GEOPHYSICAL
RESEARCH
LETTERS,VOL. 11, NO. 4, PAGES287-290, APRIL 1984
MAPPING
CONVECTION
IN THE
MANTLE
Toshiro Tanimoto and Don L. Anderson
Seismological
Laboratory,CaliforniaInstituteof Technology,
Pasadena,CA 91125
Abstract. Long-period(100-250sec.)Love and Rayleigh
wavesare usedto map heterogeneityand azimuthal anisotropy in theuppermantle.Sphericalharmonicdescriptions
of
anisotropyup to f = m = 3 and 20 are derived. Azimuthal
anisotropyobtainsvaluesas high as 1« ø7o.There is good
correlationof fast Rayleighwavedirectionswith upper mantle return flow directions derived from kinematic considera-
tions. This is consistent with the a-axis of olivine being
Heterogeneity
Figure1 showsmapsof Rayleighwavephasevelocities
with fmax = 6 for a periodof 200 sec.Thesewavesare most
sensitiveto SV-velocitiesbetween about 150 and 400 km. Re-
gionsof fasterthanaveragevelocityoccurin thewesternPacific, the westernpart of the African plate, AustraliasouthernIndianOcean,part of thesouthAtlantic,northeast-
alignedin the flow direction.The main differencesbetween
the flow modelsand the Rayleighwave azimuthal variation
ern North America m western north Atlantic, and northern
mapsoccurin the vicinityof hotspots.Hawaii, for example,
appearsto perturbthe return flow. Thereis strongcorrela-
relationsfound by Nakanishiand Anderson[1984]. Dense
Europe.Theseareall relativegeoidlowsconfirmingthecor-
regionsof the mantlethat are in isostatic
equilibriumalso
tion of the geoid and surfacewave velocityat f =4 and 5.
generategeoid lows [Haxby and Turcotte, 1978; Hager,
Slowregionsat thisscaleare associated
with geoidhighsand
1983].Denseregions
in dynamicequilibrium
generate
geoid
high heat flow, consistent
with upwellingconvectiveflow or
lowsif theviscosity
doesnot increase
too rapidlywith depth
with isostaticallycompensated
regionsof low density.The
[Hager,1984].Highdensity
andhighvelocityarebothconsiscorrelationof azimuthalanisotropywith upper mantlereturn
tent with cold mantle. Geoid highsoccur near Tonga-Fiji,
flow directions,rather than with plate directions, suggests Andes,Borneo,Red Sea,Alaska,northernAtlantic, and
southernIndian Ocean.Theseare generallyslowregionsof
that part of thereturnflow isin theuppermantleandthis,in
the mantleand are thereforepresumablyhot. Uprisingpluturn, impliesa low viscositychannel.
meswould be consistentwith theseobservations.The upward
deformation of boundaries counteractsthe low density asso-
Introduction
ciatedwiththebtioyant
material
and,for uniformviscosity,
Understandingconvectionin the mantle is one of the
mostimportantgoalsof geophysics.
To date,the geoid,heat
flow, and elevationhavebeenthe main constraintson theoretical models of convection. However, we still have a poor
understanding
of thescaleof mantleconvection
andthe driving mechanism
of platetectonics.Three-dimensional
global
mapsof seismicvelocityanomaliesare startingto become
available [Nakanishiand Anderson, 1984; Masterset al.,
1982]and promiseto help constrainthe natureof the flow.
Seismictechniquescanbe usedto map anisotropyas well as
heterogeneity
and, in principle,can determinecrystalorientation. Global mapsof transverseisotropyhave previously
beenusedto map regionsof upwellingand downwellingin
the mantle[Nataf el al., 1984].Wereportherethe resultsof a
firstattemptto obtainandinterpretglobalmapsof azimuthal
anisotropyfrom long-periodsurfacewaves.The methodwe
useis described
by TanimotoandAnderson,[1983].The data
setis phasevelocityoverabout560pathsfor Rayleighwaves
and 380 pathsfor Lovewavesin the periodrange100to 250
seconds.Thesewavesgivea goodsamplingof velocitiesin the
outer 400 km of the mantle. The data are simultaneouslyinverted for heterogeneityand azimuthalanisotropy.For heterogeneitywe use a sphericalharmonicrepresentation
includingtermsup to f = m = 6. For anisotropywe solvefor 20
terms and displayresultsfor f = m = 1 to 3.
Copyright1984by the AmericanGeophysical
Union.
Paper number 4L0373.
