calcium, alkalinity, total CO2, nitrate, phosphate,and silica
concentrationsand the GEOSECS station 89 oxygen,alka-
linity,total CO2,nutrients,
and •3C values(Chen[1982];also,
seedata listingsof Huber et al. [1983]) all correlatelinearly
g
o
with salinity from surface down to the WDW core, which
againindicatesthat the distributionof thesechemicalproper-
300
400
-+
-
-
tiesin the upperwater columnbelowthe ice is predominantly
controlled by conservativemixing processeswith little productionor utilization of chemicals[Weiss et al., 1979;Edmond
-
et al., 1979; Minas, 1980].
3. The assumptionregardingthe mixed layer prior to the
500•4.1
•4.•
I •4.5•4.7,
icecoverperiodis straightforward,
sinceoxygenequilibriumis
Salinity (%o)
Fig. 1. Potential temperature,salinity, and oxygen stratification
at Somov station 22 at 62ø12'S, lø05'E on November 5, 1981. The
thermohaline data are derived from the CTD system.The oxygen
data are from titration of water samples obtained from a rosette
system.There was a 100% ice cover with few leads [Ackley and Smith,
1982]. The hydrographicdata are reportedby Huber et al. [1983].
mixes with the saline WDW
that is diffused into the mixed
layer during the springmelting period (as discussedbelow).
3.
MIXED
LAVER OXYGEN
The oxygencontent of the entire mixed layer below the sea
ice averages7.40 (with a +0.1 ml/1 distribution about the
mean) or 86% of saturation (Figure 2). This is about 1.1 ml/1
below the full saturation value and is similar to the oxygen
levels of' the summer period temperature minimum (Gordon
and MolineIll [1982], seetemperature-oxygenrelation for the
vertical sections,plates 109 and 195). The WDW saturation
levelsare seasonallyinvariant near 57% to 60% of full oxygen
expectedduring the cooling period prior to the ice cover formation. Possibly some entrainment might occur before ice
formation,and the resultingwater doesnot equilibrate;however, this is reflected in the total entrainment determined
below.
4.
RATES OF DEEP TO SURFACEWATER HEAT FLUX
The potentialtemperatureversusoxygenrelationships
for
all Somovdata points(Figure 3a) can be usedto determinethe
ratio of WDW to the surfacewatercharacteristic
of theperiod
immediately
prior to winterice formation.A one-partWDW
(0.5øCand 4.50 ml/1)to three parts surfacewater (-1.87øC
and 8.54 ml/1) blend is required to produce the observed
OxygenSaturation(%)
50
6O
70
saturation.
The origin of the mixed-layer oxygen undersaturation is
likely due to entrainmentof oxygen-poorWDW by the winter
mixed layer. The oxygencontentcan be usedto determinethe
amount of entrained WDW if we assume'(1) oxygenexchange
between ocean and atmosphereis effectivelyblocked by the
presenceof a more or lesscomplete (greater than 90%) snow
and seaice cover,(2) the net biologicalproductionand utilization of oxygen below the sea ice is zero, and (3) the mixed
layer immediatelyprior to the ice cover is at the fleezingpoint
and at full oxygen saturation of 8.54 ml/1. Support for these
assumptionsis offeredbelow.
1. The sea ice collectedin the study region is dominated
by frazil ice structure [Ackley et al., 1983] with few brine
channels. Thus the gas permeability is expected to be low
[Weiss et al., 1979; Chen, 1982]. The depletion in oxygen is
probably not due to rapid oxidation of organic matter after
the pack ice is formed becausethe surfacewater oxygen consumption rate is not large enoughto generatea 14% oxygen
undersaturation within a period of months [Packard et al.,
1971' Skopintsev,1976; Knauer et al., 1979].
