JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. 12, PAGES 30865-30879,
DECEMBER 10, 2001
Causes for axial high topography at mid-ocean ridges
and the role of crustal
thermal
structure
AnjanaK. Shah
• andW. RogerBuck
Lamont-DohertyEarth Observatoryof ColumbiaUniversity,Palisades,New York, USA
Abstract. Mid-oceanridge topographyis modeledas the flexural responseto loadsusinga thin
plate approximationand settingthermalstructureof the lithosphereto allow, but not require,a
region of rapid coolingnear the axis. Loads on the lithospherearise from the presenceof lowdensitymelt, densificationdue to coolingwith distancefrom the ridge axis, and thermal
contractionstresses.
We find two end-memberclassesof temperatureand melt structurethat can
produceaxial high topographyand gravity observedat the East Pacific Rise (EPR). One classis
very similarto previousmodels,requiringa narrow columnof melt extendingto at least30 km
depthwithin the mantle and lithospherewhich coolsand thickensvery graduallywith distance
from the ridge axis. The other is a new class,predictinglithospherewhich coolsrapidly within a
few kilometersof the axis and then slowly farther from the axis, with melt which is contained
primarily within the crust.The latter solutionis consistentwith tomographyand compliance
studiesat the EPR which predictrapid crustalcoolingwithin a few kilometersof the axis that is
attributedto hydrothermalcirculation.This solutionalso allows the melt regionto be coupledto
crustalthermalstructureand requiresno melt anomalywithin the mantle.Model fits predict030% melt in the lower crust,dependingon how temperatures
are distributedwithin the lithosphere
and the degreeto which thermalcontractionstressesare assumedto contributeto topography.The
model generallypredictsa wider axial high for lithospherewhich is thin over a wider regionnear
the axis.This is consistentwith previouscorrelationsbetweenlargecross-sectional
areaof the high
and indicatorsof highermelt presenceor a warmer crustalthermalregime.For a slightly slower
rate of lithosphericcoolingat distancesmorethan •5 km from the axisthe modelpredictsa trough
at thebaseof the axial high. Suchtroughshavebeenpreviouslyobservedat the baseof the high on
the westernflank of the southernEPR, where subsidence
ratesare anomalouslylow. Finally, thick
axial lithospherereducesthe amplitudeof the high, making it sometimesdifficult to distinguish
from long-wavelengthsubsidence.
This morphologyis comparableto that of someintermediate
spreadingridges,where topographyis relatively flat, suggestinga transitionfrom fast to
intermediatestyle morphology.
1.
Introduction
contrastsin viscosity. Furthermore, recent seismic tomography
resultsfrom the Mantle Electromagnetic
and Tomography(MELT)
For a distancespanningover 4000 km of the fast spreadingEast
Experiment[Forsythet al., 1998; Hung et al., 2000] do not show
PacificRise(EPR) andpartsof othermid-oceanridges,an elongate
evidenceof any low-velocity zone suchas would be expectedin a
topographichigh 3-20 km wide and rising 200-400 m above
narrow region of high melt fraction.
surroundingtopography marks the ridge axis (Plate 1). The
Previous models which considerthe flexural responseof the
physicalphenomenathat producethis topographyare still debated.
lithosphere[Kuo et al., 1986; Wangand Cochran, 1993] require
The high haslong beenmodeledasthe resultof a narrowregionof
elastic lithospherewhich thickens gradually with distancefrom
low-density mantle material which buoyantly pushes up lithothe ridge axis (for example,the best fits by Wangand Cochran
sphere,originally proposedby Madsen et al. [1984]. Wang and
[1993] require lithospherenot more than 1 km thick at a distance
Cochran [1993] and Magde et al. [1995] determinedthat such a
of 10 km from the ridge axis). In these models the mechanical
region must extend to depths well within the mantle, between
structureof the lithosphereis linked to the thermal structureof
depthsof 20-30 km and50-70 km respectively,
asgravitydatado the crust when fitting bathymetry and gravity observations,so
not exhibita sizablecorresponding
low which would be presentfor
that the crustmust cool slowly with distancefrom the ridge axis.
a shallowerregion (once topographicrelief has been accounted
This type of thermalstructuremay be inconsistent
with the rapid
for). However, analysesof the viscosity and density structure
coolinginferredfrom seismicvelocity structuresdeterminedwith
requiredfor such an anomaly [Eberle et al., 1998] showedthat
tomographyexperiments[Vera et al., 1990; Toomeyet al., 1994],
thepresenceof sucha narrowregionwouldrequireextremelylarge
compliancestudies[Crawford et al., 1999], and studiesof the
responseof near-axial lithosphereto topographic loads [e.g.,
Cochran, 1979; McNutt, 1979]. Models of axial thermal structure,
•Alsoat Department
of EarthandEnvironmental
Sciences,
Columbia suchas thoseby PhippsMorgan and Chen [1993] and Henstock
University,New York, USA.
et al. [1993], also predict rapid cooling away from an axial
magma chamber(AMC), due to cooling effectsof hydrothermal
Copyright2001 by the AmericanGeophysicalUnion.
circulation.
Papernumber2000JB000079.
Eberle and Forsyth [1998a] proposeda mechanismfor axial
high topographywhich does not require low-density mantle or
0148-0227/01/2000JB000079509.00
3O865
30866
SHAH
AND
BUCK:
AXIAL
HIGH
TOPOGRAPHY
AT MID-OCEAN
RIDGES
Plate 1. East Pacific Rise topography,15ø- 17øS, looking southward.Data are from Scheireret al. [1996]
(anonymous
FTP). Note somesegments
(suchasnear17øS)exhibita wide axialhigh,whereasothers(suchasnear
15øS)exhibita narrowaxial high. Verticalexaggeration
is 5X.
crustalmaterial below the axis. They suggestthat large stresses varieswith distance.We developan approachto the sameproblem
maintainedin a high-viscositylower crust, coupled with low that differs only in the way material is accretedat the axis. To
stressesmaintainedin upper crust near the ridge axis (where modelthe deflectionof a movingplate,Kuo et al. [ 1986] assumed
extensionalstressis relieved by dike injection), create a plate that the plate is initially stress-freeat the axis. They then formubendingmoment,which in turn createsan axial high. They also lated an expressionfor the changein stresswith each step of
assumelithospherewhich thickensslowly with distancefrom the accretion,assumingthat elasticequilibriumis maintainedat each
ridge axis, combined with constantviscosity aesthenosphere step.This expressionwas integratedto find a relationshipbetween
beneathit (their best fits require elastic lithospherewhich is 2 momentand deflection,yielding a fourth-orderdifferentialequakm thick at a distanceof 10 km from the ridge axis). This type of tion for deflection. Additional boundary conditions were zero
andshear
stress
attheaxis(d3w/dx
3 -- d2w/dx
2 = 0 atx
mechanicalstructurealso suggests
thermallithospherecoincident curvature
with the mechanicallithosphereand thuscrustwhich coolsslowly = 0, where w is deflection). It is important to note that no
restrictionswere placedon the deflectionat the axis.
with distancefrom the ridge axis.