0094-8276/84/004L-0373503.00
287
the net resultis a geoidhigh(Hager, 1983).An isostatically
compensated
columnof lowdensitymaterialalsogenerates
a
geoidhighbecause
of the elevationof the surface.Correlation coefficientsbetweenphasevelocityand the geoid are
shownin Fig. 2. Lovewavesfor periodsbetween100and200
s generallyhavea strongnegativecorrelation(geoidhighs
correlatewith slowvelocity)for f = 4, 5, 6. Rayleighwaves
generally
correlate
wellwiththegeoidfor f = 6 and,at some
periodswith f = 5 (Fig. 1 and Nakanishiand Anderson,
1984).
Hager [1984]found an excellentcorrelationbetweenthe
observedgeoidand the 'slabgeoid' for f =4, 5 and 7-9 and
weak correlationat f = 6. The slabgeoiddoesnot explainthe
geoidlowsin Siberia,Canadianshieldm westernAtlantic,
and the SouthAtlantic or the geoidhighsin the southIndian
Ocean,the Red Sea, and the North Atlantic. Theseare high-
velocityandlow-velocityregions,respectively.
The slab-geoid
correlation can be understoodin terms of a large amount of
dynamicallysupporteddensematerial either in the upper
mantleor in both the upperand lower mantlesin the vicinity
of active subductionzones[Hager, 1984]. The surfacewave
-- geoidcorrelation,whichapparentlyexplainsthe missing
f = 6 componentof the slabgeoid,however,mustbe due, at
leastin part, to an anomalousmassdistributionin the shallow mantle. Theseresultssuggestthat featuresof the geoid
havingwavelengths
of about4,000to 10,000km are generated in the uppermantle.Geoidanomaliesof thiswavelength
generallyhave an amplitudeof about 20 to 30 meters.An
isostaticallycompensateddensityanomaly of 0.5% spread
over the upper mantle would give geoid anomaliesof this
288
Tanimoto and Anderson: Mapping Convection
LOVE
ISO
+1
-!
-!
LOVE •-00
Fig. 1 Phasevelocitiesfor 200 sec.Rayleighwaves.Spherical harmonicsup to t'- m-6 are included.
size. It therefore appearsthat a combination of slabsand
broad thermal anomaliesin the upper mantle can explain the
major featuresof the t'-4-9 geoid. The longer wavelength
part of the geoid, t'-2-3, correlateswith velocitiesin the
deeper part of the mantle, i.e. lower mantle [Dziewonski et
al., 1977; Hager, personalcommunication]and transition region [Masters et al., 1982; Woodhouse and Dziewonski,
1983]. Fig. 3 showsthe actual distribution of Love wave
phasevelocitiesand that computedfrom the geoid assuming
a linear relationshipbetweenvelocityand geoidheight. Most
subductionregionsare slow at short periods,presumablybecause of backarc basins and hot, upwelling material above
the slab.
Azimuthal Anisotropy
SEC
+1
-!
SEC
o
RAYLEIGH
1SO SEC
RAYLEIGH
•-00
SEC
-!
CORRELAT I ON WI TH GEMLP-
Fig. 2 Correlation coefficients(ordinate) betweensurface
wave phase velocitiesand the geoid. The horizontal axis
givesthe order number of the sphericalharmonic. Error
bars represent1 a rangein Fisher'sasymptotictheory (Anderson, 1958).
for Rayleigh wavesand low Love wave velocities.In regions
of descendingflow, Rayleighwavesare fast becauseof low
temperaturesand the effectsof crystalorientation. For both
horizontal and vertical flow the nature of the anisotropy is
approximately20 for Rayleighwaves,and the fast directionis
in the flow plane. For Love wavesthere is a strong cos 40
component, and the fast directionsare oriented 45 ø to the
fast directions for Rayleigh waves. Therefore, if olivine
orientation controlsthe anisotropyof the upper mantle, the
fast direction of Rayleigh wavesshouldmap the flow direction.