2. The bacterial and biological activities are also low at
the time of observation[Marta et al., 1982], suggestinga low
rate of oxygenproduction and consumption.The oxygenconcentration
in the remnant
winter water at GEOSECS
station
89 (60ø01'S, 0ø01'E, January 22, 1973; Bainbridge [1981]),
which is lessthan 35 km from Somovstation 33, is only 0.02
90
8O
I00
.,j.Mixed
Layer
ß
ßß
I00
%'
ß
Pycnocline ß
ß
'1'
ß
ß
200
3OO
'i
Deep Water
ß
ß
400
ßßß
õoo
Fig. 2. Oxygen saturationfrom all rosettesamplesobtainedby
Sotnov.
The saturationis determinedby usingthe equationgivenin
the UNESCOInternationalOceanographic
Tables[1973].
GORDONET AL.' MIXED-LAYERENTRAINMENT
IN WEDDELLWATER
IO
trainment must balancethe,annual Ekman-inducedupw•elling
of the pycnocline.The abovecalculationsuggests
an effective
WDW entrainmentof 27 m into the mixed layer during the
winter-ice-coveredperiod. This agrees quite well with the
I 1i i i i i i
_
639
ß
AI•,
1Warm
WDW
Cells
annual averageupwellingrate of 1 x 10-'• cm/s (31 m/yr)
Cold
WDW
determinedfrom Ekman pumpingcalculationsby usinga climaticallyaveragedwind field for the regionof the Sotnovdata
[Gordon et al., 1977].
The annual average heat flux from WDW to the mixed
layer of 9-16 W/me is somewhatbelowthe annualocean-toatmosphereheat flux calculatedfrom meteorologicalparame-2..0
.'3470
-
/
\
ters.Zillman[1972] calculates
a heatlossof 18 W/m2 at 60øS
C'water
south of Australia (Zillman's Figure 3); while Gordon[1981]
_
finds 31 W/m2 averagefor the 60ø-70øScircumpolarbelt.
WDW
•,
ß
34.60
_
However, it is noted that the Sotnovresults pertain to the
59ø-62øSregion and would be expectedto be lower than the
60ø-70øSaverage but somewhat above the Zillman value becausethe Weddell pycnoclineis weaker than the circumpolar
AABW
ß
ß
average
[MartinsOn
etal.,1981].
In viewoftheuncertainty
in
_
..• 34.5o
•.,
the diffusive heat flux determined during the ice-free period
and the differencein the type of calculation, agreementis
reasonablygood.
_
_
'E
._
5.
or) 34.40-
_
ß
34.30-
_
.•,. Surface _
Water
ßß ß•
ß
'
'
'
'
9.0
Dissolved Oxygen (ml/I)
Fig. 3. Potential temperatureversusoxygencontent(a) and salinity versusoxygen content (b) from all rosette samplesobtained by
Sotnov.WDW is Weddell Deep Water and AABW is Antarctic
Bottom Water. The two linear mixing lines AB and A'B are marked
with percentof A water type (WDW) relative to B water type. Point
D is the freezing temperature extension of the line fit to the
temperature-oxygentrend of deepand bottom water colder than 0øC.
mixed-layeroxygenof 7.4 ml/1(line AB on Figure 3a). However, the temperatureof this mixture would be 0.63øC above
the freezingpoint. For the averagemixed-layerthicknessof
108 m the heat accompanyingthe upward transferof WDW is
RATE OF DEEP TO SURFACE WATER SALT FLUX
The salt introduction to the surfacewater mixed layer by
the effectiveentrainment of 27 m of WDW during the five
winter ice cover months requiresfreshwaterinput of 34 cm to
reducethe WDW salinity (34.680%0)to the annual mean surface water salinity (34.250%0,representinga 7:5 blend of the
34.224%0average summer salinity from lslas Orcadas data
with 34.287%0winter salinity from the Sotnovdata). During
the ice-freeperiod, salt diffusionacrossthe pycnoclinewould
place additional requirements for compensatingfreshwater
input.UsingK: of 0.1 and 1.0cm2/sintroduces
0.078to 0.78
gm of salt per centimetersquared,respectively,into the surface
water over 7 months, requiring a freshwaterinput of 2.3 to 23
cm to producethe annualmean surfacewater salinity.