We instead assume an initial condition for the deflection at the
We proposethat alternatethermaland magmaticscenarioscan
produceaxial hightopography.
To examinepossiblescenarios,
we axis and then consider changes in deflection, in responseto
use a simple one-dimensionalflexural model to predict ridge the changesin loads,as the plate accretesand movesaway from
profile topographyand considera greaterrange of lithosphere the axis. The initial conditionthat we assumeis local isostasyat the
by an expectation
and melt structuresthan previousstudies.We parameterizetwo- axis, followingBuck [2001]. This is suggested
dimensionaltemperature
andmelt structures
andexaminetherange that eruptionsat the EastPacificRise are likely to occuroftenover
of parameters
whichcanfit bothbathymetryandgravitydata.Once scalesof severalthousandsof years.With frequentdiking, the cut
is likely to frequentlysettleto a positionof localisostasy.
a setof fit parameters
is found,we examinethe effectsof changing lithosphere
For a moving,accretingplateactedon by a fixed distributionof
themslightly.The resultingchangesin topographyarecomparedto
observedintersegment
and intrasegment
variationsin axial high loadsq(x), we determinethe changein deflectionof the plateas it
(Figure 1) by assumingelasticequilibriumis
morphology
andothergeologicindicators
of thermalandmagmatic movesa distancezhoc
structure.
maintainedat each step.Thus
2.
2.1.
Model
Formulation
d2z•;B
•+dx 2
ApgAw= Aq;
Flexure of a Moving Plate
Observationssuchas the presenceof moatsaroundseamounts
and hot spot islandsand the bendingof platesas they approach
subduction zones [Cochran, 1979; McNutt, 1979] strongly
suggestthat the lithosphererespondsflexurally to applied loads.
This deflectionhas frequentlybeen modeledusing a thin plate
approximation.We take this approach,modeling profiles of
topographyof the ocean floor due to the densificationof
buoyant material below the lithosphereor thermal bending
stresses.The fact that the oceanlithosphereis createdat a ridge
axis and accretedonto the plate and staysin continuousmotion
away from this axis plays a significant role in the model
formulation
Kuo et al. [ 1986] determinedthat a plate in motionwill respond
differentlythan one which is still, i.e., static,if the plate rigidity
(1)
d2Aw
- o dx--5'
(2)
where Aq(x) = q(x + z•c) - q(x), Aw(x) is the changein plate
deflection,z•/B(x) is the changein bendingmoment, D(x) is the
plate rigidity, and Ap is the density contrast between the
lithosphereand water. The initial conditionof local isostasyat
the axisimpliesApgw(0) = q(0). We canthenshiftw(0) andq(0) to
an arbitraryreferencelevel of zero.The totaldeflectionis foundby
summingthe changesin deflectionat each accretionarystepand
addingtheseto the initial deflection:
w(x)
-iaw
o
(3)
SHAH AND
BUCK:
AXIAL
HIGH
TOPOGRAPHY
AT MID-OCEAN
RIDGES
30867
Level of local isostasy
water
lithosphere
aesthenosphere
Thermal
stresses
AT smaller, less contraction
Density loads:
Increasedweight due to
solidificationand cooling
causesplate to bend down
AT larger, more contraction
thermalcontractionat bottom
causes
plate
tobend
down
With seafloorspreading,
plate movesaway from axis.
New
material,..,,, ;..,..., Newmaterial
rises
tosame
.•,•:•.•:•::...,
':•:•/:•
.:.•?•
level
oflocal
isostasy
Figure 1. Illustrationof how incremental
loadscancontribute
to axialhightopography.
The plateis assumed
to be
brokenat theaxis.(top)At theaxis,meltrisesto a heightconstant
overtime.(middle)As newmaterialmovesaway
from the ridgeaxis,it densitiesbecauseof coolingand solidification,producinga downwardload. Thermalstresses
arisebecausematerialnearthe seafloorusuallyremainsnearwatertemperatures
but materialat depthcontinually
cools.The greaterchangein temperature
at depthcausesthebottomof the lithosphere
to contractmorethanthetop,
causingtheplateto benddown.(bottom)At thesametimethattheseloadsact,thelithosphere
spreads
awayfromthe
axis, andnew materialis accretedat the sameheightas before.The resultis a high at the axis.
Changesin deflectionare determinedfrom (1) to (3) via a fourth-
curvatureat the axiscansignificantlyaffectthe resultingdeflection
[Buck, 2001].
To assurelocal isostasvat the axis, we assumeboundary
The differencein boundaryconditionsmay or may not have a
conditions
d2Aw/dx
2 = d3/•w/dx
3 = 0 atx = 0. Thefactthatthese strongeffecton the resultingdeflections,dependingon the rigidity
imply local isostasyat the axis is most easily illustratedby at the axis. The modelsare equivalentif zero rigidity is assumed
integrating(1) and (2) into the form ofKuo et al. [1986, equation at the axis, since this implies local isostasy there for both
(9)]:
formulations.
However,the formulationusedin this studypredicts
the same depth at the axis for different lithosphererigidities
becauseof the assumptionof local isostasythere, whereasthe
d(Dd3w/dx
3)
+ Apgw: q.
(4) formulationby Kuo et al. [ 1986] predictsthatthe depthof the axis
dx
dependson the strengthof the lithosphereat the axis and the
In theintegrated
formtheboundary
conditions
become
d3w/dx
3 = magnitudeof the applied load. This arisesbecausetheir formulad4w/dx
4= 0 atx = 0,yielding
Apgw(0):q(0)whenapplied
to(4). tion placesconstraintson the curvatureand shearstressat the axis,
The key differencebetweentheseboundaryconditionsandthoseof but none on deflection;the deflectionmustbe set accordinglyso
Kuo et al. [1986] is thatthey allow curvatureto developat the axis, that curvature and shear stress are zero. The formulation that we
sincenorestrictions
areplaced
ond2w/dx
2. Thedevelopment
of use fixes the depth of the axis. Curvatureand shearstressmay
order finite difference
scheme.
30868
SHAH
AND
BUCK:
AXIAL
HIGH
TOPOGRAPHY
2.2.2.
Table 1. Valuesof Material PropertiesUsed
Property
Young's
modulus
Poisson's ratio
Value
E
9 x 10IøPa
Ow
Pc
Om
o•
Thermal
RIDGES
contraction
stresses.
