Download Mechanisms for the Origin of Mid-Ocean Ridge Axial Topography: Implications

JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 92, NO. B12, PAGES 12,823-12,836, NOVEMBER
10, 1987
Mechanismsfor the Origin of Mid-OceanRidgeAxial Topography:
Implicationsfor the ThermalandMechanicalStructureof AccretingPlateBoundaries
JASON PHIPPS MORGAN
Departmentof Earth, Atmospheric,and Planetary Sciences,Massachusetts
Instituteof Technology,Cambridge
E.M. PARMENTIER
AND J. LIN
Departmentof Geological Sciences,Brown University,Providence,Rhode Island
To better understandthe implicationsof ridge axis morphologyfor the thermal and mechanicalstmcture of accretingplate boundaries,we examinemechanismsfor the creationof stress-supported
axial topography and its dependenceon parameterssuch as spreadingrate, asthenosphereviscosity, and plate
thicknessnear the ridge axis. Three basic mechanismsare considered:(1) asthenospheric
upwelling in
a narrow, steady-stateconduit beneatha ridge axis; (2) mantle flow stressesdue to plate spreading,
extending ridge axis lithosphere, or melt segregationand associatedmantle compaction; and (3)
topographysupportedby momentsdue to horizontal extensionalstressesin a thickeninglithosphere.If
mid-oceanridge topographyis due to asthenosphere
rising in a narrow conduit at the ridge axis, then
the conduit structurecannot be thermally controlled, as the associatedthermal structurehas relatively
broad, flat isothermsinsteadof a conduitlikeshape.Mantle flow associatedwith plate spreadingalone
inducesno stress-supported
topography. Thus the intuitive notion that divergingflow at the ridge axis
due solely to plate spreadingproducesthe axial valley is incorrect. Vertical mantle flow at the baseof
a stretching,accretinglithosphereand mantle flow associatedwith melt segregationcan, however, lead
to stress-supported
axial topography.However, for thesemantle flow related processesto producesignificant amounts of axial relief, the mantle viscosity beneath the ridge axis must be on the order of
1020Pas (1021P (poise)),
significantly
higherthangenerally
accepted
valuesof 1018Pas (1019P).
Horizontal extensional stressesin a strong, brittle lithosphere that thickens with distance from the
ridge axis can produceaxial topographyof the form and amplitudeobservedon slow spreadingridges.
A continuumidealizationof deformationdue to faulting is used to examine this mechanism. This model
predictsthe axial valley width is controlledby the plate thicknessnear the ridge axis. An 8-km-thick
plate near the ridge axis would producethe 30-km-wide axial valley observedat slow spreadingridges.
An increasedlithospherethicknessof only several kilometers over the half-width of the axial valley
can producekilometer-scalerelief. To examine whether a plate 8-10 km thick at the ridge axis that
thickensby severalkilometerswithin 15 km of the axis is plausibleat a slow spreadingridge, thermal
modelsthat includeboth the heat of magmaticcrustalaccretionon the ridge axis and upwellingmantle
flow beneaththe axis are formulated. Hydrothermalcoolingthat increasesthe effective conductivityby
about a factor of 10 is required for an 8-km-thick plate to exist at a slow spreadingridge axis.
However, even with this enhancedhydrothermalcooling, the plate thicknessat a fast spreadingridge
axis and the resultinghorizontalforce in the plate are too small to result in appreciabletopography.
While mid-oceanridge axial topographyis stronglyinfluencedby spreadingrate, other factors also
shapeaxial structure. For example,the anomalouslyshallow slow spreadingReykjanesRidge has an
axial structuremorelike that of a fast spreadingridge, and the anomalouslydeepintermediatespreading
Australian-Antarctic
Discordancehas a medianvalley axial structuretypical of a slower spreadingridge.
In addition, within a given spreadingsegmentthere is often a systematicdeepeningof the ridge axis
toward transform offsets. These non-spreading-rate-dependent
axial topographicvariations may be
producedby variationsin magmaticheat input associatedwith crustalemplacementwhich shapesthe
thermalstructureand lithospherethicknessnear the ridge axis.
INTRODUCHON
slow spreadingrates but vanishesat faster spreadingrates.
Since seafloor bathymetry is the most frequently acquired
The well known difference in the axial topography of
and widely available geophysicaldata, it is also important
slow and fast spreadingmid-oceanridges is shownin Figure
to understandthe possibleimplicationsof ridge axis topog1 by typical topographicprofiles across the axes of slow,
raphy for the thermal and mechanicalstructureof accreting
medium, and fast spreadingridges. The characteristic1-kinplate boundaries.
deep axial valley and flanking crestalmountainsthat form at
In the few areas where data of sufficient quality and
slow spreadingrates do not exist at faster spreadingrates,
resolutionhave been obtained,gravity anomaliesprovide an
where instead relatively low relief axial topography is obimportant observationalconstrainton the origin of the axserved. Although this spreadingrate dependenceof ridge
ial valley and particularly the possiblerole of crustal thickaxis morphology is widely recognized, there still are no
ness variations in producing the axial valley topography.
conclusive explanations of why an axial valley exists at
Gravity data for a segmentalong the Mid-Atlantic Ridge
from about 13ø to 15øN has been reportedby Collette et al.
Copyright1987 by the AmericanGeophysicalUnion.
[1980]. The amplitudeof the observedgravity anomaly
showsthat the ridge axis topographycannotbe isostatically
Paper number7B5032.
0148-0227/87/007B-5032505.00
compensatedat a depth as shallow as 6-8 km and so cannot
12,823
12,824
PHIPPSMORGANMr AL: THE ORIGINOFMOR AXIAL STRUCRJRE
PB
VV
PB
VV
i
PB
FAST
( EPR3 øS)
i
PB
INTERMEDIATE
( EPR 21øN )
PB
I
v
MAR 37 ø N )
VE ,.-, 4x
AXIS
I
,
2:0
I
I0
,
I
,
I
0 KM
,
I0
I
,
20
I
30
Macdonald
(1982)
Fig. 1. Axial topographyalong profilesperpendicularto typical slow (5-25 mm/yr), intermediate(25-45 mm/yr), and
fast (>45 mm/yr) spreadingridge axesfrom Macdonald [1982]. A 1- to 2-km-deep,30-kin-wide axial valley with flanking
crestalhighs is presentat slow spreadingridges.At fasterspreadingratesthe axial topographyis much more subdued.The
symbolsV and PB on the profiles delineatethe width of the regionof active volcanismalong the spreadingcenterand the
boundariesof the region of active faulting, respectively. EPR is East Pacific Rise; and MAR, Mid-Atlantic Ridge. The
profileshave a vertical exaggeration(VE) of 4.
be explained by crustal thicknessvariations [Collette et al.,
1980; Parmentier and Forsyth, 1985]. Furthermore,seismic
refraction studies along the Mid-Atlantic Ridge [Purdy and
Detrick, 1986; Louden et al., 1987] do not show abnormally
thin crust beneath the axial valley. Thus, both gravity and
seismic
refraction
studies
indicate
that the crust within
the
prescribedso that the horizontally moving plate thickens
rapidly with distancefrom the ridge axis, forming a conduit
at the axis with a width that is comparableto the width of
an axial valley. Flow in a mantle half-space of uniform
viscosity occurs due to both the horizontal motion and accretion of the plate.