Thus the annual freshwater input required to balance the
total WDW salt flux into the surfacelayer is 36 to 57 cm/yr. A
value of 46 cm/yr would correspondto the 12 W/m2 best
guess
(K: of 0.5cm2/s).
Estimates
of annual
freshwater
flux into the 60ø-70øS
belt
by excess precipitation over evaporation and continental
6.66x 103 cal/cm• (2.78x 108J/me).If the warmWDW cells runoff (glacial ice meltwater) are as high as 40 cm/yr [Gordon,
[Gordon and Huber, this issue] are responsiblefor the re- 1981]. However, the mean snow cover on the sea ice was only
gionally depressedmixed-layeroxygen,the heat transfer is 20 cm [Ackley et al., 1982], which translatesto only 2-6 cm of
slightlyincreased
(seeline A'B on Figure3a) to 7.93x 103 water, thus a value of 40 cm/yr may be an overestimate.Adcal/cm:(3.31x 108J/me).Thusthe averageheatflux during ditional freshwater input could be derived if there is a net
the 5-monthice-coveredperiod [Gordonand Huber, this issue] advectionof seaice into the region.
Support for this suggestionis derived by consideringthe
is 20 to 25 W/m :. If the verticalheat transferacrossthe pycnocline is taken as zero for the 7-month ice-free period, the approximate salinity balance for the five ice-coveredmonths.
A 1:3 mix of WDW to the surfacewater just prior to the ice
average
annualheatfluxis 9 to 11W/me.
While entrainment of WDW
would cease with the onset of
cover would result in an end-of-wintersalinity of 34.338%0.To
the seasonalpycnocline,some diffusive heat flux is expected reduce the salinity to the observedaverage of 34.287%0reduring the ice-freepart of the year. A vertical mixing coef- quires 20 cm of sea ice (with a salinity of 5%0,Ackley et al.,
ficientK: of 0.1 cm:/s wouldaccomplish
a cross-pycnocline[1982]). A meteoric source of water is unlikely during the
heatfluxduringthe 7-monthice-freeperiodof 1 W/me; a K: winter since the snow on the ice is
of unity yields10 W/m:. Therefore,the total deepto surface into the oceanuntil the springmelt.
water heat flux (ice cover plus ice free periods)may be in the
rangeof 9-16 W/me. A valueof 12 W/me is suggested
for a
workingvalue,reflecting
a K: of 0.5cm:/s.
How realistic is the winter period entrainment value and
heat flux? For an annual steadystate the rate of winter en-
not available
for release
Melting would be encouragedby the heat flux discussed
above; the mixed-layer temperature slightly above freezing
may be a direct evidenceof this process.Sea ice melting of 20
cm requiresabout 20% of the winter heat flux, the rest would
be lost to the atmospherein leads and thin ice. It is probable
640
GORDON
ETAL.:MIXED-LAYER
ENTRAINMENT
IN WEDDELL
WATER
that much of the ice melting occursin October, when the
ocean heat flux into the atmosphereis reduced from the
winter maximum•[Gordon,1981], but the entrainmentof
Ackley,S. F., D. B. Clarke, and S. J. Smith,Reportsof the Weddell
PolynyaExpeditionof October-November
1981: vol. 4, Physical,
Chemical
andBiologicalProperties
of Ice Cores,U.S. Army Corps
WDW (whichis dueprimarilyto icemovement
relativeto the
Bainbridge,
A. E., GEOSECSAtlanticExpedition,
v. 1, Hydrographic
ocean; Gordon and Huber [this issue]) continues. The
dynamic-thermodyanmic
model
ofHiblerandAckley
[1983,
Eng. Cold Reg. Res.Eng. Lab., Hanover, N.H., 1983.
