GEOPHYSICAL RESEARCH LETTERS, VOL. 21, NO. 18, PAGES 1943-1946, SEPTEMBER 1, 1994
The possiblereflection of mantle discontinuitiesin Pacific Geoid
and bathymetry
P•i Wessel,David Bercovici,and Loren W. Kroenke
Schoolof OceanandEarthScienceandTechnology,
Universityof Hawaiiat Manca,Honolulu
Abstract. Geoid anomaliesover the Pacificplate showlineated
undulationsapproximatelyorientedin the directionof absolute
plate motion. Conventionalspectralanalyseshave revealeda
broadrangeof dominantwavelengths,
but as filteringis direction-dependent,
resultsaredifficultto interpret.Here,we present
a new approachdesignedto quantifythe correlationbetweenthe
geoid undulationsand Pacific plate motion. We calculatethe
spatial correlation between geoid lineations and arbitrarily
oriented,axisymmetricsinusoidalundulationsof given wavelength. The pole (i.e., the orientation)of the sinuscidwhich
undulations
have linear volcanic seamcunt chains at their crests.
Systematicfilteringhasrevealedgeoidanomalieswhicharepreferentially elongatedin the east-westdirection and have average
amplitudesof ~0.3 m and dominantwavelengthsof 750 km and
1100 km [Cazenaveet al., 1992]. While the longer wavelength
geoidundulationsmake a manfiedynamicorigin moreprobable,
a lithosphericmechanismcan not be precludedsinceinterpretation of geopotentialdatais nonunique(i.e., manydifferentmechanismsmay give rise to identicalgeopotentialanomalies).
While previousstudies[BaudryandKroenke,1991;Cazenave
maximizes the correlation is determined. The distance between
et al., 1992;Maia andDiament,1991]haveclearlydemonstrated
thispoleandthePacifichotspotpoleis calculatedandrepresents that the lineatedgeoid undulationsare not artifactsof filtering,
a measureof how well a geoidlineationof a given wavelength theydisagreeaboutthe dominantwavelengthsof the undulations,
alignswith Pacificplate motion. This distancevarieswith undu- with estimatesranging from 400 to 1100 km. Some of this
lation wavelength and has discrete minima for several wave- scattermay be relatedto directionalbiasintroducedby examinbands.These minima, moreover,occur at wavelengthswhose ing power spectraof sea-surfaceheightsalong satelliteground
valuesare remarkablycloseto the depthsof seismicallyinferred tracks[Cazenaveet al., 1992;Maia andDiament,1991]or along
mantle discontinuities. A similar analysis of available north-southprofilessampledfrom griddeddatasets[Baudryand
bathymetrycorroborates
thesefindings. If thesecorrelationsare Kroenke,1991]. Taken together,it appearsevidentthatwhile the
significant,
theysuggest
thatgeoid(andbathymetry)
undulations geoidover the Pacificplate exhibitssignificantpowerat many
are influencedby mantle structureand thusare likely to reflect wavelengths,the inferreddominantwavelengthis dependenton
the directionalongwhich oneanalyzesthe data.
mantledynamics.
Previousstudiesof Pacificgravity and geoidundulationshave
noted their apparentalignmentwith the absolutemotionof the
Introduction
Pacific. This alignmentis deemedimportantas it is generally
The availability of altimeterdatafrom the Seasatand Geosat
interpreted
as a resultof uppermanfieconvection.It haslong
been known that three-dimensionalconvectionpatternswill be
missionshas providedunprecedented
coverageof the Earth's alignedinto cylindricalrolls by the shearingof an overriding
gravity field over oceanicregions[Haxby, 1987;Sandwelland plate[RichterandParsons,1975;SparksandParmentier,1993],
McAdoo,1990],andfacilitatedrapidadvances
in ourunderstand- althoughthis alignmentonly occursabove somecritical plate
ing of lithosphericand sublithosphericprocesses.One of the
major findingsduring the last decadewas the discoveryof a
lineatedpatternof gravityanomaliesoverthe youngerportionsof
the fast-movingPacific and Indo-Australianplates [Haxby and
Weissel,1986]. The wavelengthsof the gravity undulations
(150-300 km) areshortenoughto accommodate
severalpossible
explanations,mostnotably small-scalemantleconvection[Buck
and Parrnentier,1986; Haxby and Weissel, 1986], tensional
cracksand magmaticintrusions[McAdooand Sandwell, 1989;
Winrefer and Sandwell, 1987], and regional variationsin the
lithospheric
coolingprocess
[Cazenave
et al., 1992];theirorigin
thusremainscontroversial.More recently,intermediate-wavelength(400-600 kin) geoid undulationshave alsobeendetected
after along-trackfiltering of the Seasataltimeterdata [Baudry
and Kroenke, 1991; Maia and Diament, 1991]. These linearions
appearto be roughlyparallelto the absolutemotionof thePacific
plate (Fig. 1) and are continuous acrossfracture zones; some
Copyright1994by the AmericanGeophysical
Union.