The steady-state thermal structure
based on these velocities is shown by isothermsat specified
fractionsof the deep mantle temperatureT,n. The shapeof
the bottom of the plate clearly differs greatly from that of
the isotherms.While the localized upwelling at a ridge axis
due to the presenceof a conduit transportsheat into the region beneath the ridge axis, cooling within the rigid plate
is due primarily to vertical heat conduction,resulting in the
shallow, genfiy sloping isothermsshown in Figure 2. The
release of latent heat beneath the ridge axis would raise the
temperatureand elevate isothermsto shallower depths. The
axial valley is essentially the same thickness as that of
older seafloor. Therefore, the axial valley must be a dynamically maintained, stress-supportedtopographicfeature.
In this paper we examine simple models for the origin of
ridge axis topography. While a number of previousmodels
have been presented,these models do not generally provide
a clear indication of the origin of vertical forces responsible
for the large-amplitude topography at slow spreadingridge
axes. To provide a framework and motivation for our discussion of simple models, we begin by reviewing previous
models for slow spreadingridge structure.
isotherms would, however, maintain their gently sloping
character
since this is controlled by vertical heat conducPREVIOUS MODEI3 FOR AN AXIAL VAT J.FY
tion.
Sleep [1969] and Lachenbruch [1973, 1976] have suggestedthat the structureof a slow spreadingridge axis consists of a vertical conduit through which asthenosphererises
to form a thick plate near the ridge axis. This is presently
the only model which explicitly addressesthe origin of vertical forces producing the axial valley morphology. In this
model, the viscous pressure drop associatedwith vertical
flow in the conduit creates the axial valley depression.
Vertical forces resulting from shear stresseson the conduit
walls support the elevated flanking crestal mountains. The
principal difficulty of the steady-state conduit model is to
explain the existenceof a conduit in terms of thermal structure and reasonable rheological behavior. Specifically, if
the lithosphere forms by conductive cooling and the
strength or viscosity of mantle rock is primarily a function
of temperature, then a conduit of the type envisioned by
these studies should not form. This is shown by the example in Figure 2. The methodsused to obtain this result will
be discussed
later . In this example,the plate thicknessis
The
above results
indicate
that no conduit
would
be
presentif the viscosity of mantle rock dependsprimarily on
temperature.
It has frequently been suggestedthat a conduit could form
due to a weakeningeffect of partial melt or water. However,
studiesof magma migration suggestthat even small amounts
of melt forming a connected network can rapidly migrate
out of a solid matrix. Studies of the strength of olivine
containing basalt melt [of. Cooper and Kohlstedt, 1986]
suggestthat the principal effect of small amountsof melt
will be to enhance deformation related to grain boundary
diffusion. For deformation that occurs by a combinationof
dislocationcreep and grain,boundary diffusion, the presence
of a few percentmelt enhancesthe deformationrate only by
a factor of 2-5 [Cooper and Kohlstedt, 1986]. A recent
study [Karato, 1986] suggeststhat the presenceof a small
amount of melt may actually strengthen partially molten
rock becausewater, which weakens mineral grains, is partitioned into the melt. Therefore while the effect of partial
melting on the strength of rock is not fully resolved, our
PttIP•MORGAN
ETAL:TIlEORIGIN
OFMORAXIAL
STRUCTURE
.3
.5
.7
.9Tm
50 km
Fig. 2.
Thermal and mechanicalstructureof a slow spreadingmidocean ridge with a prescribedconduitlikemechanicalstructure. The
lithosphere (dot shaded) moves horizontally and thickens rapidly
near the ridge axis forming a conduit. Streamlinesshow viscous flow
beneaththe plate due to plate motion and accretion assumingthe
mantle is a uniform viscosity half-space. The thermal structure
corresponding to this velocity field is shown by isotherms at
specifiedfractionsof the deepmantletemperatureTm. The bottomof
the lithosphereclearly does not correspondto an isotherm, thus a
steady-stateridge axis conduit cannot be present if the strength or
viscosity is solely a function of temperature.
current understandingindicatesthat small amountsof partial
melt will not reduce the strength by the several orders of
magnitudethat would be neededto form a ridge axis conduit.
Compositional change resulting from melt extraction will
raise the solidus temperatureand therefore the viscosity of
the residualmantle rock. The viscositydue to thermally ac-
12,825
sated by elastic flexure of the lithosphere producing the
flanking uplift of the crestal mountains. This is essentially
the Vening Meinesz [1950] model for rifts. In its application to mid-ocean ridges, the model does not explain the
amplitude and width of the ridge axis depressionin terms of
other physical variables, such as extension rate and plate
thickness. Furthermore,a variety of evidencesuggeststhat
the lithosphere deforms by faulting near the ridge axis.
Studies of seafloor structure [Macdonald and Luyendyk,
1977; Macdonald and Atwater, 1978; Laughton and Searle,
1979; Macdonald, 1982] have concludedthat axial valley
relief is a consequenceof faulting. Studies along the MidAtlantic Ridge south of the Kane fracture zone [Toomey et
al., 1985] show that seismicityextendsto depthsof about 8
km and that microearthquakesoccur beneath both the axial
valley floor and the crestal mountains. Deformation due to
faulting is not well describedby simple elastic flexure.
The numerical models of Sleep and RosendaM [1979] were
the first to include the effects of a viscoplasticplate and
quantitatively predict the formation of an axial valley.
However, the geologiclike complexity of the assumed
thermal and theological structure combined with limited
numericalresolutiondoes not permit a simple understanding
of the mechanism(s)causing the calculated axial valley
morphology.
Our approachhas been to examine simple models which
isolate potentially important physical mechanismscausing
seafloor topography near a ridge axis. We will show that
horizontal extensionalstressesin a strong continuouslydeforming plate near the ridge axis can produce an axial valley-like ridge axis morphology. Stressesdue to mantle flow
and melt segregationbeneath an extendingplate can produce
a similar morphology,but a mantle viscosity significantly
higher than generally acceptedvalues would be required to
explain the observed axial valley relief.
TOPOGRAPHY DUE TO MANTLE FLOW STRESSES
tivatedcreepis proportional
to exp(ATm/T
) whereA ~ 40
If lithosphericstretchingis occurringnear the ridge axis,
and T m is the melting temperature[e.g., Brace and
Kohlstedt,1980]. Thus,if meltingincreases
Tm by 100øC then either vertical mantle flow or magma intrusion into the
as suggestedfrom petrologic studies,this would increase the
viscosity by approximatelytwo ordersof magnitude. While
this effect has not been previously considered,it is potentially important and could result in the formation of the
strong lithosphere forming conduit walls [cf. Lachenbruch,
1973]. Alternatively, if the compositionchanges affect the
solid fraction of conduit manfie and the presence of melt
does not significantly reduce the viscosity, this effect could
actually increasethe viscosity of material in the conduit.
It is also important to question whether a conduitlike
thermal structure may result from hydrothermal cooling.
This questionwill be explored in more detail later, but hydrothermal cooling that is simply describedby an enhanced
thermal diffusivity will produceeven flatter isothermsin the
mantle beneath the ridge axis. The simple example in Figure 2 does not prove that a steady-stateconduit cannot exist,
but shows that special assumptionsabout mantle theology
or hydrothermalcooling are required.