Anisotropy of the upper mantle most likely originates
Figure 4 is a map of the azimuthal resultsfor 200 s Rayfrom preferredorientationof olivinecrystals.Studiesto date
leigh wavesexpandedup to t' = m = 3. The linesare oriented
indicate that the a-axes of olivine-rich aggregatescluster
' in the maximum velocitydirection,and the lengthof the lines
around the flow direction, the a- and c-axesconcentrate in
the flow plane, and the b-axesalignperpendicularto the flow
PHASE VELOCITY
LOVE •00 SEC
L = 4-6
plane [e.g., Nicolasand Poirier, 1976;Christensenand Salisbury, 1978;] For P-wavesthe a-, b-, and c-axesare, respectively, the fast, slow, and intermediatevelocitydirections.If
the flow plane is horizontal, the azimuthal P-wave velocity
variation is 4070for natural olivine-rich aggregates[Christensenand Lundquist, 1982]. The correspondingazimuthal SV
variation is 2ø-/o.This latter value is close to that found in the
presentstudy.Rayleighwavesare mostsensitiveto SV velocities and have lesssensitivityto P-waves.The high anisotropy
of P-waves,however,meansthat the azimuthal anisotropyof
Rayleighwaveswill be affectedby the anisotropiesof both P
and S waves. The azimuthal
variation
of both P and SV
PREDICTED
PHASE
VELOCITY
wavescan be describedwell by a cos20 variation, where 0 is
measuredfrom the a-axis (fast) direction. The variation of
SH velocity in the flow plane is four-lobed. The fast directions are at 45 ø to the a-and c-axes;i.e., the fast direction for
Love wavesis not parallel to the fast directionfor Rayleigh
waves. The SH anisotropycan be expectedto be hard to detect, sincethe variation is small and occursin only 45ø.
For vertical flow, i.e. vertical a-axis, the SV and P aniso-
tropiesin the horizontalplaneare low for olivine-richaggregates, the averagehorizontal P-wave velocityis low, and
SH < SV. The fast direction for P is in the flow plane, and SV
is nearly isotropic.SH hastwo lobesin the horizontalplane,
oriented45o to the flow plane. Regionsof ascendingand descendingflow will be characterized
by low azimuthalvariation
Fig. 3 Love wave phasevelocities(t'= 4-6) at 200 sec. and
phasevelocitiespredictedfrom a least squareslinear fit
betweenphasevelocityand geoid height.
Tanimoto and Anderson: Mapping Convection
P89
isproportionalto the anisotropy.Maximum velocitiesareorientedapproximately
NE-SW underAustralia,theeasternIndian Ocean, and northern South America and E-W under the
central Indian Ocean; they vary under the Pacific Ocean
from N-S in the southerncentralregionto more NW-SE in
the northwestportion. The fast directionis generallyperpendicular to plate boundaries.There is little correlationwith
plate motion directions, and little is expected since these
waves are samplingthe mantle beneath the lithosphere.Pn
velocity correlateswell with spreadingdirection(Bibee and
Shor, 1976). The lack of correlationfor long-periodRayleigh
strongly
coupled
totheoverlying
plate,andthisinturnir•-
Fig. 5 Flow linesat 260 km depthfor the upper mantle
kinematicflow modelof HagerandO'Connell(1979).The
modelincludesa low viscositychannel(10'9poise)in the
plies a low-viscosityasthenosphere,
Hager and O'Connell
[1979] have calculatedflow in the upper mantle taking into
accountthe drag of the platesand the return flow from subductionzonesto spreadingcenters.Flow lines for a model
that includesa low-viscositychannelmantleare shownin Fig-
Andersonand Regan[1983]foundthat SH > SV in the upper
mantle under the Pacific except near the East Pacific Rise,
where ascendingflow is likely. These results are consistent
wavessuggests
that the flow in the asthenosphere
is not
upper mantle.
ure 5. The low viscosityunder the lithosphereminimizes withthefastdirection
beingcontrolled
bytheflowdirection.
drag, and the return flow is controlledmainly by the scomeThe goodagreement
betweenFigures4 and 5 suggests
tha•
try of plate boundaries. Flow under the large fast-moving
plates is roughly antiparallel to the plate motions. Thermal
buoyancyis ignoredin thesecalculationsand thereis no lateral variation in viscosity.Hager and O'Connell also calculate
shallowmantle flow for a modelwith a relativelyhigh upper
mantle viscosity.In this modelthereis somecouplingbetween
theplateandthe underlyingmantle;consequently,
materialis
draggedalong with the plate. There are major differencesin
the orientation of flow lines in thesetwo models. The Rayleigh wave fast directionsare similar to the flow directionsin
the low viscositymodel but divergefrom those of the high
viscositymodel, particularly under Africa, Australia, India,
Greenland, the south Atlantic, and the Tasman Sea. In the
kinematicflow model, with a low viscosityasthenosphere,
the flow is nearly due south under Australia, shifting to SW
Under the eastern Indian Ocean; i.e., the return flow is
directly from the subductionzonesto the ridge. In the anisotropic map the inferred flow is SW under Australia, parallel
to the platemotion,and, E-W in the easternIndian ocean.