Data 1972-1973, 121 pp., National ScienceFoundation, Washington, D.C., 1981.
Chen,•C.T. A., On the distributionof anthropogenic
CO2 in the
AtlanticandSouthern
oceans,
Deep-Sea
Res.,29,563,1982.
Edmond,J. M., S.S.Jacobs,
A. L. Gordon,A• W. Mantyla,andR. F.
melting in the north. The above calculations favor the net
Weiss,Water columnanomaliesin dissolvedsilica over opaline
meltingvalue.Net meltinghastheeffectof transporting
freshpelagicsedimentsand the origin of the deep silicamaximum,0r.
Geophys.Res.,84, 7809-7826, 1979.
water into the area, even in the presenceof Ekman diverGordon,A. L., Seasonality
of SouthernOceanseaice, d. Geophys.
gences.
Figure 8] suggests
a net ice advectionwithin the Sornovregion
of +10
cm of accumulation
in the south to 25 cm of net
Res., 86, 4193-4197, 1981.
Assumingthere is no heat conductionthrough the sea ice
and that leads make up 5% of the area, the averagewinter
Gordon,A. L., The US-USSR WeddellPolynyaExpedition,Antarct.
heatlossin theleadsamountsto about350W/m2.Thisvalue
Gordon, A. L., and B. A. Huber, Thermohaline stratification below
is similar to estimatesfor' Arctic Ocean heat loss within leads
[Maykut, 1978]. It is noted that leads, though effectivein
removingheat,and perhapsfreshwater,by evaporation,would
not be effectivein enhancingoxygen exchangeor freshwater
input by precipitation.
5.
DISCUSSION
The potential temperature-oxygen
scatter(Figure 3a) shows
that for all conservative
linear
mixtures
of WDW
end mem-
bers with a freezingpoint, surfacewater end membersrequire
the surfacewater to have oxygen saturation as low or lower
than that observed from SOreGr. Conservative
behavior
for
oxygen in the Southern Ocean is suggestedby Weiss et al.
[1979-] and Edmondet al. [1979-], so it is not likely this relationshipis due to in situ oxygenconsumption.Deep water
colder than 0øC possesses
a slightly steeperslope,indicating
that the Antarctic bottom water (AABW) requiresa freezing
point surface water component with oxygen of 6.8 ml/1 or
80% saturatio•n(point D, Figure 3a), suggesting
that a 35%
contributionfrom WDW might be more appropriatefor regionsfurther polewardof the Somovregion.
The salinity-oxygen(S/O2) distribution(Figure 3b) shows
that the mixed-layerpointshavea negativeslopesuchthat the
mixed-layer water with higher salinity has slightly lower
oxygen.This relationis expectedfrom the WDW origin of the
reducedmixed-layeroxygen.
Calculations of the oxygen consumption rate have frequently been made with the use of the measuredapparent
oxygenutilizhtion (AOU) value and the estimatedage of the
water [Jenkins,1980]. A hidden assumptionin the calculation
d. U.S., 17, 1982.
•
the SouthernOceanseaice,J. Geophys.
Res.,thisissue.
Gordon, A. L., and E. M. Molinelli, SouthernOceanAtlas: Thermoha-
line ChemicalDistributions
and the Atlas Data Set, 11 pp., 233
plates,Columbia University Press,New York, 1982.
Gordon, A. L., and E. I. Sarukhanyan,American and Soviet Expedition into the Southern Ocean sea ice in October and November 1981, EOS Trans. AGU, 63, 2, 1982.
Gordon, A. L., H. W. Taylor, and D. T. Georgi, Antarcticoceano-
graphiczonation,in Polar Oceans,
editedby E. Dunbar,pp. 45-76,
Arctic Institute of North America, 1977.
Hibler, III, W. D., and S. F. Ackley, Numerical simulationof the
Weddellseapack ice,J. Geophys.
Res.,88, 2873-2887, 1983.