Tapponier and Francheteau [1978] first suggestedsteadystate necking as a conceptualmodel for slow spreadingridge
axes. Their model consists of two parts: first, that extension of the plate creates a seafloor depressionat the ridge
axis and, second,that this depressionis regionally compen-
stretching lithosphere is required to balance lithospheric
thinning due to stretching and thus maintain a steady-state
lithosphere thickness distribution. Vertical manfie flow at
the base of a stretchingand accretinglithosphereis capable
of producingstressesthat can supportridge axis topography
[Phipps Morgan and Parmentier, 1984]. However, in the
following analysiswe will show that mantle flow can create
a significant axial valley depressiononly if mantle viscosities beneath the ridge axis are at least two orders of magni-
tudelarger(1020Pas or 1021P) thancommonly
accepted
values(1018Pa s or 1019P). Mantleflow will be induced
by both vertical and horizontal motion at the bottom of the
lithosphere and by melt segregation. We will first consider
mantle flow induced by motion at the bottom of the lithosphere and discussthe effects of melt segregationon mantle
flow in the following section.
Considerflow in a mantle half-spaceof uniform viscosity
beneath a planar, horizontal lithosphere-asthenosphere
boundary. Flow in the half-space induced •'Oyvertical and
horizontal flow along the top, z=0, can be representedas a
superposition of Fourier harmonics in the horizontal x
coordinate. For each Fourier component of horizontal or
vertical velocity on the top of the mantle half-space, u or w
12,826
PttIPPS
MORGAN
ETAL:THEORIGIN
OFMORAXIAL
STRUCTURE
'
U
I
'
•
)•I I•_•+
I
u(x
dx)
Velocities:
u/U
1
I
L,J
w
0
0
x/L
I
2
I
I
4
Topography:
3
•UH/ApgL2
Fig. 3. Axial topography
dueto verticalmantleflow at the baseof extending
lithosphere.(Top)Modelin which
extending
lithosphere
thickens
slowlywithdistance
fromtheridgeaxis.Thethickness
variation
shownis exaggerated
for
clarity.(Middle)Verticalmantlefloww across
theapproximately
planarbaseof thelithosphere
(dashed
line)canbe found
by considering
flow into the baseof a stretching
columnof lithosphere
with horizontal
velocityu(x) thatis neededfor
steaidy-state
materialconservation.
The assumed
errorfunctionplatespreading
distribution,
corresponding
to a Gaussian
upwellingdistribution,
produces
the axial topography
shown.(Bottom).Here •5 is the topography,
•t is themantle
viscosity,
U is the half-spreading
rate,H is the platethickness
in the stretching
region,L is the half-widthof the
stretching
region,Ap= Pm-Pw is thedifference
between
mantleandwaterdensities,
andg is theacceleration
of gravity.
respectively, the induced normal and shear stresseson the
viscosity
[x=1021
P (1020Pa s), an axialvalleyhalf-width
top of the half-spaceare •Yxz= -2•tku and•Yzz= -21.tkw,where
k is the wavenumber.The stressesresultingfrom any prescribeddistributionof horizontal or vertical velocity can be
obtainedby the superpositionof Fourier components.Thus
any horizontal distributionof velocity (w=0) on the top of
the mantle half-space will produce flow-induced shear
L=15 kin, a ridge axis lithospherethicknessH=8 km, and a
half spreadingrate U=20 mm/yr (20 km/m.y.), this mechanism predictsa 1-kin-deepstress-supported
axial valley.
Smaller mantle viscosity, smaller lithosphericthickness
near the ridge axis, and smaller amountsof lithospheric
stretching
wouldall reducethe amplitudeof the topography.
Note that in calculatingthe seafloortopography,mantle
flow inducednormalstressesare assumedto be supported
simple result contradictsthe intuition that the diverging only by buoyancyforces arising from topographyat the
flow due to plate spreadingwill producean axial valley hole crust-waterboundarywith no contributionfrom the strength
at the ridge axis [cf. Nelson, 1981].
of the lithosphere.This will overestimate
the topography
if
For a lithosphere-asthenosphere
boundarythat is nearly someof the verticalforceat the bottomof the plateis supbut not exactlypl•anar,mantleflow into a stretchingsteady- ported by stresseswithin the plate.
To consider lithosphere thicknessvariations in the more
statelithospherecan be approximatedas shownin Figure3.
The net upwar
d flow is simplythe difference
in thehorizon- general case of a highly nonplanar lithosphere-asthenotal flow enteringand leaving a thin vertical slice of height sphereboundaryandto assess
the accuracy
of the aboveapH, sowI z=0= HOu/Ox,
whereH is thelithosphere
thicknessproximationof a nearly planarboundary,boundaryelement
stresses at the bottom of the lithosphere but no vertical
normal stressesthat can support seafloor topography.This
outsidethe axial region of stretchingand accretion. With a
prescribed spreading velocity u=Uerf(x/L), the calculated
normal-stress-supported
topographyis shown in Figure 3.
Stressesresultingfrom the prescribedvertical velocity were
calculatedusinga standardfast Fouriertransform(FFT) algorithm with 256 uniformly distributedpoints. For a mantle
solutions for the mantle flow induced normal stress distribu-
tion were obtainedfor the severalplate thicknessdistributionsshownin Figures4a-4d. For this problem,the boundary elementmethod(BEM) has two basic advantages
over
other methods:(1) for arbitrarily shapedtwo-dimensional
regions it is a simpler task to discretize a one-dimensional
PftIPPSMORGAN ET AL: •
ORIGIN OF MOR AXIAL S'IRUCTURE
12,827
1
Spreading
Velocity:
u/U
1
1
Topography:
•UH/A0gL 2
•UH/A0gL 2
-3
-3
Flowlines:
Fig. 4a
Spreading
Velocity:
Fig. 4b
u/U
u/U
1
lO
Topography:
]JUH/A0gL2
-30
-3
Flowlines:
Fig. 4c
Fig. 4d
Fig.4. Mantleflowandaxialtopography
for several
prescribed
distributions
of lithosphere
(dotshaded)
thickness
and
horizontal
extension
rate.Spreading
velocity
distribution
andcorresponding
topography
areshown
at thetopof each
figure. Streamlines
of themantleflowareshownat thebottomof eachfigure. Symbols
andnotation
arethesameasin
Figure
3. (a) Constant
thickness
lithosphere
thatis emplaced
entirely
at theridgeaxisandspreads
witha uniform
velocity.
(b) Constant
thickness,
stretching
andaccreting
lithosphere
equivalent
to themodelof Figure
3. (c) Slowly
thickening
stretching
andaccreting
lithosphere.
(d)Ridgeaxisconduit
withcorresponding
thermalstructure
shownin
Figure 2.
