Submarine rifting at mid-ocean ridges

109

Tectonophysics, 94 (1983) 109-122 Elsevier Science Publishers

SUBMARINE

B.V., Amsterdam

- Printed

in The Netherlands

RIFTING AT MID-OCEAN

RIDGES

G.T. JARVIS Department of Geology, University of Toronto, Toronto, Ont., M5S IA1 (Canada) (Revised

version

received:

June 11, 1982)

ABSTRACT

Jarvis,

G.T.,

Processes

1983. Submarine of Continental

An analytical interpreted

rifting

at mid-ocean

model for the formation

as a belt of localized

ridges.

of mid-ocean

extension

of width

ridges is presented 2W centred

occurs passively below the zone of extension

asthenosphere distances

greater

than W from the ridge axis the lithospheric

no. The

model

is thermally

topography

across

and

mechanically

the rift zone plus the vertical

below the zone of extension.

Measurements

estimates

of the width of the zone of intrusion.

thickness

of the lithosphere

A comparison actively

of the thermal

and

B.H.

Baker

(Editors),

structure

and

predicts

structure

horizontal

the surface

and the thickness

of ridge heat flow and topography

rift zone is

heat

of the mass. At velocity

flow

can be used to constrain to the

in some models of mantle convection.

at a ridge crest as produced

passively

similarity.

to plate formation

and

of the lithosphere

This width may be as large as 100 km-comparable

cell shows a qualitative

cause and effect with regard

to conserve

plates move at a uniform

consistent thermal

in which the central

on the ridge axis. Upwelling

at the rate required

and that of mantle plumes, as proposed

by a mantle convection

in distinguishing

In: P. Morgan

Tectonophysics, 94: 109- 122

Rifting.

by horizontal

This similarity

illustrates

extension

and

the difficulty

and motion.

INTRODUCTION

have been few developments of thermal models of the oceanic lithosphere since the “plate model” was introduced by McKenzie (1967). The continued success of this model in accounting for large scale oceanic bathymetry and heat flow variations (Sclater and Francheteau, 1970; Davis and Lister, 1974; Parsons and There

Sclater, 1977) is due to the fact that far from the ridge crest the heat flow and topography are not very sensitive to details of the initial conditions. Any hot axial zone will initially cool according to the same physical laws (Parsons and Sclater, 1977; Parsons and McKenzie, 1978). Indeed the predictions of all subsequent thermal models of the lithosphere converge with those of McKenzie’s plate model for sea-floor ages greater than about 10 Ma (and less than - 80 Ma). Consequently a physical understanding of the mechanism of rifting and plate formation is only 0040-1951/83/$03.OO

0 1983 Elsevier Science Publishers

B.V.

possible

by examining

ocean-floor

The various weaknesses

thermal

of the ocean

floor close to the ridge ;IXIS

models differ most strongly

of previous

overcomes

models

these. Although

a significant rifting

features

aav for

ages less than 20 Ma.

improvement

are examined

at the ridge crest. The principal

and a new model is proposed

this new model has its own weaknesses. over earlier models in that it attempts

which

it nevertheless

is

to model the actual

process below the ridge crest.

CONDITIONS

AT THE RIDGE

In Fig. 1 isotherms

CREST

in the vicinity

of mid-ocean

profiles below the ridge crests. as predicted

ridges and vertical

by three different

temperature

models, are compared.

In each model the temperature, T,of the upper surface is assumed to be fixed at O*C and that of the lower surface (of the lithosphere) is assumed to be a constant T = T,, McKenzie’s

(1967) plate model, denoted

model I, is shown in Fig. la. In this model

it is assumed that magma from below the plate, at a temperature T = T,.is injected along the axial plane. This magma produces new plate material which accretes onto

t=o ai0

j

/ : (b)

1

c

,_t’

TFig. I. Isotherms

in a plane normal

Model I, the plate model proposed and Nikitina

by McKenzie

(1975) (in this case the parameter

here (in this case the parameter temperatures

to the ridge axis and vertical temperature

of 0°C and

/3 = 16). c. Model III, the extensional

G’= 411). The upper

r, respectively.

The curved

where T is temperature.

The vertical profiles

Iabelled r = 00 represent

the temperature

profiles in the axial plane. a.