velocity [Rabinowiczet al., 1990]. However,the alignmentof
thegeoid/gravityundulations
with platedirectionhasneverbeen
rigorouslydemonstrated,and we seek herein to quantitatively
assessthis alignment.
Directional Analysisof Geoid and Bathymetry
First, we determinethe actualorientationof the Pacificgeoid
undulationsby calculatingtheir correlationwith spherically
axisymmetric sinusoidalundulationsdefined in an arbitrary
referenceframe (Figure 2). We use a combinedSeasat/Geosat
altimetricgeoid (W. F. Haxby, pers.comm., 1990.) Sincethe
geoid undulationsappearat severalwavelengths,we carry out
thiscalculationfor a full spectrumof sinuscidwavelengths
(1502000 km). To avoid bias due to filtering we use a spherical
harmonicgeopotential
modelto removeonly the longestwavelengths(> 3200 km) from the datasetandcosine-taper
the coefficients for the intermediate wavelengths(1600-3200 km).
Originalfeatureswith wavelengths
< 1600km thusremainunaltered. We chooseto limit thedataareato a polygonalportionof
the platewherethe linearions
are mostclearlydeveloped
(see
Paper number 94GL01815
0094-853 4/94/94GL-01815503.00
Figure 1). Next, we searchfor the north pole of the sinusoid's
referenceframe that maximizesthe geoid-sinusoid
correlationin
1943
Intermediate Wavelength Geoid Anomalies
Fig. 1. Intermediatewavelengthgeoidanomaliesoverthe Pacific
oceanfrom combined Geosat/Seasataltimetry. The white polygon outlinesthe region studiedin this paper. Yellow arrows
indicatedirectionandrelativeamplitudeof absoluteplatemotion
Fig. 2. An exampleof axisymmetricsinusoidalgeoid undulationsfor a 600 km wavelength.Light anddark areascorrespond
to positive and negativeamplitudes,respectively. We search,
usinga grid centeredon the Pacifichot spotpole, for the pole
orientation(P) for thisundulationwavelengththatgivesthe maximumcorrelation
with thedatashownin Fig. 1. Onlydatainside
thepolygon
wereusedin theoptimization.
for thePacific,Nazca,andCocosplates.The lineatedanomalies sinusoidpolesare frequentlymorethan 25 sphericaldegrees
can best be seen subparallelto the direction of absolutemotion
for the Pacificplate and obliquelycrossmajor fracturezonesin
the area. In this geoidimagethe lineationsare mostvisiblenorth
away
fromthePacific
hotspot
pole(i.e.,A-1< 0.04).Theshortestwavelengths
(< 300 km) determined
by thismethodaremost
likely the so-called"Haxby-lineations"
first detectedin gravity
of the yellow arrow indicatingPacificplate motionas subtle anomaliesderived from Seasataltimetry [Haxby and Weissel,
1986]. The remainingdominantwavelengths
correspond
to the
geoid undulationsreporteda few years later [Baudryand
undulationssuperimposedon the backgroundgeoid.