12,828
PHIPPSMORGAN ET AL: THE ORIGIN OF MOR AXIAL STRU•
boundary than the whole two-dimensional region, and (2)
there are no numerical complicationsneeded to enforce the
incompressibilitycondition. The BEM is an extremely convenient technique for solving problems in a piecewise homogeneousmedium where an exact Green's function solution
is known. In the BEM, this singular solution is integrated
to find the solution for a particular Green's function
distribution over a line segment; for example a constant,
linear, or quadratic distribution could be employed. The
boundaryis discretizedinto a f'mite numberof boundaryline
segments or elements, and influence coefficients are calculated that relate the contribution
to the stresses and veloci-
ties on one element from given stressesor velocitiesacting
along another element. In the present application of the
BEM, each boundaryelement is a line segmentwith a uniform distribution of normal and tangential force acting
along it. This results in unknown normal and tangential
force magnitudesfor each element. The velocity or stress
distribution along the boundary is prescribed,and with velocities evaluated at the center of each element, the distribu-
tion of boundaryforces which will producethis prescribed
boundary velocity and stress distribution at each element
midpoint is calculatedby solving a linear systemof equations for the unknownmagnitudesof the boundaryforce distributionfor each boundaryelement. The known boundary
force distribution
can then be used to calculate
stretchingw(x)= H(x)3u/3x. (2) Alongthe ridgeaxis(x=0)
a symmetry condition is assumed(u=0, Xxz=O). Computationally, elementson the right-hand side of the ridge axis
which mirror thoseon the left-handside of the ridge axis are
constructed. Becauseof this symmetry only unknownsfor
the right-handside of the ridge axis need be computed,and
no boundaryelementsare neededon the vertical boundary
directly beneaththe axis. (3) Along the bottom of the box,
stress-freeboundariesare assumed. (4) At the right-hand
side of the box (x=L) the horizontal and vertical velocities
are prescribedas the solutionfor a planar half-spacewith a
uniform horizontal velocity along the top which is at a
depth H(L). At least 50 elementsalongthe top and 40 elementsalong the fight side and bottomwere used. Boundary
solutions will
H*=lw(x)H(x)a/lw(x)a
be least accurate near the boundaries
defined.
Thecalculated
ridge
axis topographyfor a slowly varying thickness H=H(x) and
w=HOu/Ox in Figure4c is almostidenticalin both form and
amplitude to that calculated with a constant lithosphere
thicknessH=H* andw=H*Bu/•x (Figure3 or 4b).
The componentof mantle deformationthat producesaxial
valley-like topographycan be seen in the mantle streamlines of Figure 4. The streamlinesbeneaththe ridge axis
convergeas they near the base of the lithosphere,indicating
a vertical stretchingof the mantle beneath the ridge axis.
The corresponding tensional vertical deviatoric normal
stresssupportsthe axial valley depression.
For large variations in lithosphere thickness near the
ridge axis, as in the case of a ridge axis conduit, the
approximations
of a nearly planar lithosphere-asthenosphere
boundarybreak down. Boundary element solutionscan still
be obtainedfor thesecases.The examplein Figure 4d shows
that the presenceof a conduitlocalizingupwardmantleflow
at the ridge axis greatly increasesthe predictedridge axis
topography.The increaseover that in Figure 4c is by about
a factor of 10 for this particular lithospherethicknessdistribution.
the stresses
or velocities at any point within the region.
The program (TWOFS) used in the presentstudy is describedby Crouch and Starfield [1983], who also presenta
more complete developmentof the BEM. The following
boundary conditions are prescribed. (1) Along the lithosphere-asthenosphereboundary, velocities are set to the
horizontal plate velocity u(x) and vertical velocity due to
element
sphere-asthenosphere
boundary. To comparethe two results,
an average lithospherethicknessin the stretchingregion
TOPOG•HY
DUE TO 1VIELTSF_.I3REGATION
The steady state segregation of melt fi'om mantle matrix
and the resulting matrix compactiondue to the loss of melt
volume
will
create an effective
volume
sink within
the man-
tle. The mantle flow to fill in this mass deficit in the segregating and compactingregion can produceaxial topography.
Melt segregationand associatedmantle compactionis idealized as occurring at a single line sink beneath the ridge
axis. The line sink may be regardedas a small compacting
region of cylindrical cross section. A more realistic segregating and compactingregion can be constructedby superimposing•these line sink solutions. The normal-stress-supported topographydue to a line sink at a depth D beneath
the surface of a viscous halfspace, in this case the crustmantle boundaryat the ridge axis, can be found by addinga
line sink solution at a depth D below the surface to an image sink a distanceD above the surface. The resulting normal-stress-supported
topographyis shown in Figure 5. For
a melt removal rate equal to the crustalproductionrate 2UH
at the ridge axis, where H is the crustal thicknessand U is
the half-spreadingrate, the maximum axial valley depression
is approximately
gUH/ApgD
2, where
Ap--Prn-Pw,
}xisthe
of the region, where the assumeddiscontinuousforce distribution is an imperfect approximationto continuousvelocity
or stressboundary conditions. However, accordingto Saint
Venant's principle, solutionswill become increasinglyaccurate away from the boundaries of the region. From the
agreement between boundary element and semi-analytical
FFT solutionsfor the planar half-spaceproblem (Figures 3
and 4b), stressesat the element midpointsalong the lithosphere-asthenosphere
boundaryare expectedto be accurateto
better than 5% for all the lithospherethicknessdistributions
shown in Figure 4.
viscosity of the mantle matrix, g is the acceleration of
gravity, and D is the depth to the segregatingregion.
This solution, which is formed by superimposingtwo line
sinks [cf. Batchelor, 1967, p. 89], produces the correct
normal stressbut satisfies a shear stress-freeboundary condition instead of a no horizontal velocity boundary condition at the surfaceof the half-space.To solve for the contribution to mantle flow from melt segregation beneath a
spreading center, a complementary solution to cancel the
horizontal flow generated at the crust-mantle boundary by
Figure 4c showsthe mantle flow and associatedaxial to-
This complementary solution can be obtained by the complex-variable techniques developed, for example, by
Muskhelishvili [1953, p. 584]. Since it involves only horizontal flow at the surface of the half-space, this comple-
pography due to stretching and accretion of a variable
thicknesslithosphere.This is almost identical with the earlier result of Figure 3 which assumesa nearly planar litho-
the two
line
sink
solution
must
be added
to this solution.
PHIPPS
MORGAN
ETAL:TIlEORKEN
OFMORAXIALSTRUCRJRE
Topography:
x/L
12,829
tered 15 km beneath the crust-mantle boundary would produce a 30-km-wide axial valley. For a mantle viscosity of
1020 Pa s, a 1-kin-deep
axial valleywill resultfrom an
along-axis
crustalproduction
rate rn = 2UH = 230m2/yr
correspondingto U = 20 mm/yr and H = 6 km. Melt segregation occurringat greater depthswill producea broader and
shallower axial valley for otherwise identical model parameters. For a similar mantle viscosity, depth of melt segregation, and crustal thickness,ridge axis topographyassociated
with melt segregationshould be greater on faster spreading
ridges. If crustal thickness and mantle viscosity are
approximatelythe same on fast and slow spreadingridges, a
larger-amplitudetopographyat slower spreadingrates could
be explained by shallower or more localized melt segregation. However, melt segregation can contribute significantly to axial topography only if there is a strong
localization of melt segregation and the asthenosphereis
moreviscous(1020Pa s) thanit is usuallythought
to be
(1018Pa s). Streamlines
in Figure5 showtheflow in a
mantle half-space due to melt segregationin a small cylindrical region 30 km beneaththe crust-mantleboundarycombined with flow due to plate spreading. The plate spreading
flow is described by vertical and horizontal velocities u=
1
2
2
2U[tan(x/z)-xz/(x
+z2 )]/n andw=-2Uz2 /[n(x2+z
)], respec-
tively, with streamlinesshownin Figure 4a. Note that flow
induced by melt segregation and associated mantle comFig. 5. (Top) Axial topographydue to mantle flow into a small paction tends to localize the region of mantle upwelling becylindrical region (line sink) of melt segregation.Here•5 is the neath the ridge axis as shown by comparing the streamlines
topography,I• is the mantleviscosity,U is the half-spreading
rate,H in Figure 5 with thosein Figure 4a.
is the crustalthickness, L is the depthto the segregating region,
andAp=pm-Pw. More complicated
andrealisticdistributions
of melt
RtDGE AXiS TOPOGIUa•e DUE TO PIATE EXTENSIONAL STRESSES
segregation could be constructedby superimposingline sink
solutions.