Thermal
stresses arise
when different depths of a material are cooled by different
Symbol
v
Density
of water
Density
of cmst(bulk)
Density
of melt
Density
of mantle
Coefficient
of linearexpansion
AT MID-OCEAN
0.25
amounts.If a material is cooled at a bottom surface,the cooled
areawill contract,causingthe materialto bend downwardif it is
allowedto deflectfreely or to crack if it is held fixed. Thermal
stresses
have beenusedto explaindeflectionsat transformfaults
1000kgm-3
3000kgm-3
near ridge-transformintersections
of up to a kilometer,due to
2700kgm-3
sizable differencesin temperaturesand cooling rates acrossa
3300kgm-3
1 x 10-5 øC-1 transformfault [e.g., Parmentier and Haxby, 1986]. They may
also contributeto deflectionsnear the ridge axis: Lithosphereat
depth will continueto cool as it moves away from the axis,
whereaslithospherenear the seafloorhas alreadycooledto nearwater temperatures,and experiencesrelatively little subsequent
develop accordingly.Both models achieve a plate which is changein temperature(Figure 1). This differencewill causethe
"broken," or discontinuous
at the axis, yet the axial depth still lower part of the lithosphereto contractmore than the top,
dependson plate thicknessfor the Kuo et al. [1986] formulation. creatinga moment,so that the plate will bend downwardwhile
This formulationmay be more appropriatefor regionswith less it is movingaway from the ridge axis. Downwarddeflectionwith
frequenteruptions,such as at intermediateand slow spreading motion away from the ridge axis will leave a high remainingat
the axis.
ridges.
Deflection createdby thermal stressescan be estimatedas
follows.As an elasticmaterialundergoes
a changein temperature
2.2. Loads on the Lithosphere
changein stressis, for a plate which is
We considerthree types of loads which are likely to affect AT, the corresponding
lithospheric deflection. Two have been consideredfor most allowedto deflectfreely,
Maximumaesthenosphere
temperature
Tm
1200øC
previous models of axial high topography:that of the solidification of melt below the ridge axis (qm) and the thermal
densificationof the lithospherewith distancefrom the ridge axis
(qc) (the latter has been usedto model subsidence
of the ocean
basins over scales of thousandsof kilometers [Parsons and
Schlater,1977]). The third is bendingdue to thermalcontraction
stresses(qt). There are some difficultieswith modelingthermal
stresses
usinga thin plate approximation,discussed
below, so we
will consider cases both with and without this load. The final load
distributionused in (2) is
q(x) -- qc(X)+ qm(X)q-qt(x).
(5)
2.2.1. Density changes. As the lithosphere cools and
becomes denser, its increasing weight will contribute to its
deflection. The associated load is
hm(x)
h
Aør(x'z)
= 1-Ev2o•AT(x,z)(8)
J1-Ev2o•AT(x,z')dz',
0
where o• is the linear coefficientof thermal expansion,h is the
thicknessof the lithosphere,
and z is the depthbelowthe seafloor.
The first term of (8) arisesfrom strainassociated
with thermal
contraction.
The secondterm is neededif the plate is allowedto
deflectfreely in the vertical directionat one end, as it forcesthe
integratedstressover the thicknessof the plate to be zero. For
accretinglithosphere,
temperatures
changeaslithosphere
coolsand
the platemovesa distanceZ3•c,so
AT(x,z) = T(x,z) - T(x- Zha:,z)
(9)
assuminga steadystatetemperaturefield fixed in space.
Thermalbendingstressesact from within the plate but can be
incorporated
into the one-dimensional
flexure equationvia a load
term, followingParmentierand Haxby [1986]. Thermalbending
stresses
contributeto the momentterm on the left-handsideof (1),
so deflectionscandeterminedby incorporating
this contributionas
qc(x)
= / gpa•[r(x,z)
- Tm]dz, (6)
o
whereo• is the volumetriccoefficientof thermalexpansionandhm
is the depthat which materialreachesTm,an estimatefor melting
temperature,
in thisstudy,1200øC(Table1). We assume
thatbelow
this depth, temperaturesdo not vary considerablyfrom melting
temperatures
andwill not contributesignificantly
to theloadsothat
Tmrepresents
the maximumaesthenosphere
temperature.
We also consider the effects of melt solidification
and densift-
cation within the lower crust and mantle. In this case,
qm(X)-- ½ApmgH(x
),
qr(x)
=-d2Mr(x)
dx
2 ,
(10)
where
Mr(x)--ior(x,z)zdz:i(i
(11)
o
o
(7)
where½is thevolumefractionof melt,with a densitycontrastApm
relativeto surrounding
rockat 1200øC,distributed
overa column
of heightH(x). The melt fractionis, in fact, likely to vary both
verticallyand horizontallywithin the crust,but this variabilityis
poorly constrained.
We simplifythe situationby considering
½ as
an averagemelt fraction below a region defined by hm(x),the
1200øC isotherm.
a load:
Table 2. Variable Parameters
Parameter
Symbol
Thermal structure
Depthto 1200øCisothermnearaxis
Depth(of 1200øCisotherm)to whichdistance-squared
coolingis used
Width over which 6-km cmstwould reachtemperatures
below 1200øC,if distance-squared
cooling
Theseloadsare comparableto that proposedby Buck [2001],
exceptthat Buck simplifiedthe situationby applyingthe loads
due to solidificationand cooling at one point, at the end of the
continuedbelow hl
plate (this simplificationassumesthat most cooling and solidCoefficientfor squareroot of distancecooling
ificationoccurover a shortspatialscale).In this study,we trace Melt
Percentof lower cmstwhich is melt
the solidificationof melt with distancefrom the axis according
to thermal structure(equation(7)), with cooling accountedfor Strength
Strengthreductionfactor
in (6).
ho
hi
W
S
qb
co
SHAH
1. Very shallow
isotherms
within
1 km of axis
AND
BUCK:
AXIAL
HIGH
TOPOGRAPHY
AT MID-OCEAN
RIDGES
30869
2. Quadratic cooling
nearaxis(x2)
Temperature
(C)
todepthH1
0C
0
200
1200
Temperature(C)
0
200
1200
Profile
B
HO
i
i
i
1200C isotherm
.....
4. Square-root of age
cooling away from axis
(S*•/x)
_
Profile
A
Figure 2. (left) Model parameters.The region is horizontallydivided into three sections,with differenttypes
of coolingfor each.Within 1 km of the axis, the depthof the 1200øCisothermis held at a constantvalue
ho. Startingat 1 km from the axis, the 1200øCisothermdeepensas distancefrom axis squared,to a depth
hi. W is the distancefrom the axis at which quadraticcooling would reach 6 km depth. Away from the
axis, isothermsdeepenas the squareroot of age (S*v/x +
c, where c is used to make the isotherms
continuous).(right) Associatedthermal structure.For profile A, temperaturesincreaselinearly with depth,
from 0øC at the top to 1200øC.For profile B a percentage
of the plate is held at a constanttemperature
of
200øC near the surface,simulatinghydrothermalcooling,with temperatures
increasinglinearly with depth
below
that.
the momentcreatedby thermalstresses.
We notethat if therewere
no buoyancyterm in (1) (e.g., the platefloatedin air, ratherthan on
a viscousmantle), the bendingmomentwould matchthe thermal
momentexactly.
Using a thin plate approximationassumesthat thermal contractionin a directionhorizontallyparallel to the plate is much
greaterthan that vertically perpendicularto the plate. For lithospherewhich thickensrapidly over a shortdistance,this assumption may not hold, and the actual deflection due to thermal
stresseswill be overestimatedby the thin plate approximation.