Kroenke, 1991; Cazenaveet al., 1992; Maia and Diarnent, 1991],
a least-squares
sense. Figure 3 showsexamplesof the spatial including a 1400-km wavelengthundulationwhich appearon
variations of the correlationsfor both geoid and bathymetryat
powerspectraof along-track
sea-surface
heights[Cazenave
et al.,
two wavelengths.The pointof maximumcorrelationrepresents
the locationof the best-fittingsinusoldpole. The pole for the
80'
300-km-wavelengthsinusoid(cross-hair)is very close to the
[750
Pacifichot spotEulerpole (circleat ~68øW/69øN),while thepole
o
for the 750-km-wavelengthsinusoldare far from the hot spot
pole. To constrainthecalculations
we only searched
for poleson
60'
a grid surroundingthe hot spotpole (the longitude-latitude
extent
of this area is indicatedin Figure 3). It is possiblethat global
40'
Igeoidl
Igeodlmaxima exist outside this area; however, undulationsaligned
with polesthat far away are certainlynot relatedto Pacific plate
240'
280'
320'
240'
280'
320'
motion. Finally, for all sinusoldwavelengths, the spherical
80'
distanceA betweenthis optimalpole and the Pacific hot spot
Euler pole (at -68øW/69øN) is calculated. The great circle
distanceA is a measureof how closely the geoid lineadonsof a
given wavelengthalign with Pacificplate motions. We further
i
accentuate
thisdependency
byplotting
theinverse
distance
(A-t)
i
i
i
60'
as a function of wavelength. For completeness,
we subjectthe
ETOPO5 bathymetrydata [NationalGeophysical
Data Center,
40'
1988]tothesameanalysis
(afterremoving
theaget/2-dependency
[Parsonsand Sclater, 1977]).
Itopoli
240'
!
280'
!
320'
240'
280'
320'
Fig. 3. Exampleof thecorrelations
betweenthe axisymmetrical
sinusoldandthe datafor a rangeof sinusoldpoles. BlackindicaResults
indicate
thatA-1varies
strongly
withgeoidundulationtions the highestcorrelation;white areashave correlationsless
Results
160 km, 225 km, 287 km, 400 km, 560 km, 660 km, 850 km,
than 70% of the maximum. The elongatedshapeof the correlationsreflectsthefactthatpolesawayfromthecrosshair
butalong
a greatcirclenormalto the actualundulations
may still correlate
1000 km, and 1400 km. For other wavelengths,the best-fitting
well.
wavelength (Figure 4a) and appearsto have maxima within
severaldiscretewave bands,centeredon wavelengthsequal to
WESSEL ET AL.' PACIFIC
200
a)
300
400500
700
1000
GEOID
AND BATHYMETRY
UNDULATIONS
1945
geoidlookedlike the syntheticundulationin Figure2.) Hence,
rather small correlationsbetween the syntheticand geoid-
2000
bathymetry
undulations
canbe expected
andstandard
testswill
0.2
render the correlationsstatisticallyinsignificant. We are therefore primarilyconcernedwith relativevaluesof the correlations.
10'
Moreovei
•, weha•ietested
Ourtechnique
onrandom
Gaussian
20'
noise and found correlation maxima two orders of magnitude
smallerthanthoseinferredfrom real data,thusimplyingthatthe
correlations
with the dataare notrandom. However,we feel the
0.0
strongestsupport for the significance of the geoid correlations
comesfrom the bathymetryanalysis. Althoughthe batbyrne.try
coveragein thisregionis sparse,it is clearthatthe bathymetry
resultscorroborate
the geoidanalysis.
0.2
10'
20'
Discussion: Possible Reflection
Discontinuities
of Mantle
An intriguing outcome of this study is that the dominant
wavelengthsare very nearlyequivalentto the depthsof various
0.0
.
seismic discontinuities
in the mantle.
Several well-documented
discontinuities
'existin theEarth's
mantle,
mostnotably
theones
0.3
at depthsof 410 krn (presumedto be the exothermicolivine-
spinel
phase
change
[Ringwood,
i975])and660krn(probably
the
0.2
10'
0.1
20'
endothermie
spinel-perovskite
phasechange[lto andTakahashi,
1989]),thelatterseparating
theupperandlowermantles.