(Bottom)
Streamlines of mantle flow due to plate
spreading
and melt segregation
with associatedmantlematrixcomRidge axis topographycan also be producedby horizontal
paction. Analyticalsolutionfor manfieflow due to line sinkmelt extensional stresses in a strong plate that thickens with
segregationis given in text. Note, by comparingwith Figure 4a,
that melt segregationlocalizesupwellingbeneaththe ridge axis.
distancefrom a ridge axis [Parmentieret al., 1985;Lin and
Parmentier, 1986; Parmentier, 1987]. A perfectly plastic
material is considered as a continuum description of
mentarysolutiondoesnot contributeto the surfacenormal deformationdue to slip on many closelyspacedfaults. The
stress. The mantle flow due to melt segregationin a line strengthof the plate in this case arisesfrom the frictional
sink beneatha spreadingcenteris found by addingthe two resistanceto slip on the faults. Simple models to examine
line sink and complementarysolutions
u+iw=•{2t.Z
2+ +Z2
+ •'2+iz[z2
+
+•'{•X
2+(Z-Zl)
=+X2
+(Z+Zl)
2]
Zl + +Z+Z
l }
+•{X
2+Z(z-z)2
m
1
x
x
where u and w are velocities in the x (horizontal) and z
(vertical) directions, respectively, and rn is the melt
the form and amplitude of ridge axis topographywill consider a prescribedplate thicknessvariation. With the bottom of the strongplate definedby a prescribedtemperature,
the plate thicknessvariation will be controlledby thickening of the plate due to coolingaway from the ridge axis and
by localizedthinningof the plate near the ridge axis due to
plate extension. As discussedlater, plate extensionof the
magnitudeinferred from seafloor faulting and seismicmoment release will make a smaller contribution than cooling
to plate thickeningaway from the axis. Thermal modelsto
examine plate thicknessvariation are describedin a later
segregationrate into a line sink a depth zI beneath the section.
The mechanismproducingtopographyas a variable thicksurface of the half-space or crust-mantleboundary. The
complexvariables•=x+iz and •= x-iz, wherex is the real nessplate extendscan be understoodqualitativelyfrom Figand z is the imaginarypart of the complex variable, have ure 6a. Because the plate thicknessvaries, the horizontal
force F within the plate acts at different depths on the two
vertical sides of a material column, thus creating a moment
melt compactionmay be substantialif melt removaloccurs M. This moment, distributed horizontally over the region
at shallowdepthbeneaththe ridge axis and if ridge axis as- where the thickness varies, bends the plate. The vertical
been used to conciselyexpressthe solution.
The normalstress-supported
axial topographyproducedby
thenosphere
viscosities
areontheorderof 1020Pas (1021 force due to the resulting seafloor topographymust balance
P). Since, as shownin Figure 5, the depth to the segregat- the appliedmomentand thushas the form shown:a central
with flankinguplifts. Sincethereis no net vering region is the half width of the resultingtopographic depression
feature, melt removal occurringin a cylindrical region cen- tical force acting on the plate, only moments, the topogra-
12,830
PItlP• MORGAN
ETAL:THEORIGINOFMORAXIALSTRUC'RJRE
(a)
(b)
O(x)
O(x)
-
dh
Oxz-Oxxd-•
Fig. 6. (a) Force(F) and moment(M) distributioncan produceaxial topography
by flexuraldeformationof a strong
viscousor plasticplateof variablethickness
thatis beingpulledapartby externalforces.Platethickness
variations
result
in changes
in depthof the horizontalforce,thuscreatingmoments
withinthe platethatmustbe balanced
by moments
due
to topographic
forcesresultingfrom flexuraldeformation.(b) For a strongplatewith slowlyvaryingthickness,
stresses
due to changesin plate thicknesscan be represented
by an effectiveshearstress(•xz actingon the baseof the plate.
Considerthe horizontalforce balanceon the darkly shadedtriangularmaterialelement: the horizontalforce Oxxdh acting
on the vertical side of this triangle must be balancedby the force (•xz dx acting along the horizontal side. Becausethe
mantle is assumedto be a very weak fluid, no horizontalforcesact on the hypotenuseof the triangle. This force balance
showsthat the inducedshearstress(•xz is givenby the productof the meantensilestress(•xx and the rate of changein
platethickness
i•h/i•x. The shearstress
Oxz produces
internaldeformation
shownby the schematic
streamline.Seetextfor
further
discussion.
phy averagedacrossthe ridge axis must vanish. Deforma- to be small comparedto the plate thicknessso that the intion of the plate in responseto the applied momentscould ducedshearstresscan be appliedat the bottomof a layer of
be approximated as flexure of a viscous or plastic plate. uniform thickness H. This approximation has been freHowever, since the half width of an axial valley is not large quently applied in theoreticalstudiesof folding and boudicomparedto the plate thickness,a more accuratedescription nage. The strengthof the plate and thereforeC•xxis alsoasof the topographycan be obtained by consideringtwo di- sumed to be independentof depth within the plate. The
mensional deformation or flow within the plate rather than boundary conditionsat the bottom of the layer (z=H) are
(Sxz=(Sxx
•h/•x and(Szz=0,andthe boundaryconditionsat the
flexural approximations.
and
As shown in Figure 6b, considera strongplate of per- top of the layer (z=0) are (Sxz=(Sxx•J/•x,(Szz=Apg•J,
fectly plasticmaterial that restson a very weak fluid mantle w=•(u•J)/•x. The last equationstatesthat the surfacez=•J(x)
substrate. The presenceof a horizontal applied stress C•xx is a particle path with material at the top of the plate movthat causesextensionof the plate resultsin an induced shear ing along this surface. The perturbationflow due to the
stressC•xzthat is requiredto maintain equilibrium of the shear stress{Jxz at tl•.•::bottom of the layer can be represmall, darkly shadedmaterial element at the bottom of the sented as a superpositionof Fourier harmonicsin the x dilayer. This inducedshearstresscausesflow within the layer rection. The velocity distribution associatedwith any horiwhich is superimposedon the flow due to horizontalexten- zontal wavenumber is given by solution of equations(10)
sion and which results in a central depressionand flanking and (11) of Zuber and Parrnentier [1986].
Figure 7 showsthe topographyresultingfrom a prescribed
uplifts. When the plastic plate is kept at yield by the apvariation
of theformh exp[-(x/L)
2] where
plied stressC•xx,stressesdue to gravitational attraction on platethickness
the topography at the top surface of the layer also cause the width of the plate thicknessvariation L = 0.5H, H, and
flow which opposesthat of the inducedshearstress. For a 2H. The surfacetopographyand velocity distributionwithin
prescribedplate thicknessvariationh(x), the equilibriumto- the layer which satisfiesthe above boundaryconditionswere
pographywill be that for which the verticalvelocity at the calculatedusing a standardFFT algorithm with 256 points
uniformly distributed over the length of the examples
upper surfacevanishes.