There are severalpossiblecausesfor anisotropyin a convectingmantle. Anisotropic crystalsare alignedby flow and
by stress.In olivine-rich aggregatesthe crystalsare aligned
suchthat thefastdirectionisin the flow direction[e.g.Christensenand Salisbury,1979]. At shallowdepthsthe Pn velocity is 'fastin the spreadingdirection[Bibeeand Shor, 1976].
the fast seismicdirection does indeed correlate with flow direction. Models With more uniform viscosity [Hager and
O'Conneil,1979;Chase,1979]donotcorrelate
aswell,suggestingthat low viscosityis a characteristicof the shallow
mantle.
-'
The directionof flow in the shallowmantle is fairly independentof the the viscositymodel in someregions.For example, the Hager-O'Connell and Chase modelsgive the following orientations:Siberia (NW-SE), North America (NW-SE
in the north changingto N-S in the south), Europe (E-W),
Nazca plate (E-W), SouthernSouth America (NW-SE), and
N.E. Pacific(NW-SE).Theseare approximately
the directions indicatedby the seismicanisotropyin theseregions.In
addition, the low-viscositymodel (Model VII of Hager and
O'Connell)givesdirections
in generalagreement
with the
seismic results for much of the Pacific and south Atlantic.
Somemajor differencesare apparentwhich we interpretwith
the assumptionthat the fast seismicdirectionsmap the flow
linesin the mantle.The return flow acrossthe Pacificappears
to be affected by the presenceof a thermal anomaly near
Hawaii. The flow in the north is toward North America,
while flow in the south appearsto be diverted to the south
Pacific. Flow under the southern part of South America is
directed toward the south Atlantic, while flow under the
northern part of SouthAmerica is directedtoward the north
Atlantic. The divergenceof flow occursnear the Rio Grande
Rise. The Indian OceanRidgeappearsto be fed by material
subducted under New Guinea and the Sunda Arc.
The direction of flow under Tibet is more N-S than E-W.
The flow of the material subducted from the Aleutians
Kamchatka
and
is to the NW rather than directed toward North
America. The flow betweenKerguelenand the Afar is more
E-W than N-S. The flow in the vicinity of other hotspots,
suchas Iceland, Tristan, Azores, Tahiti, and Reunion is different from that predictedby the flow calculations.Thermal
buoyancy, including upwelling under hotspots, will affect
.._ 2 per cent
Fig. 4 Azimuthal anisotropyof 200 sec.Rayleighwaves.
Themapincludes
cos20, sin20 andf = 1, 2 and3 terms.
The lines indicate the fast phase velocity direction. The
lengthof the linesis proportionalto the anisotropy.
flow in the mantleand is unaccounted
for in the return flow
calculations.The extensivelow-velocity anomaliesnear Kerguelen, Red Sea-Afar, Tasman Sea-Tonga, western North
America, and the central Pacific may representupwellings
that will alter the return flow patternscalculatedfrom simple
290
Tanimoto and Anderson: Mapping Convection
kinematic considerations.Likewise, the high velocitiesunder
western Africa and the south Atlantic may representdense
sinkers, also unaccounted for in the kinematic models. Becauseof the temperaturedependenceof viscosity,the flow in
theseregionsmay violate the predictionsof the models that
assumeradially symmetricviscosity.
Azimuthal anisotropy of Rayleigh waves appearsto be
causedby flow in the upper mantle with the fast direction
beingparallel to the flow lines.The observedazimuthalvariation of velocityis consistentwith that expectedfor olivinerich aggregates.There is good agreementbetweenthe seismic
resultsand the kinematicupper mantle flow model of Hager
and O'Connell [1979] that includesa low viscositychannel.
Hotspotsappear to affect the flow. Azimuthal anisotropyis
low under the North American plate, Europe and the eastern
Antarctic plate. There is a goodcorrelationof global surface
wave velocitieswith the f = 4-6 geoid. High velocityareascorrelate with geoid lows. Isostaticallycompensatedcolumns
with a density contrast of about 0.5% spread over about
300 km can explain the velocity-geoidcorrelation.
Acknowledgments. We thank Ichiro Nakaniski who
kindly providesus with data. Digital data from the SRO and
IDA networksmade this studypossible.We thank Brad Hager for many stimulating discussionsand for reviewing the
manuscript. This researchwas supportedby NSF grant No.
EAR811-5236 and NASA grant No. NSG-7610. Contribution number 4007, Division of Geological and Planetary
Sciences,California Institute of Technology,Pasadena,California
91125.
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(Received
revised
January
March
5,
accepted March 6,
6,
1984;
1984;
1984.)