(1967). b. Model II, the model proposed

labelled

and lower isotherms

surfaces

are labelted

of all three

models

have

with the values of r/r,.

t = 0 are the axial temperature

after the spreading

by Lubimova

model introduced

profiles,

ptates have cooled for an infinite

while those time.

111

the laterally the magma

diverging

plates.

must rise infinitely

Because

the plane

of injection

is infinitesimally

fast in order to replace the diverging

lithosphere

finite rate. Hence the injected magma could not cool during intrusion. ture profile with T(z) = r, along the entire axial plane is therefore which

is consistent

deficiency

with

the mechanical

conditions

the axial plane

(where

T = T, and

T = 0 at the upper

singularity surface)

at a

The temperathe only one

of the model.

of this model is the fact that the mathematical

thin,

An

obvious

at the surface of implies

an infinite

surface heat flux at the ridge crest. In an attempt to overcome this deficiency

Lubimova

posed the model illustrated

model II here. In model II it is again

in Fig. lb, denoted

and Nikitina

(1975) pro-

assumed that magma is injected along the axial plane from below at T = T,, but that due to conductive cooling near the upper surface the axial temperature profile takes the piecewise

linear form shown. This profile is characterized

by a parameter

p such

that for a total plate thickness, a, the temperature of the upper region (of thickness a/P) varies linearly with height from T, to 0 while that of the lower region (of thickness a(/3 - I)//?) is T = T,. The surface heat flux at the ridge crest, F,, is therefore F0 = /IF,, where F, is the equilibrium heat flux which would occur after cooling for an infinite time. (F, = KT,/a, where K is thermal conductivity.) Lubimova and Nikitina (1975) found that p = 2.8 gave a good fit to the mean heat flow in the vicinity of ocean ridges. (The appropriate value of p must be increased considerably if only reliable heat flow measurements (Sclater et al., 1976) from well sedimented regions are averaged.) Although model II has the advantage of predicting a finite heat flow at the ridge crest, the magnitude of which can be adjusted through /3, the initial thermal and mechanical conditions the plates diverge from the axial plane with uniform heights,

magma

the axial plane.

must be injected Under

at infinite

these conditions

speed along the entire vertical

a linear

conduction

the upper zone is not possible. Model II is self-consistent in which case it is identical to model I. The problems magma injection extent. However

are not consistent. horizontal velocity temperature

Since at all

extent of profile

in

only in the limit of /3 + 00

of the first two models discussed here stem from the assumption of along an axial plane rather than into a zone of finite horizontal a piecewise linear temperature profile, identical to the axial profile

of model II, has been successfully

employed

as the initial temperature

distribution

in

one-dimensional models of the evolution of sedimentary basins (e.g. McKenzie, 1978). In this context the initial profile results from an instantaneous stretching of a portion of the lithosphere and overlying crust by a specified factor, /3. Before stretching, the temperature profile is assumed to vary linearly from T, to 0°C across the height, a (as for the f= cc profiles in Fig. 1). Upon stretching the lithosphere by a factor p, the piecewise linear profile of model II is produced. Subsequently temperatures at all heights cool back towards the f = cc temperature profiles and the associated thermal contraction produces a shallow basin which may be filled with sediments. This model is similar to the M.O.R. (mid-ocean ridge) models discussed

above

in that divergence

spheric material

of neighbouring

at T = T, is involved.

plates and passive

However,

upwelling

of astheno-

it differs in that the upwelling

not occur along a plane,

but rather

in a zone of finite width (of the order

below a lid of attenuated

lithosphere

and crust. Across this lid an initial

gradient

of /3T,/a

The relevance ment and lithosphere

does

100 km)

temperature

exists. of the model

II axial temperature

profile

to a stretching

environ-

the success of this model for the thermal structure of the oceanic at old ages, suggest that M.O.R.‘s may form where continental crust and

lithosphere are stretched and thinned along a belt of finite width. However, direct application of an instantaneous finite stretching model is not appropriate for two reasons. The first is that the amount of “stretching” at a mature M.O.R. is essentially infinite (i.e. p = ‘x;): hence the predicted vertical temperature profile would be the same as the axial profile of model I (see Fig. la) and an infinite heat flux would be predicted across the entire zone of stretching. Secondly. the assumption of instantaneous stretching is only valid for stretching events of relatively short duration.