Flow within the plate is describedby the equilibrium shown. The amplitude of the relief is proportional to the
equationsand the incompressibilitycondition. To obtain magnitude of the layer thicknessvariation, h, and depends
parameterS=(Sxx/ApgH,where is
analyticalsolutions,the thicknessvariation h(x) is assumed on a single dimensionless
PHIP• MORGAN ET AL: TIlE ORIGIN OF MOR AXIAL STRUCIIJRE
12,831
Fig. 7. Axial topography
due to defomaation
resultingfrom horizontalextensional
stresses
in a lithosphere
that thickens with distancefrom a ridge axis. The prescribed
thicknessvariationis shownat the bottomof eachfigure and the
resultingtopography
alongthe top. All casesconsidera perfectlyplasticlithosphere
with the samevalueof the strength
parameterS definedin the text.Differentlithosphere
thickness
variationsare considered
by varyingthe half-widthof the
thickeningregion L =0.5H, H, and 2H.
the mean horizontal applied stress,Ap = P,n- Pw,g is the to producethe 1 km of seafloorrelief typically observedon
accelerationof gravity, and H is the lithospherethickness slow spreadingridge axes.
near the ridge axis. Similarresultsfor a rangeof S values
showsthat the amplitudeof the relief is approximatelyproRIDGE AXIS THERMAL MODELS
portionalto S and inverselyproportionalto L. If the width
As an extending plate thickens with distance from the
of the plate thicknessvariation is comparableto or smaller
of the thickeningof
than the plate thickness,the predicted width of the axial ridge axis, the dynamic consequences
valley, measuredfrom flanking high to flanking high, is 3- the deformingplate may createor at least contributesignifi4 times the plate thickness. A wider plate thicknessvaria- cantly to the axial morphologyof slow spreadingridges. It
tion producesa broaderaxial valley, but the predictedwidth is important to emphasizethat the total amount of extenof the axial valley is not less than about four plate thick- sion that accumulatesin a thin vertical section of plate as it
nesses. With a brittle plate thicknessof about 8 kin, as in- moves through the axial valley is relatively small. Based
ferred from the depth of microseismicityon the axis of the on observeddistributionsand heights of fault scarps,MacMid-Atlantic Ridge southof the Kane fracturezone [Toomey donald and Luyendyk [1977] and Macdonald and Atwater
et al., 1985], the predictedflank to flank width of the axial [1978] estimate only 10-20% extension. Similarly, the avvalley would be about 30 kin, which agreeswell with the erage seismic mo•aent release along slow spreadingridges,
observedaxial valley width along this segmentof the ridge. as reported by Solomon et al. [1986], can be interpreted to
Frictional sliding on faults will result in a yield stress indicate that only 5-10% of the total spreadingvelocity is
that increaseslinearly with depth [cf. Brace and Kohlstedt, due to seismicfault slip. As seen at the seafloor, most of
1980]. For faults containinghydrostaticwater pressureand the plate spreadingvelocity developswithin a 1- to 2-kinon which frictional sliding occurs with a laboratory-mea- wide neovolcanic zone at the ridge axis where spreadingis
sured friction coefficientof 0.85 [Byerlee, 1978], the depth- accommodatedby dike intrusion. The spreading velocity
averagedvalue of Oxxis S=0.4. The absenceof water pres- increasesonly slightly away from the axis due to horizontal
sure resultsin the larger value S=0.7. For S=0.4 resultslike extensionof the lithosphere. While the amplitude of the
those in Figure 7 predict seafloortopographywith a relief topography depends on the magnitude of plate thickness
of about 30% of the plate thicknessvariation. Therefore a variation near the ridge axis, the plate thickness variation
plate thicknessvariation less than about 3 km is sufficient cannotbe solely a result of plate extension. Extensionwill
12,832
PHIPPS
MORCaAN
Er AL:TIIEORIGIN
OFMORAXIALSTRUC'ruRE
tend to thin the plate, but if the above estimatesof exten- to 3-kin-deep seismicreflectionsinterpretedto be the top of
a magma chamber.
In the following models, to examine the effects of hydrothermalcooling in a simple way, heat transfer due to hydrothermalconvectionis representedas an increasedthermal
conductivity. The ordinary thermal conductivityis enhanced
by a factorNu, the Nusseltnumberfor hydrothermalconvecwhich the thermal structure for a prescribedvelocity field tion in a permeable layer. Rock at a temperature greater
was determined[e.g. Sleep, 1969, 1975; Kuznir, 1980;Reid than 400øC or at a depth greater than 6 km is assumedto be
and Jackson,1981]. The modelsof Sleep [1969, 1975] as- impermeablebecauseit cannotsupportopen fractures. Since
sumepurelyhorizontalvelocitiesequalto the half spreading water as hot as 400øC dischargesfrom vents on the seafloor,
rate and include heat resulting from the solidification and this a minimum value of the maximum temperatureof rock
sion are correct, this effect must be relatively small. If the
bottomof the strong,brittle plate is definedby a prescribed
temperature,
the thermalstructuredue to mantleflow beneath
the ridge axis and crustalaccretionon the axis will control
the plate thicknessvariation.
A numberof ridge thermalmodelshave been presentedin
cooling of magmatically emplacedcrust on the ridge axis. throughwhich water must circulate. Studiesof the Samall
Ophiolite [Gregory and Taylor, 1981] indicate that subsolidus oxygen isotope exchange with seawater occurred
viscosityhalf-spaceas shownin Figure 4a. This modelthus primarily within the upper 5-6 km of the ophiolite, thus
includes the effect of vertical mantle flow beneath the ridge giving an estimateof the maximum depth of water penetraaxis but ignoresthe heat resultingfrom crustal emplacement tion.
on the ridge axis. Since both effects are likely to be
The thermal models in Figures 8c and 8d were calculated
important,the two modelshave simplybeencombined.The for Nu=3 and 10, respectively,with the same slow spreading
velocity field consideredis shown by the streamlinesin rate as in Figure 8b. With Nu=3 the lithosphere,defined by
Figure 8a. Crustemplacedon the ridge axis moveshorizon- the 600øC isotherm, at the ridge axis remains thinner than
tally at the half spreadingrate, and underlyingmantle flows the crust. However, with Nu=10, the lithosphere is clearly
like a uniform viscosity half-spacebeneaththe spreading thicker than the crust and generally consistentwith depth of
crust. Heat associated with solidification and cooling of seismicity observed at the Mid-Atlantic Ridge. The plate
crust on the axis is treated as a concentrated axial heat
thickensby about 3 km over a distanceof 10 km from the
source distributed over the thickness of the crust, in a manridge axis. This thickeningof the plate with distancefrom
ner analogous
to that of Sleep [1975]. The crustalthickness the ridge axis is sufficient for plate extensionto contribute
(6 km) anddeepmantletemperature(1200øC) are prescribed. significantly to ridge axis topographyon slow spreading
The temperature
of magmaticallyemplacedmaterialis taken ridges. For a faster half spreadingrate of 50 mm/yr and
to be greaterthan the deep mantle temperatureby an amount Nu=10, the lithosphere at the ridge axis remains much
(320øC)representing
the heat of fusionof moltenbasalt(80 thinner than the crust as shown in Figure 8e.
Reid and Jackson [1981] calculated the temperaturedistribution for mantle flow due to plate spreadingon a uniform
cal/g).