We will thus examine cases with a thermal stress contribution and
1200øC),and a secondwherea fractionof the upperpart of the
plate is assumedto cool to 200øCbut then increases
linearlyto
1200øC at depth. The latter scenariois intended to mimic
hydrothermal cooling of the crust. These distributions are
illustratedin Figure 2.
Depth to the 1200øC isothermis defined as a function of
distancefrom the axis. The plate is divided horizontally into
three sections,with different types of cooling for each (Figure
2). Within 1 km of the axis (where a magma chamberis likely
to be present)a constant1200øCisothermdepthho is assumed.
Beginning 1 km from the axis (where hydrothermalcirculation
without, recognizingthat reality shouldlie somewherebetween might quickly cool the crust), isothermsdeepen as the square
the two.
of distance,up to a depthhi for 1200øC.Beyondthat distance,
Some degree of thermal bending stress should naturally isothermsdeepen more slowly, as the squareroot of distance
develop within the ocean lithosphere,dependingon the litho- (approximatingconductive cooling). Associatedparametersfor
sphericthermal structure,yet the effect on axial topographyhas the outer two sectionsare S, the coefficientof the squareroot
not previouslybeen studiedin detail. This may be due to the fact of distance cooling, and W,, defined as the distancefrom the
that for lithospherethat coolsas a functionof the squareroot of axis where quadraticdeepeningwould place the 1200øC isoage, there would be minimal deflectiondue to thermal bending therm at 6 km depth. W can be roughly interpretedas the
stresses[Parmentier and Haxby, 1986]. An assumptionthat the distance from that axis at which the entire crust has cooled to
lithospherecools at a rate other than proportionalto the square submelt temperatures. These parameters are summarized in
root of age is necessaryfor thermalbendingstresses
to contribute Table 2.
to a high at the axis.
2.3.2. Lithosphere strength. The thicknessof the effective
elasticlithosphereis frequentlydefined as an isothermroughly
2.3. Parameters Controlling Deflection
describingthe brittle-ductiletransition.The temperaturerange
2.3.1. Thermal structure. Model deflectionswill depend over which this transitionoccurs,however dependson various
strongly on the geometry of lithosphericthickening, which, in conditions: Hirth et al. [1998], for example, summarize
turn, dependson the thermalstructureof the crust.Thermal and estimates of the brittle-plastic transition of shallow oceanic
lithosphere structures are only somewhat constrained by lithosphere which can vary up to 200øC, depending on
currently available data and models, so we considera group whether there is a dry or wet diabaserheology. Other factors
of lithospherethicknessdistributionsdefined by a set of four complicate estimatesof lithosphericstrength, such as plastic
parameters.The two-dimensionaltemperaturestructureis then weakeningand faulting. Determiningthe preciseeffects of the
defined as a function of the plate thickness.We considertwo latter requires knowledge of the magnitudeand distributionof
vertical temperature distributions: one where temperatures weakening, which is beyond the scope of this study. We
simply increaselinearly with depth from 0øC at the seafloor combine the effects of weakening and imprecision in
to 1200øCat depth(assumingcrustalmelt temperatures
are near estimating a brittle-ductile transition by assuming that the
30870
SHAH
AND
BUCK:
AXIAL
HIGH
TOPOGRAPHY
AT MID-OCEAN
RIDGES
Total RMS
80
70
60
50
40
30
20
10,
10
20
30
40
50
60
70
5O
6O
7O
50
60
70
TopographyRMS (m)
•E 70 :•:
• 60 •
o
N50 •
'• 40
E
'• 30 •
c3 20
10
2
10
20
3O
4O
Gravity RMS (mgal)
80
70
60
50
40
30
20
10
10
20
30
40
lithospherecoolingwidth (km)
Figure3. Contours
of RMS misfitto stacked
profilesof theEastPacificRise,8ø-8ø15'S(top)for bathymetry
plus gravity (scaledby range of each data set before summing),(middle) for topographyonly, and (bottom)for
gravity. The lowest RMS value over a range of trapezoidwidths was used at each point. Other parametersused
areh0= 1 km, hi = 6 km, S = 0 m]/2,andco= 0.33.Thewidthof at thebaseof themeltzonewastakenat 4
km, sincethis value achievedthe lowestRMS valuesover all valuesof I,Vand melt zone depth.The bulk density
of the zone simulatesbetween•2 and5% melt over70 km, equivalentto 30 and70% melt over 5 km, for densities
shownin Tables 1 and 2. Data are from the RIDGE Multibeam Synthesisand GEODAS Worldwide Geophysics
Databases.
effective elastic thickness is a fraction of the depth to the
1200øC isotherm. We have
D -- E[coh(x)]3/[12(1
- v2)],
(]2)
where E is Young's modulusand v is Poisson'sratio, h is the
effectiveelasticthickness,and cois a parameterbetween0 and 1
[e.g., seeTurcotteand Schubert,1982]. Then, for example,a value
of co: 0.5 suggests
that eitherthe lithospherehasweakenedto half
SHAH AND BUCK: AXIAL HIGH TOPOGRAPHY AT MID-OCEAN RIDGES
Previous
New Model
Models
Distancefrom axis (km)
Distancefrom axts(km)
0
10
30871
20
0-J
30
•
40
50
I
I
t4L
o
o'
10
20
30
40
I
I
I
I
ht
E
tiw
50
la,ti• Lithospher•
-2
1200øC Isotherm
-4-
-6-
-8
Meltprimarily
-10 incrust
1200øC
Isotherm
Melt in mantleup to 80 km
-20 -
Plate2. Illustration
ofthetwoclasses
of solutions
yielding
bestfitstoobservations.
Oneclass
issimilar
toprevious
models,
requiring
a deep,
narrow
column
ofmeltinthemantle
andtemperatures
which
decrease
veryslowly
with
distance
fromtheaxis.Theother
requires
lessmeltinthemantle
andtemperatures
whichdecrease
rapidly
overa short
distance from the axis.
its elasticthicknessor that the brittle-ductiletransitionlies at the
eachpointwereused).Thesecontours
revealtwo broadparam-
regionswhichcanfit the data:onewherethe litho600øCisothermfor the casewheretemperatures
increaselinearly eter-space
coolsovera longdistance
fromthe axis(W large),and
withdepth,
ora combination
of thetwo(thelastscenario
beingthe sphere
most likely).
3.
Results
3.1. Forward Models Fitting Observations
meltextendsto at least40 km depth,comparable
to theresultsof
Kuo et al. [1986]and Wangand Cochran[1993];anda second
wherethelithosphere
coolsovera shorter
distance
fromtheaxis
(W small),anda greaterrangeof meltdepthsis feasible.
These
differentscenariosare illustratedin Plate 2. The large widths of
cooling
forfirstcaseimplyconditions
similarto local
We examinea generalrangeof lithosphere
and melt region lithospheric
for a significant
distance
fromthe ridgeaxisso thata
geometries
whichwill fit observed
topography.
Sincetheimplied isostasy
of meltis needed
to support
thehigh.The second
thermalstructure
will alsoaffectthe gravityanomalyvia density largedegree
variations,
gravitydataarealsousedto furtherconstrain
therange caseillustratesconditionswherethe flexuralresponseof a plate
to topography.
of possible
structures.