Recent
seismicmodelsof Earth'sradial structurehavegivencompelling
evidence
for a discontinuity
at520kmdepth[Shearer,
1990],and
o.o
200
300
400 500
700
1000
'2000
Wavelength (km)
tenuoussuggestions
of onesat 220 km [Anderson,1979], 840 km
[Shearer, 1990], 700 km and 900 km [Revenaughand Jordan,
1991]. Of theeightdominant
wavelengths
indicated
in Figure4a,
Fig. 4. a) Inversedistance,
A-1,in spherical
degrees
between six of them are within 5% of the depth of a distinctor suggested
geoid undulationpoles and Pacific hotspotpole at 68øW/69øN.
discontinuity.The numberof dominantwavelengthsthat are
Distances
rangefrom4.5' to ~50ø. b) Theinverse
distance
(4-1) nearlyequivalent
to discontinuity
depths
argues
against
this
as a function of wavelengthfor bathymetryin the sameregion.
correlationbeing a coincidence.It would seempossible,there-
c) Thegeometric
meanof A-1forthetwodatasets.Thistrans- fore, that the geoid undulationsaligned'with the Pacific plate
formationhighlightsthe wavelengths
associated
with geoidand motion are reflectingmantle structure.
bathymetry
undulations
thatareapproximately
copolar
withthe
If the apparentrelationbetweenthe copolargeoid/bathyme•
Pacificplatemotion.It should
benotedthatwhilethegeoid undulations
andmantlediscontinuities
is significant,
it suggests
coverage
in thisareaisuniform
thebathymetry
coverage
ismuch that geoid and bathymetryundulationsare influencedby manfie
sparser.
dynamics2
In general,
thegeoidexpression
of complex
mantle
dynamicswill be'difficult to infer from surfaceobservations
1992].Thevariation
in A-1forbathymetry
isdisplayed
in Figure since lithosphericprocessesoverprint the manfie contribution.
4b. It is evident that the dominantwavelengthsdeterminedfrom.
the geoid are to a large extent also presentin the bathymetry.
Moreover,
thebathymetric
expression
Willbesubdued
by the
dampening
effectof theelasticlithosphere
andsedimentation'.
This connectionis further highlightedin Figure 4c which
However,in the regionof the equatorialPacific,plate motion
presents
thegeometric
meanof A-1for thetwodatasets;this possibly organizes mantle flow into coherent, axisymmetric
whose
geoidandbathymetry
signatures
aredetectable
estimatewill be large only whenboth the geoidand bathymetry structure
polesare closeto the .hotspotpole. We have labeledthe most
pronounced
wavelengths
thathavecopolarexpressions
in both
geoid and seafloor relief. It should be noted that while the
bathymetricundulationscannotbe seendirectly in bathymetry
maps,their presencehas beenpreviouslydemonstrated
by twodimensionalfiltering [Cazenaveet al., 1992].
the location
of maximum
thecauseof theundulations,
it cannot
easilyexplaintheabove
results.First, it is not clearwhy so many discontinuities
should
influencethe scaleof convectioncells.While the 660 km phase
change may impose multi-layer flow [Tackley'et al., i993;
Weinstein,1992], the 410 km boundaryshouldfacilitatecross-
boundary
fl0w [Scl,tbertetal., 1975].Unless
thedestabilizing
effectof an exothermic
'phasetransition
imposes
a preferred
Significanceof Correlations
While
with the techniquepresentedhere.