The steadystate thermalstructurewas calculatedusingfinite differenceapproximations
with the distributionof grid
points shownin Figure 8a. The isothermsof the resulting
thermal structurefor a half spreadingrate of 10 mm/yr are
shownin Figure 8b. As inferredfrom the depthof oceanic
intraplate seismicity [Bergmanand Solomon, 1984; Weins
and Stein, 1984], the bottom of the plate shouldcorrespond
to a 600ø-700øCisotherm. Even at this slow spreadingrate,
the plate thicknesson the ridge axis is significantly less
than the crustal thickness. Seismicity at 8-kin depths beneath the ridge axis [Tooracyet al., 1985] would not be expectedon the basisof this model.
Hydrothermalconvectionof seawaterthroughpermeable
oceanic crust is widely recognized as an important mechanism of heat transfer, particularly in young oceanic crust.
Hydrothermalcooling is one obviousexplanationfor a narrower magmachamberon fast spreadingridges[Lewis and
Garmany, 1982;McClain et al., 1985; Detrick et al., 1986]
than would be expectedbased on thermal models [Sleep,
1975; Kuznir, 1980]. Several studies of hydrothermalconvection in a permeable crustal layer have been reported
[Ribando et al., 1976; Fehn and Cathles, 1979; Fehn et al.
1983]. However,a recentstudyby Morton and Sleep[1985]
appearsto be the only previousstudy which addressesthe
effect of hydrothermalcooling on the large-scale thermal
structureof a spreadingcenter. Representing hydrothermal
cooling as a prescribeddistributionof heat sinks within the
upper crust, the heat sink distribution was constrainedby
requiring that the 1185øC isothermin the modelsmatch 2-
Based on studies of the relationship between Rayleigh
number and Nusselt number (cf. Combarnous, 1978, Figure
4), a Nusselt number of 10 for hydrothermalconvectionin a
6 kmthicklayerrequires
a permeability
of about
4x10
-16
m2, withothervalues
of thermodynamic
andtransport
properties appropriatefor water and water-saturatedrock in the
oceaniccrust. Permeabilityhas been inferred or measuredin
several Deep Sea Drilling Project (DSDP) holes [Anderson
and Zoback, 1982; Hickman et al., 1984].
However, the
only in situ measurementof permeability at a depth greater
than about 600 m in the oceanic
crust was obtained
at DSDP
hole 504B in crust 6.5 m.y. old, severalhundredkilometers
away from the axis of the Costa Rica Rift on the Galapagos
SpreadingCenter [Andersonand Zoback, 1982]. The mea-
sured
permeability
decreases
withdepthto a valueof 10-17
m2 at depths
greater
than500m. Thislowvaluewouldnot
account for hydrothermal convective heat transfer with a
Nusselt number as large as 10. However, near the ridge axis
where active faulting and cracking associatedwith rapid
cooling occur [Lister, 1974], it is not unreasonableto expect larger permeabilities. Further from the axis, cooling
cracks and inactive faults are likely to have been filled by
hydrothermally depositedminerals.
Thus, if hydrothermalcooling can accountfor a relatively
thick plate near the axis of a slow spreadingridge, the results of the present study suggest that horizontal extensional stressesin a strong plate near the axis of a slow
spreadingridge may explain the formation of the axial valley. The transport of magma through the strong mantle
layer is a questionof obvious importancethat is not directly
(b)
(c)
(d)
(e)
(f)
Fig. 8. Mid-oceanridgethermalstructurein a verticalcrosssectionperpendicular
to the spreading
axis includingthe
effectof hydrothermalcooling. Streamlinesof the flow fiold (Figure 8a) correspond
to horizontalmotionof crust
eraplaced
on theridgeaxisandmantleflow dueto platespreading,
like thatin Figure4a, beneath
the crust. Grid spacing
usedin finite differencecalculations
is shownby tick marksalongthe sidesof the region. Isotherms(Figures8b-8f) are at
temperatureintervalsof 100øC. Magmaticaccretionof the cruston the ridgeaxis is represented
by a heat sourcethat
extends to the bottom of the crust. (The base of the crust is shown by the solid horizontal line.)
Lithosphere,
corresponding
to materialwitha temperature
below600øC,is shaded.Hydrothermal
coolingis represented
asthe ordinary
thermal conductivityenhancedby a constantfactorNu representingthe Nusseltnumberfor hydrothermalconvective
cooling. Isothermsare shownfor a 10-mm/yrhalf-spreading
rate ridgewith Nu=l (Figure8b), 3 (Figure8c), and 10
(Figure 8d) and a crustalthickness
of 6 km. Isothermsare shownfor a 10-mm/yrhalf-spreading
rate ridgewith Nu=10
(Figure8e) anda crustalthickness
of 12 kin; andfor a 50-mm/yrhalf-spreading
rateridgewith Nu=10 (Figure8f) anda
crustal thickness of 6 km.
See text for further discussion.
12,834
PHIPPS
MORGAN
ETAt.:TltEORIt'aNOFMOR AXIALSTRUCq'LIRE
addressedby the simple models presentedabove. This may
explain episodicity of the spreading process and possibly
the large difference in frequency of episodicity inferred for
fast and slow spreading ridges [cf. Macdonald, 1982].
Magma generatedin the upwelling mantle beneaththe ridge
axis may episodicallypenetrate the strongplate at the ridge
axis in cracklike bodies resulting in periods of reduced extensional stress in the plate near the ridge axis. As shown
in Figure 1, volcanism at a ridge axis is restricted to a 1- to
ity halfspace is approximately 4n•t/ApgL, where L is the
widthof theaxialvalley. WithL=30 km andI.t=1020Pas
(1021P), asrequired
formantle
flowstresses
toproduce
a 1kin-deep
axialvalley,therelaxation
timeis 6x104years.
Clearly, the mechanismsproducing the episodiccharacter
of spreadingrequire further study. However, axial valley
formation by horizontal extensional stressesin a strong
plate that deforms by faulting is consistentwith episodic
spreadingand with the preservationof axial topographyon
2-km-wide
neovolcanic
zone that is much narrower than the
extinct ridges.
The axial structureof mid-oceanridges dependsstrongly
width of the axial valley and the region of plate extension.
If plate extension is to create the stress-supportedaxial val- on spreadingrate. However, axial structureis also clearly
ley, it is sufficient for a continuous strong plate to exist influenced by factors other than the spreadingrate. In the
most of the time. During times that magma penetration vicinity of hot spots where ridge axes are much shallower
weakens the plate in a narrow zone at the ridge axis, hori- than normal, an axial valley may not be present even at
zontal extension of the plate outside this region will stop. slow spreadingrates. The Reykjanes Ridge is an often cited
If the plate behaved as a simple viscous material, the axial example. In contrast, at the Australian-Antarctic Discorvalley topography would tend to relax during such times of dance, a deeper than normal section of the intermediate
reduced horizontal extension or stress. However, because
spreadingrate Australian-Antarctic Ridge, the ridge has a
the axial valley is produced by faulting, if stressesdue to well-defined axial valley that is not presenton adjacentsecaxial valley topography alone are insufficient to cause slip tions which are at a more normal depth [Weisseland Hayes,
on faults then the axial valley topography will remain 1974; Forsyth et al., 1987]. Ridge axes also deepen sysfrozen-in during these periods of reduced horizontal stress. tematically approachinga transform fault, and the axial valIn our idealizedmodels,stressesdue to axial topographyare ley becomescorrespondinglymore pronounced. This correinsufficient to cause yielding of the plastic plate. This ex- lation of ridge axis structurewith seafloor depth may be expected freezing-in of topography is consistentwith the ob- plained by the relative rates of magmatic heat input associservation that extinct slow spreadingridges in the Labrador ated with crustal formation. In areas where the crustal proSea [Kristoffersen and Talwani, 1977], the northeasternAt- duction rate is low, the seafloor is deep, the magmatic heat
lantic Ocean [Talwani and Eldholm, 1977], and the Coral Sea input at the ridge axis is low, and the plate is thicker than
[Watts, 1982] preserve their axial valley morphology and normal for that spreading rate. The thicker, and therefore
associated gravity anomalies. After extension stopped, the stronger,plate will result in a more pronouncedaxial valley.
frozen-in topography should be supported by elastic In contrast, areas of high crustal production will be shallower and will have higher magmatic heat input and therestrengthof the plate as suggestedby Watts [1982].