Huber, B., S. Rennie,D. Georgi,S. Jacobs,and A. Gordon, ARA Islas
OrcadasData Reports, Cruise 12, Ref CU-2-81-TR2, LamontDoherty Geol. Observ.,Palisades,N.Y., 1981.
Huber, B. A., J. Jennings,C.-T, Chen, J. Marra, S. Rennie,P. Mele,
and A. Gordon, Reportsof the US-USSR Weddell Polynya Expedition, vol. 2, HydrographicdaIa, 115 pp., L-DGO-83-1, U.S.
Army
Corps
Eng.ColdReg.
Res.
L•D.,Hanover,
N.H.,1983.
Jenkins,W. J.,Tritiumand 3Hein the Sargasso
Sea,J. Mar. Res.,38,
533-569, 1980.
Knauer, G. A., J. H. Martin, and K. W. Bruland,Fluxesof particulate
carbon,nitrogen,and phosphorusin the upperwater columnof the
northeast
Pacific,Deep-Sea
Res.,26A,97-108,1979.
Marra, J., L. H. Burckle, and H. W. Ducklow, Sea ice and water
column plankton distributions in the Weddell Sea in late winter,
Antarct. J. U.S., 17(5), 111-112, 1982.
Martinson,
D. G.,P.D. Killworth,
and•. L. Gordon,
A convective
model for the Weddell Polynya,J. Phys. Oceano•7r.,
11, 466-488,
1981.
Maykut, G. A., Energy exchangeover young sea ice in the Central
Arctic,J. Geophys.Res.,83, 3646-3658, 1978.
Minas, H. J., Production Primaire et Secondaire,Colloque FrancoSovietique,Publ. 10, pp. 21-36, CNEXO (Actes du Colloque),
Paris, 1980.
Packard, T. T., M. L. Healy, and F. A. Richards,Vertical distribution
of the activity of the respiratoryelectron transport systemin
is that the AOU is near zero when the water was last at the
marine plankton, Limnol.Oceano•7r.,
16, 60-70, 1971.
surface.Obviously, this assumptionneedsto be modified for Skopintsev,B. A., Oxygen consumptionin the deep watersof the
ocean,Oceanology,
15, 556-561, 1976.
AABW or any water that has a componentof the winter
Toole, J. M., Sea ice, winter convection,and the temperatureminiAntarcticsurfacewater. Similarly,cautionmust be exercised mum layer in the SouthernOcean,J. Geophys.Res.,86, 8037-8047,
when one calculatesthe age of water or the oceaniccirculation
1981.
Tables,vol. 2, 141 pp., Paris,
ratesby usingAOU and the independently
estimatedoxygen UNESCO, InternationalOceanographic
1973.
consumption rate.
Weiss,R. F., H. G. Ostlund,and H. Craig, Geochemicalstudiesof the
Weddell Sea,Deep-SeaRes.,26, 1093-1120, 1979.
Acknowled#ments.
Fu6dingfor the US-USSRWeddellPolynya
Expeditionwas receivedfrom the Divisionof Polar Programsof the Zillman, J. W., Solar radiation and sea-air interaction south of Australia, in Ahtarctic Oceanology1, The Australian-NewZealand
National ScienceFoundation, grant DPP 80-05765for the physical
Sector,
vol. 19,editedby D. E. Hayes,pp. 11-40,AGU, Washoceanography,
and from the Departmentof Energyfor the geochemington,D.C., 1972.
istrysupportof Chen81 EV 10611.Commentsfrom HsienWang Ou,
Bruce Huber, and John Marra are appreciated.Lamont-Doherty
C. T. A. Chen,Oregon StateUniversity,Corvallis,OR 97331.
GeologicalObservatorycontribution3549.
A. L. Gordon and W. G. Metcalf, Lamont-DohertyGeological
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Lab., Hanover, N.H.,
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(ReceivedApril 28, 1983;
revisedAugust 25, 1983;
acceptedSeptember8, 1983.)