While manfie convectionmay be a first obviouscandidatefor
correlation
for each wave-
wavelength
on convection,
the410 km discontinuity
shouldhave
lengthis Wellresolved
(Figure3), thecorrelations
themselves
are
litfie influenceon cell size.Secondly,if convectioncellsbetween
rather small (r < 0.1). This occursbecausethe correlation coef-
thesurface
(orbaseof thelithosphere)
anda discontinuity
arethe
thentheyhaveanomalously
small
ficientisnormalized
bythestandard
deviation
oftheentire
geoid causefor theundulations,
(or bathymetry)data set,while mostof the observeddata are not
aspectratios. Convectionis, however,not necessarilythe only
Otherformsof m•fie dynamics
are
duetocopolar
undulations,
e.g.,geoidanomalies
associated
with causefor theundulations.
the "Superswell" [McNutt and Fischer, 1987], fracture zones,
isolatedseamounts,
etc. (Unity correlationwouldmeantheentire
alsopossible,e.g., multiple, long-livedmanfieplumes[Fleitout
and Moriceau, 1992] and superplastic
instabilitiesassociated
:
1946
WESSEL ET AL.: PACIFIC
GEOID AND BATHYMETRY
with phasechanges[Parmentier,1981]. Furthermore,
thecorre-
lation for wavelengthsin the 800-1000-rangemay possibly
reflectperiodicities
inthehotspotdistribution
[Yarnaft,
1992].
Conclusion
We havequantitatively
demonstrated
an apparentcorrelation
betweenthe directionof absoluteplate motionand alignmentof
UNDULATIONS
Maia, M., and M. Diament, An analysisof the altimetricgeoidin various
wavebandsin the centralPacific ocean:constraints
on the origin of
intraplatefeatures,Tectonophysics,
190, 133-153, 1991.
McAdoo, D.C., and D. T. Sandwell, On the source of cross-grain
lineationsin the central Pacific gravity field, J. Geophys.Res., 94,
9341-9352, !989.
McNutt, M. K., and K. M. Fischer,The southPacific superswell,
in
Seamounts,islands and atolls, vol. 43, edited by B. H. Keating, P.
Fryer, R. Batiza and G. W. Boehlert, pp. 25-34, American
geoidandbathymetry
anomalies
forseveral
discrete
wavelengths. Geophysical
Union,Washington,
D.C., 1987.
Our analysisreconcilesthe differingresultsof earlierstudies NationalGeophysicalData Center,ETOPO-5 Bathymetry/Topography
data, Data announcement 88-MG-02, National Oceanic and
[Baudryand Kroenke,1991;Cazenaveet al., 1992;Maia and
Atmospheric
Administration,
U.S. Dept. of Commerce,1988.
Diantent, 1991] by showingthat all the previouslyreported
lineafionsareindeedpresentin thePacificgeoidandalignedin Parmentier,E. M., A possiblemantle instability due to superplastic
deformationassociated
with phasetransitions,Geophys.Res.Lett.,8,
the directionof absoluteplate motion. Interestingly,the wave-
lengthsof theselineafions
possibly
correspond
to thedepths
of
!43-146, 1981.
Parsons,B., andJ. G. Sclater,An analysisof the variationof oceanfloor
bathymetryand heatflow with age,J. Geophys.Res.,82,803-827,
seismicdiscontinuitiesin the upper and lower mantle. The
agreementbetweenthe analysesof geoidandbathymetry
data
1977.
lendscredenceto theseresults. Our findingspossiblyvindicatea Rabinowicz, M., G. Ceuleneer, M. Monnereau, and C. Rosemberg,
long held belief that the geoidis diagnosticof internalmantle
Three-dimensionalmodelsof mantleflow acrossa low-viscosityzone:
implicationsfor hotspotdynamics,Earth Planet. Sci. Lett., 99, 170dynamics [Richards and Hager, 1984; Runcorn, 1967].
184, 1990.
Traditionally,the relationbetweenlarge scalegeoidanomalies
and mantle flow is indirectlyinferredfrom the combinationof Revenaugh,I., and T. H. Jordan,Mantle layeringfrom ScSreverberations, 2, The transition zone, J. Geophys.Res., 96, 19,763-19,780,
geoid-topography
correlations
and fluid-dynamicmodels;this
1991.
relationis somewhatnonunique.If our findingsare significant,
Richards,
M. A., andB. H. Hager,Geoidanomalies
in a dynamicearth,J.
theyconstitute
thefirstdirectevidenceof a distinctmanfiesignaGeophys.