To modela "typical"axial high,we whichis relativelythicknearthe axiscontributes
dueto nearconsidered
stackedprofilesof the southern
EastPacificRiseat This, in additionto a greaterdegreeof densification
cooling,impliesmuchlessmeltis required.
The
8ø-8ø15'S[Cochranet al., 1993].This regionis particularly axislithospheric
coolsovera distance
comparable
to thatoverwhich
favorable
formodelcomparisons
because
alongmuchof itslength, lithosphere
within
therearefew offsets,largeseamounts
within20 km of theaxis,or melt solidifies,and melt may evenbe entirelycontained
near-axisfeaturesassociatedwith recentridgejumps or propaga- the crust.We note that for both scenariosthe rangeof parameters
is broad, particularlyfor the depth of
tion.Forthisinitialstudywe focuson lithosphere
coolingwidth which fit observations
and the dimensionsof the melt region.
melting.
The shapeof RMS misfitcanbe understood
by considering
gravityandbathymetry
RMSmisfitseparately,
shown
in Figures
3
Changing
thedepthof themeltregion
density
to vary.Thebulkdensity
of theregionwasscaled
with (middle)and3 (bottom).
sincethebulkdensity
of themeltregion
verticallengthof theregionin orderto produce
a highof 400 m will notaffectbathymetry,
accordingly.
Thereisa slightincrease
in bathemetry
RMS
at the axis;changingthe depthof the regionwill thenhaveno changes
coolingwidthscentered
near10 km. Othermodel
effecton topography
for a givenbulk density.
We compare
the for lithosphere
a differentvalueof lithosphere
weakening
(w),not
dependence
of topography
andgravityon thedimensions
of the runsassuming
shifted
melt regionto effectsof changing
the widthof lithosphericshown,reveala similarpattern,butwiththeRMS increase
as c• increases.
RMS
coolingW.For a closercomparison
to previous
models,effects slightlywherethe worstfit W decreases
of gravitymisfitshowa highcentered
near18kin.These
of thermalcontractionstresses
were not included(recall that the contours
canbe understood
by considering
the residual
gravity
modelformulation
is equivalent
to thatof Kuo et al. [1986]for patterns
for several
crustalthermalstructures
(theresidual
anomlithosphere
with zerothickness
at the axis).We assumeconstant anomaly
astheobserved
free-airanomaly
lessthemantle
valuesof h0, h •, $, and c• and temperatures
that increase aly is defined
correction
for topography
andlessthe contribution
of
linearlywithdepth.Synthetic
gravityanomalies
werecalculatedBouguer
usingthe methodof Talwaniet al. [1959],usingobserved crustalthermalstructure).Figure 4 showsthe mantleBouguer
anomaly
(MBA) andresidual
anomaly
for threevaluesof W.For
bathymetry.
forby crustal
thermal
Contours
of RMS misfitto gravityandtopography
for a range W< 5 kin,nearlyall theMBA is accounted
of lithosphere
coolingwidthsandmeltregiondepthsareshown structure.For W > 5 km the contribution from crustal thermal
is sogreatthata denseobjectwouldneedto be present
in Figure3 (thebestfit meltregionwidthandbulkdensity
for structure
We assumed
thatthe melt regionhasa trapezoidal
shapewith
variable dimensionsand allowed its depth, width, and bulk
30872
SHAH
•
AND
BUCK:
AXIAL
HIGH
TOPOGRAPHY
AT MID-OCEAN
2
RIDGES
2
0
2
4
6
0
10
20
10
W = 02 km
20
10
w = 20 km
1
2'0
o
o
1
1
2
2
3
3
4
4
5
5
6
1'0
o
20
W = 80 km
20
6
o
1'0
20
Distance from axis (km)
Figure4. (top)MantleBouguer
anomaly
(dashed
lines)fortheEPR8ø-8ø15'Sassuming
a 6-km-thick,
constant
densitycrust.Residualgravityanomaly(solidlines)(free-airanomalylesstopographyand thermalcontributions)
assuming
variousthermalstructures.
(bottom)Depthto 1200øCisothermfor thermalstructures
corresponding
to
aboveresidual
anomaly.
Wasshown,
ho= 1 km,hi = 6 km,and S = 0 m•/2.
below the axis in order to match observations. For W > 30 km the
For both temperaturedistributionsthe model temperatures
decreaserapidly over a narrow range near the axis and then
almost negligibly away from the axis. Fits without thermal
contraction stressesrequire 30% melt when temperatures
increaselinearly with depth but only 12-15% melt when the
lithospherehas been cooled by hydrothermalcirculation.This
seafloor.
reductionin requiredmelt arisesbecausea greateramount of
the lithosphereis cooledwith the latter temperaturedistribution,
increasingthe densificationload qc and allowingthe melt load
3.2.
Model Inversion
qm to decrease.Thermal contraction stressesalso reduce the
The forward models suggesta scenahoin which lithosphere amountof melt neededto negligibleamountsfor this temperand melt structuresare coupled and melt may be entirely ature distribution. This reduction occurs because deflections
containedwithin the crust.We thus assumeda new shapeto the associated with the contraction stresses add over 100 m of
melt region, where the boundariesare definedby the 1200øC relief to topography,the sameamountof relief createdby the
isotherm and the base of the crust at 6 km depth. We then melt load (for caseswith linear temperatureprofiles, thermal
examined the range of thermal structureswhich can produce contractionstressesadded at most 50-60 m relief, but the melt
observedtopographyand gravityby varyingall parametersshown contributed•200 m). Figures 5b and 6 show caseswhere we
in Table 2. To searchfor a best fit to data, we consideredthe RMS
have assumedthat 75% of the depth to the 1200øCisotherm
differencebetweenobservedand predictedtopographyand grav- has cooledto 200øC, which may be a large amount.Other
ity and minimizedthe scaledsumof theseover a rangeof model model runs with less of the plate cooled(not shown)predicted
parameters.The minimization,performedusing a Nelder-Meade 5-20% melt for 50% coolingand 17-26% for 25% cooling.
technique[e.g., Presset al., 1986], provideda set of parameters Thermal stresses
predicta much greatereffectiveelasticthickwhich can fit both typesof data,shownin Figures5a and 5b for nessfor both temperaturescenarios.
For caseswith hydrothermal
the two types of temperaturedistributionsin Figure 2. The temperature
distributions
thischangeis quitesubstantial,
from co=
contributions
to topographyfrom threedifferentsources,thermal 20-22% for no thermal stresses to co = 70-74%. This occurs
bending stresses(load qt), lower crustal melt (load qm), and becausethe narrow peak near the axis of the thermal stress
cooling of the lithosphere (load qc) for the best fit set of deflectionprofile allows the deflectionsdue to other sourcesto
parametersand temperature structure assuminghydrothermal be wider. We note that at distancesfar from the axis, thermal
coolingare illustratedin Figure 6. We note that the broadrange contractionstresses
contributelittle to the overalltopography,as
of data fits shownin Figure 3 suggests
a fair marginof errorfor the squareroot of distancecoolingproducesno load contribution
thesebest fit parameters.