An axial valley that is created by viscous flow in a ridge fore thinner ridge axis lithosphere with an axial structure
axis conduit should disappear after spreadingstops. The re- characteristicof a faster spreadingrate. This is shown by
laxation time required for seafloor elevation at the top of a the example in Figure 8f, where the crustalthicknessis douridgeaxisconduit
to adjust
to changes
in pressure
withinthe ble that in Figure 8d while all other parametersof the therconduit is 121xH/Apgd•, where H is the conduitheight, d is mal model remain the same. The lithosphere thickness at
the conduit width, Ap is seafloor rock-water density differ- the ridge axis was approximately halved by doubling the
crustal thickness. For a lithosphere at brittle failure with a
ence, and I.t is the asthenosphere viscosity [cf. Phipps Morgan and Parmentier, 1985]. The depth of the axial valley at frictional strength proportional to depth, halving the lithoa halfspreading
rateU is õ--12•tUH2/Apgd
3 [cf.Parmentiersphere thickness would decrease the horizontal force and
and Forsyth, 1985] so that the relaxation time becomes moment by a factor of 4. For a normal crustal thicknessat
simply õd/HU. For a conduitwith H=30 km and d=10 km slow spreadingrates, as shown in the example of Figure 8d,
(Lachenbruch, 1973), an initially 1-km-deep axial depres- a significant part of the ridge axis lithospherewill consist
sion at a half spreadingrate of 10 mm/yr will relax in ap- of mantle peridotiterather than crustalgabbro. The lower
proximately3x104years.The axialvalleydueto sucha ductile flow strength of gabbro relative to peridotite [Chen
ridge axis conduit would be well preservedbetweenspreading and Morgan, 1987] would increasethe ridge axis weakening
effect causedby thickeningthe crust.
episodes
occurring
each104years. However,
preservation
of the axial valley after spreadingstops would require cooling and strengtheningof mantle material in the ridge axis
SUMMARY
conduit.The timeH2/4•cfor conductive
coolingto penetrate
to a depthH is approximately
8xl 06 yearsforH=30 km Axial topography and associatedgravity anomalies proand•c=l mm2/s. Evenif theupper5-6 km of the oceanicvide an important constrainton the thermal and mechanical
lithosphere near the ridge axis were rapidly cooled by hydrothermal convection, this cooling time would remain
longer than the relaxation time. It therefore appears unlikely that topography produced by a ridge axis conduit
would be preserved after spreading stops. If the plate
thickness increases more gradually with distance from the
ridge axis, as in Figure 3c, the relaxation time for topography supportedby mantle flow stressesin a uniform viscos-
structure of spreadingcenters. Observed gravity anomalies
indicate that the axial topography at slow spreadingridges
cannot be isostatically compensatedat depths as shallow as
6 km and therefore cannot be simply explained by crustal
thicknessvariations. In this study, several mechanismsfor
the creation of axial topographyat mid-ocean ridges that is
supportedby stresseswithin a strong plate near the ridge
axis or the flowing mantle beneath it have been examined.
MOROANET AL: TIlE ORI{IN OFMOR AXIAL STR•
The relative importanceof mantle and lithospheredeformation on axial topographyhas been explored using elementary solutionsfor viscousflow problemsand simple thermal
models. The relatively low relief of fast spreadingridges
and the pronouncedaxial valley on slow spreadingridges are
the principalfeaturesthat need to be explainedby suchfirst-
12,83$
slow spreadingridges. The same mechanismwill operate at
fast spreading ridges, but the plate thickness at the ridge
axis, as predicted by our models, should be small enough
that the horizontal force in the plate is too small to produce
appreciableridge axis relief.
order models.
A narrow, vertical steady-stateconduit through which viscous asthenosphere
rises on the ridge axis is an appealingly
simple and frequently cited explanationfor the presenceof
an axial valley on slow spreadingridges. However, the
temperaturefield associatedwith flow in a narrow conduit
does not correspondto an assumedsteep-walledconduit, but
instead has the form of a thermal boundary layer, with
nearly horizontal isotherms, that thickens gradually with
distancefrom the ridge axis. Thus if a steady-stateridge
axis conduit does exist, the strength difference between asthenosphereand conduitwalls must be attributedto a significant strengthreduction due to the presenceof partial melt
in the rising asthenosphere,by an increasedstrengthof depleted residual mantle forming the conduit walls, or by some
other, nonthermally controlled mechanism.
Mantle flow due to plate accretion and melt segregation
can produceaxial-valley-like topography. However, a mantle viscosity beneath the spreadingcenter on the order of
1020Pas (1021P) is required
for thesemechanisms
to contribute significantly to the kilometer-scalerelief present on
slow spreadingridges. In the absenceof plate accretionand
extension near the ridge axis, mantle flow due to plate
spreadingalone makes no contributionto the topography.
This suggeststhat several previously consideredkinematic
models based on this mechanismdo not adequately explain
the axial valley.
Horizontal extensional stressesin a strong, brittle lithospherethat thickens with distancefrom the ridge axis can
produce an axial-valley-like topographywith relief comparable to that observed. Using a continuum idealization of
deformationdue to faulting, the axial valley width is controlled by the plate thickness. A 10-km-thick brittle plate
near the ridge axis would producea 40-km-wide axial valley
as observedon slow spreadingridges. Microseismicity,im-
plying brittle plate deformation, has been observed to
depthsof 8 km at a slow spreadingridge. Basedon accepted
values for sliding friction on faults, a plate that thickensby
as little
as several kilometers
within
the width of the axial
Acknowledgments. This researchwas supported by National
Science Foundation grant OCE-8613946. Final stages of the research and most of the writing were completed at the Irrstitute of
Geophysicsand Planetary Physics, ScrippsInstitution of Oceanography, where both J.P.M. and E.M.P. were supportedby Ida and
Cecil Green Fellowships. Special thanks are due to John Orcutt,
who helped make possible the 1 year stay of J.P.M. and the 2
month summervisit of E.M.P. Norman Sleep and an anonymous
reviewer provided helpful commentson an earlier version of the
manuscript.
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and convection in the oceanic crust near the Costa Rica Rift,
eastern equatorial Pacific, jr. Geophys. Res., 87, 2860-2868,
1982.
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(received March 2, 1987;
revisedMay 9, 1987;
acceptedJune 13, 1987.)