Res,89, 5987-6002,1984.
ture in the geoid. Furtheranalysesof the geoidandbathymetry
undulationsand validationof the correlationtechniquepresented
here will be necessaryto attachstatisticalsignificance
to such
claims.
Richter, F. M., and B. Parsons, On the interaction of two scales of
convectionin themantle,J. Geophys.Res,,80, 2529-2541, 1975.
Ringwood,A. E., Composition
andpetrologyof theEarth'smantle,pp.,
McGraw-Hill, New York, 1975.
Runcorn,S. K., Flow in the mantleinferredfrom the low degreeharmonicsof the geopotenfial,
Geophys.J. R. Astron.Soc.,14, 375-384, 1967.
Acknowledgments,This work was supported
by the NationalScience
FoundationundergrantOCE-9202926. We thankPhil Ihingerandan Sandwell, D. T., and D.C. McAdoo, High-accuracy,high-resolution
anonymous
reviewerfor helpfulsuggestions.
Thisis Schoolof Ocean
andEarthScienceandTechnology
contribution
3454.
References
Anderson,D. L., The deep structureof continents,J. Geophys.Res., 84,
7555-7560, 1979.
Baudry,N., andL. Kroenke,Intermediate-wavelength
(400-600km),
southPacific geoidalundulations:
their relationshipto linearvolcanic
chains,Earth. Planet. Sci. Lett., 102,430-443, 1991.
Buck, W. R., andE. M. Parmentier,Convectionbeneathyoungoceanic
lithosphere: Implications for thermal structure and gravity, J.
Geophys.Res.,91, 1961-1974, 1986.
Cazenave,A., S. Houry, B. Lago, andK. Dominh,Geosat-derived
geoid
anomaliesat mediumwavelength,J. Geophys.Res.,97, 7081-7096,
1992.
gravityprofilesfrom 2 yearsof the Geosatexactrepeatmission,J.
Geophys.Res., 95, 3049-3060, 1990.
Schubert,G., D. A. Yuen, andD. L. Turcotte,Role of phasetransitionsin
a dynamicmantle,Geophys.J. R. astr.Soc.,42, 705-735, 1975.
Shearer,P.M., Seismicimagingof upper-mantle
structure
withnewevidencefor a 520-1cmdiscontinuity,
Nature, 344, 121-126, 1990.
Sparks,D. W., andE. M. Parmenfier,The structureof three-dimensional
convectionbeneathoceanicspreadingcenters,Geophys.J. Int., 112,
81-91, 1993.
Tackloy,P. J,, D, J. $tovonson,
O, A, Olatzmaior,and O, Schubert,
Effects of an endothermicphase transitionat 670 km depth in a
spherical
modelof convection
in theEarth'smanfie,Nature,361,699704, 1993.
Weinstein, S. A., Inducedcompositionallayering in a convectingfluid
layer by and endothermicphasetransition,Earth Planet. Sci. Lett.,
113, 23-39, 1992.
Fleitout, L., and C. Moriceau, Short-wavelengthgeoid, bathymetryand Winterer, E. L., and D. T. Sandwell, Evidence from en-echelon crossgrainridgesfor tensionalcracksin the Pacificplate,Nature,329, 534the convectivepatternbeneaththe Pacific Ocean,Geophys.J. Inr.
537, 1987.
I10, 6-28, 1992.
Yamaji,
A., Periodichotspotdistributionand small-scaleconvectionin
Haxby,W. F., Gravityfield of theworld'soceans,NationalGeophysical
the uppermantle, Earth Planet. Sci. Lett., 109, 107-116, 1992.
Data Center, NOAA, Boulder, Colorado, 1987.
Haxby, W. F., and J. K. Weissel, Evidence for small-scalemantle
convectionfrom Soasataltimeter data, J. Geophys.Res., 91, 35073520, 1986.
Ito, E., and E. Takahashi,Postspineltransformations
in the system
Mg2SiO4-Fe2SiO4 and somegeophysicalimplications,J. Geophys. Received:March 15, 1994 Revised:June6, 1994
Res., 94, 10,637-10,646, 1989.
AcceptS: June8, 1994