[Parmentierand Haxby, 1986].
crustcoolsmuch more graduallywith distancefrom the axis, so
that not all the observedgravity anomalyis accountedfor, and
additionallow-densitymaterialis requiredbelow the axis. These
differencesin the residualanomalyillustratethe importanceof
gravity as a tool which can constrainthermal structurebelow the
SHAH AND BUCK: AXIAL
-40
-50
I
-30
,
I
HIGH TOPOGRAPHY AT MID-OCEAN
-20
,
I
-10
,
I
0
•
I
10
,
I
20
•
I
RIDGES
30
,
I
I
TBS
No TBS
1050
1050
h0=
1050
1048
W =
1995
2000
W =
1999
1998
hl =
5465
5900
hl =
5900
5896
No TBS
50
40
,
h0=
TBS
30873
S =
6.3
1.5
S =
2.5
2.8
to =
0.57
0.26
to =
0.52
0.26
(I) =
0.3
0.28
ß =
0.30
0.28
'
I
'
I
'
I
'
I
'
I
'
I
'
I
'
I
'
I
'
,
I
,
I
,
I
,
I
,
I
,
I
,
I
,
I
,
I
,
-200
-400
0
-lO
-15
-50
-40
-30
-20
-10
0
10
20
30
40
50
Distance From Axis (km)
Figure5a. Bestfit of stacked
bathymetry
andgravity
fortheEPR8ø- 8ø15'S,
assuming
temperatures
increase
linearly
withdepth.
(top)The1200øC
isotherm
andbestfitparameters.
Notethattheeastandwestsides
oftheridge
werefit separately.
Foreachflank,leftcolumn
parameters
areformodels
withthermal
stresses,
andrightcolumn
parameters
arefor models
withoutthermal
stresses.
(middle)Stacked
profiles
of bathymetry
andbestfit model
topography.
(bottom)
Stacked
gravityandbestfit modelgravity.
Dashed
linesindicate
solution
withthermal
stresses,
shadedlinesindicatesolutionwithoutthermalstresses,
andsolidlinesindicateobservations.
Forthesemodelruns,ho
waskepttoa valuenear1 km,since
mostAMCsof theEPRhavebeenimaged
atdepths
of •1 km[Detrick
etal.,
1987; Carbotte et al., 1997].
3.3. Behavior With Small Changesin Parameter Values
stress.For ho > 3 km the deflectionhas very long wavelength,
to that due to platecoolingalone.
Previous
geologicandgeophysical
observations
havesuggested comparable
3.3.2.
Long-wavelength
cooling(subsidence).Theeffectof
thatvariations
in morphology
maybe directlylinkedto thethermal
rate S is illustratedin Figure8. For S
and magmaticstructureof the crust.For a model primarily varyingthe subsidence
dependent
on thermalstructure,
we canexaminethe changes
in small a troughis visible at the base of the high, but with
S the troughdisappears.
The troughoccursnaturally,
shapeof the high with slightchangesin the valuesof some increasing
as
curvature
develops
at
the
axis,
and
its historyis maintained
off
parameters.
For simplicity,we considercaseswithoutthermal
axis. However, as S increases,so does the load qc owing to
bendingstresseffects.
If this load is greatenough,it will
3.3.1. Thicknessof axial lithosphere. Thereis an amplitude coolingof the lithosphere.
and counteract
the curvaturecreatingthe
reduction
of thehighastheaxiallithosphere
thickens(hoincreases) dominatetopography
trough.
(Figure7) because
of a combination
of two effects.With thicker
3.3.3. Width of lithospheric cooling and thickening,
axial lithosphere,
thereis a smallerregionof solidifyingmelt to
effective
plate thickness. Figure 9 showsmodel deflections
load the lithosphere.There is also less horizontaltemperature
contrastwithin the crustand thus a lower magnitudeof thermal for differentcoolingwidths W and strengthreductionfactorsco.
30874
SHAH AND BUCK: AXIAL
-50
-40
-30
HIGH TOPOGRAPHY
-20
-10
I
•
TBS
No TBS
h0=
1048
1045
W =
1995
2018
hl =
S=
5714
11.9
5839
8.5
co =
0.89
(I) =
0.043
0
I
•
AT MID-OCEAN
10
I
•
20
I
•
30
I
h0=
W =
hl =
RIDGES
•
40
I
•
50
I
TBS
No TBS
1050
1997
5711
2013
1027
5821
S=
13.3
10.4
0.30
to =
0.84
0.26
0.145
(I) =
0.001
0.124
-2oo
-400
•
0
-10
-15
'
-50
I
-40
'
I
-30
'
I
-20
'
I
-10
'
I
0
'
I
'
10
I
20
'
I
30
'
I
40
'
50
Distance From Axis (km)
Figure5b. Bestfit of stacked
bathymetry
andgravityfortheEPRbetween
8øSand8ø15'S,
assuming
temperature
structure
in Figure3 (middle),wherea percentage
of theplateis cooledto a constant
temperature
of 200øC.
Lithosphere
that is weaker,or to a lesserdegreethickensover a
narrowerdistancefrom the axis,produces
a narroweraxialhigh.
As w decreases,
there is a narrowingdue to the decreasein
flexuralwavelength.
For smallw, thereis a slightnarrowingof
thehighas W decreases,
butthereis littleresponse
to changes
in
W for largerw. The narrowingwith decreasing
W occursbecause
the maximumchangein temperature
is closerto the axisandthus
alsothe contribution
fromlithospheric
solidification
andcooling
(aswell asthemaximumchangein thermalbendingmoment),so
lithospherewhich is weak enoughto be considered
locally
supported
at the axis, (2) temperatures
which are near melting
temperatures
near the axis (exceptwithin the uppermostkilometer),whichdecrease
rapidlywithina few kilometers
of theaxis
(lithosphere
shouldhavea corresponding
structure),
(3) partial
meltwithinthelowercrust,and(4) someweakening
of theelastic
lithosphere.
The aboveconditions
will be mostoftenfoundat fastspreading ridges:A scenarioof frequentdikingis mostlikely to be
that the greatestdeflectionsare closerto the axis. This effect is associated
with a regionof discontinuous,
isostatically
supported
less apparent with larger w, since the increased flexural lithosphere.
In caseswheremagmaticactivityoccursfrequently
wavelengthcreateswider deflections,regardless
of how narrow but the axiallithosphere
is thick(sayfor a deeperaxialmagma
the load on the plate may be.
chamber),
the amplitude
of the highwill decrease,
suggesting
a
transition
to flat, intermediate-style
morphology.
At slowspreading, and someintermediate
spreading,
ridgeswe expectlitho4. Discussion
sphere
to
be
stronger
and
more
continuous,
so that stretching
4.1.
Features of the New Model
createsan axial valley. With the given model formulationthe
The abovestudiesshowthat a combination
of the following high can also be createdassumingthe presenceof a narrow
characteristics
cancreatean axialhighwith observed
dimensions, columnof melt which extendsdeep into the mantle,and lithowhichis consistent
withgravitydata,illustrated
in Figure10:(1) spherecoolsvery slowly with distancefrom the axis, similarto
SHAH
AND
[
BUCK:
I
]
AXIAL
I
[
HIGH
I
[
TOPOGRAPHY
AT MID-OCEAN
I
I
[
I
•
o-_.....
[
I
[
RIDGES
I
30875
[
I
]
[
....
- .......
-200
-400
•
I
[
I
[
I
[
I
[
I
[
I
[
[
[
[
0
-
-
• -200
-400
Cooling of Lithosphere
[ I • I ] I [ I [ I ] I ] I ] I [ I [
-200
-400
-•0
-40
-•0
-20
-• 0
0
•0
20
•0
40
•0
Distancerom axis
Figure 6. Breakdownof contributionsto topographyfor solutionsin Figure 5b for (top) melt solidification
contribution,(middle)lithosphericcoolingcontribution,and(bottom)thermalcontractionstresscontribution.Dashed
line indicatessolution with thermal stresses,shadedline indicates solution without thermal stresses,and solid line
indicatesobservedtopography.
that proposedby Madsen et al. [1984], Kuo et al. [1986], and
Wang and Cochran [1993]. The amount of melt required
dependson the type of temperaturedistributionassumedand
the degreeto which thermal contractionstressesare assumedto
play a role.
4.2.
Comparisons to Previous Models
The model formulationpresentedin this paperis equivalentto
that usedby Kuo et al. [1986] and Wangand Cochran [1993] if
lithospherethicknessat the axis is zero, yet neither of these
studies solved for the thermal structure preferred here. The
primary difference between those and our approachesis the
way that the lithospherethicknessand crustalthermal structure
are parameterized.Both Kuo et al. [1986] and Wang and
Cochran [1993] assumedlithospherethat thickens proportionately to the squareroot of age, and they associatedthe base of
the lithospherewith an isotherm estimatingthe brittle-ductile
boundary.To simulatea narrow zone of cooling,the squareroot
of age coefficientwould have to be very large, creating rapid
thickening deep within the mantle, a somewhat extreme scenario. Best fit solutionsthus required small squareroot of age
coefficients.However, a greatermelt load was then required to
supporttopography,which had to residedeepwithin the mantle
in ordernot to createa significantgravity anomaly.We note that
these two models are based on that initially proposed by
Madsen et al. [1984] and predict comparabledensity and melt
structures.
Magde et al. [1995] did considercrust which cools significantly over a few kilometersfrom the ridge axis and found that
most of the observedgravity anomalycould be attributedto the
associatedcrustaldensity structure.However, they did not take
into accountthe densityand lithospherestructurewhen determining topography,either for the contributionof changingdensities
or the flexuraleffectsof thickeninglithosphere(they assumelocal
isostasyfor the entireplate). For this reason,they still requireda
significantmelt load deepwithin the mantleto supportthe high at
the axis.
The Eberle and Forsyth [1998a] viscousstressmodel doesnot
require a region of buoyant material in the crust or mantle to
30876
SHAH AND BUCK: AXIAL
I
HIGH
TOPOGRAPHY
AT MID-OCEAN
I
I
RIDGES
I
1/2
-
-200
-
-400
-
-600
-
-800
-200
W=2km
H0=2km
H0=3
-400
km
H0=4km
- -lOOO
0
I
I
10
20
,
-1200
30
10
Distance From Axis (kin)
,
20
I
-800
30
Distance From Axis (kin)
Figure 7. Model deflectionsfor various values of ho with no
thermalstresses.
Parametersusedare W- 5 km, hl = 4 km, S = 0
m•/2,andco= 0.33.
Figure 9. Modeldeflections
for two valuescoolingwidthsWand
two valuesof weakeningcowith no thermalstresses.
Parameters
usedareho= 1 km,hl = 4 km,andS = 0 m1/2.
producean axial high and is thusconsistent
with resultsfrom the
crustnearthe axis,precludingthe development
of largestresses
MELT experiment.However,they alsorequireelasticlithosphere there.
whichthickensslowlywith distancefrom the axis.The factthatthe
crustbelowthelithosphere
hasa uniform
viscosity
of value10•9 4.3. Data Supportingthe New Model
stronglysuggeststhat the elasticlithosphereboundaryis also a
Model runssuggestthat both the proposedthermaland magthermalboundary.This placesit in a range of crustalthermal
maticstructure
proposed
hereandthatsuggested
by Madsenet al.
structures
assolutionssimilarto thoseof Madsenet al. [1984],Kuo
[1984] and otherscan fit both gravity and bathymetricdata.
et al. [1986], and Wangand Cochran [1993]. This model also
However,seismic[Veraet al., 1990] and compliance
data[Crawrequiresa relatively strong lower crust at the axis in order to
ford et al., 1999]collectedat theEastPacificRise(EPR),aswell
maintainextensional
stresses
there.This is significantlydifferent
as thermalmodels[PhippsMorgan and Chen, 1993;Henstocket
from the model we propose,where melt is presentin the lower
al., 1993], suggestthat the crust cools (and lithospherethus
thickens)rapidlywithin a few kilometersfrom the ridge axis.
Furthermore,
the presence
of a narrowcolumnof melt extending
deepwithin the mantleis inconsistent
with resultsfrom the MELT
experiment.For thesereasons,the previousmodelsseem less
preferable.We note that althoughthe thermal structureof the
1/2
-200
-400
•/2
-600
19.
-800
-lOOO
-1200
0
10
20
30
40
50
Distance From Axis (kin)
Figure 8. Model deflectionsfor varioussubsidence
ratesS with
no thermalstresses.
Parameters
usedare W = 5 km, ho= 1 km, hl =
4 km, and co= 0.33.
modelthatwe propose
is quitedifferentfromthatof theprevious
models,the effectiveelasticplatethicknessis actuallysimilarin
caseswherebestfit valuesof coare<0.5. An allowance
for plastic
weakening
of thelithosphere
maythusbe an important
component
of the model. However, crustwhich cools over a narrow distance
fromthe axisis alsocriticalto the model.The associated
density
variations
contribute
significantly
to theamplitudeof thehighand
thusreducethe amountof melt needed.Thesedensityvariations
alsoexplainmuchof the sourceof the observed
mantleBouguer
anomaly[seealsoMagde et al., 1995].
The amountof melt requiredin the lower crustis •30% for a
purelylineartemperature-depth
dependence
and0-15% assuming
that the upperpart of the lithosphere
is cooledto hydrothermal
temperatures.
Valuesnear 0% requirethe full effect of thermal
contraction
stresses. Because of the model's
one-dimensional
formulation,
effectsof thermalbendingstresses
are mostlikely
exaggerated,
so that the amountof melt neededis probably
somewhatgreaterthan 0%. Recenttomographystudiesat the
EPRnear9ø30'N[Dunnet al., 2000]suggest
the presence
of
melt within the lower crust,from amountsof 1% to 38% (the
greatest
percentages
only within a few hundredmetersdepthfrom
theaxialmagmachamber),
withaverage
estimates
roughlyranging
from •5
to 18%. These amounts are consistent with model
predictions
for temperature
profileswhich assumesomedegree
SHAH
AND
BUCK:
-40
AXIAL
-30
,
I
'
I
HIGH
-20
•
I
TOPOGRAPHY
-10
,
0
AT MID-OCEAN
10
,
I
20
,
I
RIDGES
30
•
I
30877
40
I
•
I
•
I
I
'
I
I
I
I
I
I
I • I • I a
-30
-20
-10
0
o
-200
-400
I
I
I
-!0
-15
I
-40
10
20
30
40
Distance From Axis (km)
Figure 10. Preferred
models.(bottom)Shadedareashowsdepthto the 1200øCisotherm.
Amountof requiredmelt
dependson degreeto whichthermalstresses
contribute,only roughlyestimatedin this study.Dashedlinesdepictthe
effectiveelasticplate thickness,for caseswith thermalstresses
(deeper)or without(shallower).Fits to (middle)
gravityand (top)bathymetry,
assuming
no thermalstresscontribution.
Solidline indicatesstackedbathymetryand
gravity(EPR,8ø-8ø15•S).
Shaded
lineindicates
modelprediction.
somewhat reduce the amount modeled within the crust and should
greaterdepthsthan for fast spreadingridges[Purdy et aL, 1992].
This suggests
a link betweenthermalstructureimmediatelyat the
axis and amplitudeof the high. This sort of dependencealso
occursfor lithospherethe structureof Kuo et al. [1986]. Eberle
and Forsyth [1998a], on the other hand, find that their viscous
stressmodel actually predictsa taller axial high for a deeper
not changepredictedtopography
andgravitydramatically.
A small
AMC.
amount of melt within the mantle would be consistent with Moho
A noted feature present over much of the southern East
Pacific Rise is a •70-m-deep, 5- to 10-km-wide trough at the
base of the westernside of the axial high [Eberle and Forsyth,
1998b]. Observations such as numerous seamounts on the
westernflanks of the axis [Scheireret aL, 1996], an asymmetric
low-velocity zone at shallow mantle depths [Forsyth et al.,
1998], and lower best fitting subsidencerates on the western
flanks versus the eastern flanks [Eberle and Forsyth, 1998b]
suggesta relativelywarm thermalregimeover the west flank of
the EPR in this region. For relatively small valuesof the rate at
which the lithospherecools away from the axis (i.e., reducing
our parameterS), the modelsdisplaysucha trough,thoughover
a longerdistance.The model might be able to bettermatchthe
of hydrothermalcooling. The degreeto which water cools the
uppercrustis poorly constrained,
but someamountof coolingin
combinationwith a contributionfrom thermalstresses
yields melt
amountswhich are consistentwith the tomographyresults.Incorporatinga small degreeof melt within the shallowmantle will
melt lensessuggested
by Crawfordet al. [1999] and Dunn et al.
[2000].
With an axial high that is dependenton thermaland magmatic
structureof the crust,we can examinethe responseof morphology to varyingmodel parameters.Increasingthe thicknessof the
lithosphere (ho) at the axis has the effect of reducing the
amplitudeof the high. A proxy for axial lithospherethickness
may be depth to a melt lens. At ridges with intermediate
spreadingrates,axial highsare sometimes
presentbut may show
a decreasein height [Semp&• et al., 1997; Cochranet al., 1997;
G•li et al. , 1997]. Where axial magma chambershave imaged
beneathintermediatespreadingridges, they generally appear at
30878
SHAH
AND
BUCK:
AXIAL
HIGH
TOPOGRAPHY
dimensionsof this trough if highly localized weakening effects,
such as those createdby faulting, were taken into consideration.
We note that Eberle and Forsyth [1998b] were also able to
model this trough by reducing the viscosity within the lower
crust for their viscous stressmodel. Model runs by Kuo et al.
[1986] exhibit a small trough at the base of the axial high for a
plate with minimal off-axis thickening (in the extreme, a uniform thicknessplate).
Correlationsbetween morphology and indicatorsof thermal
and magmatic structureof the crust have been observedover
much of the EPR: Regionswith a wider axial high are generally
associatedwith a lower mantle Bouguer anomaly,the presence
of a melt lens, more recent lava flows, and less fractionated
basalts [MacdonaM and Fox, 1988; Scheirer and Macdonald,
1993; Hoofi et al., 1997]. The modelswe presenthere predict a
slightly wider axial high for crust which cools over a greater
distancefrom the axis (W larger) and for which a wider region
of melt is present.This effect is most pronouncedfor caseswith
significantplate weaking (cosmall). A wider melt region seems
more likely to producemore recent eruptionsand an imageable
melt lens. These variations are likely both from segmentto
segmentand on a smallerscalealong-axis,where a wideningof
a high toward a segmentcenter suggestsa warmer and more
magmatic regime there. Models based on the work by Madsen
et al. [1984] that assume that the source of the high resides
primarily in the mantle do not implicitly reproducethis dependence. If the crust is assumedto cool over a narrow region
(implying rapid lithosphericthickening),the modelswill predict
a wider high due to the increase in the plate's strengthand
hence flexural wavelength. This effect could be offset by
narrowing the width of the melt region in the mantle and
allowing only slight variations in lithospheric cooling rate.
However, this then suggeststhat processesin the mantle, rather
than the crust, will control the width of the high. Effects of
these types of lithosphericvariations on predicted topography
using the Eberle and Forsyth [1998a] model have not, to date,
been examined
in detail.
AT MID-OCEAN
RIDGES
of small amountsof melt within the mantle, as suggestedby
previousseismicand complianceresults.
Varying model parameterssuggestthat certain morphologic
featuresarehighlydependenton thermalstructure,includingwidth
and heightof the high and presenceof a flankingtrough.Each of
the parameterdependenciesis consistentwith other geologic
observations.
A wider high is producedgiven a wider region of
warm material, consistentwith correlations between width of a
high and indicatorsof a "robust" magmaticstructure.Reducing
the rate of long-wavelengthcoolingwill producea troughat the
base of the high, consistentof such troughs observedon the
westernflank of the southernEPR between15øSand 20øS,where
thepresenceof abundantseamounts
andotherobservations
suggest
thinner lithospheresome distancefrom the axis. For thick axial
lithospherethe modelpredictsa reductionin heightof the high,
comparable
to thatobservedat someintermediatespreadingridges
and consistentwith observationsof deep magmachamberreflectors at intermediateridges.Lithosphericthicknessnear the ridge
axis can be considereda major componentof the initial transition
from fast-to intermediate-style
morphology,
until discontinuity
and
local isostasyat the axis becomeless likely, with less frequent
diking events.
Severalsimplifyingassumptions
are implicit in the model, such
as a steadystatethermalstructure,two-dimensionality,
simplistic
thermalstructures,
and simplisticlithosphericweakeningregimes.
However,the modelcanpredictsegment-scale
topography,
assuming a thermal and magmatic structureconsistentwith gravity
observations
and other data.
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(ReceivedNovember28, 2000; revisedApril 24, 2001;
acceptedApril 30, 2001.)