For events lasting

more than about

20 Ma a significant

amount

of heat is

lost to the surface by conduction before the stretching ceases (Jarvis and McKenzie, 1980). Consequently the initial post-stretching temperature profile is not a piecewise linear curve. In the major ocean basins plate divergence has occurred relatively uniformly for at least 1.50 Ma so that an ~~~n~te ~~~urjo~ of stretching at a finite rate, would be a more reasonable model approximation than instantaneous stretching. In this paper a two dimensional analytical model for M.O.R.‘s is presented in which continuous horizontal stretching of the lithosphere occurs within a limited horizontal extent 2W centred on the ridge axis--that is out to a distance W in each direction normal to the axial plane of the ridge. Passive asthenospheric upwelling occurs below the zone of extension at the rate required to conserve mass in the axial zone. Beyond the zone of extension the lithospheric plates move at uniform horizontal velocities away from the ridge. This model, denoted model III, converges to McKenzie’s (1967) plate model (model I) in the limit of W + 0 but remains thermally

and mechanically

MATHEMATICAL

consistent

DESCRIPTION

for all values of W.

OF THE MODEL

The two-dimensional geometry of the model is illustrated in Fig. 2. The origin of the (x, z) coordinate system is set on the axial plane of the ridge at the (assumed) depth of isostatic compensation of the oldest lithosphere. The model consists of two zones in the horizontal direction: the inner zone, Ix/< W, in which the lithosphere is stretched horizontally; and an outer zone, 1x12 W, in which the plates move uniformly with a constant horizontal velocity of magnitude no. The upper surface of at a constant temperature T = 0°C. while the both zones, at z = a, is maintained lower surface, at z = 0, is held at T = T,, the assumed constant temperature of the asthenosphere (i.e. for z < 0). The axial plane of the ridge (at x = 0) is assumed to be

113

OUTER

INNER

OUTER

ZONE

ZONE

ZONE 0%

0%

“oa

ya

1

Tl

I

0

T, ‘w

of the two-dimensional

inner zone which is centered rift axis at a uniform

uo

t’z 6

-w Fig. 2. Geometry

1’

stretching

model of submarine

rifting.

Rifting

occurs within the

on the axial plane of the rift, at x = 0. The outer zone moves away from the

velocity

uo.

a plane of symmetry so that solutions need only be obtained for x z 0 with the boundary conditions aT/i3x = 0 and u = 0, at x = 0. (u is the horizontal component of the velocity

field.)

Following the approach of Jarvis and McKenzie (1980) for finite stretching rates, within the inner (i.e. stretching) zone a pure shear constant strain-rate velocity field is assumed in which the horizontal component u varies linearly with x from u = 0 at x = 0, to u = u,, (the plate velocity) at x = W (and u = -u,, at x = - W). Accordingly the vertical component of velocity, o, decreases linearly with z from II = u0 at z = 0, to u = 0 at z = a. Hence for 1x1~ Wand 0 < z < a, the velocity u has the form:

[gqx, (y(u-z)]

u=(u,ll)=

(1)

while for 1x1> W: u= (ql,

0) (2) The general form of the Eulerian thermal equation which must be solved for both zones of the model is (ignoring internal heat generation): 3T

3T

i3T

a2T

aZ

ax

~+U~+“-=“~+“a,2

a=T (3)

where t is time and K is the thermal diffusivity. Within the inner zone, it is assumed that horizontal temperature gradients vanish and in the case of continuous stretching (i.e. an event of infinite duration) a steady state is achieved. Under these conditions eq. 3 reduces to the particularly simple form:

where G = ~,,/a. Equation 4 can be solved analytically the temperature T as a function of height as:

er$(1-z/4#7f]

T= T I

erfm

to obtain

an expression

for

(5)

where

G’ represents

Kenzie,

the dimensionless

1980). The surface

vertical

derivative

combination

C;’ = u’G./t~ (Jarvis

heat flow in the inner

of eq. 5, at the upper surface.

zone.

k;,. as obtained

and

ih:

2G’/‘r F,s &,= 4 erf JGf/2

(6)

The temperature vertical balance

Mc-

from the

profile

given by eq. 5 is plotted

in Fig. Ic. This is the steady

temperature distribution, throughout the inner zone, which maintains a between the rate at which heat is conducted across the upper surface and

that at which it is both conducted profile zone.

is also used as a boundary

In the outer zone the relevant

and advected condition

towards

the upper

at x = W for the solution

surface.

This

in the outer

form of eq. 3 is:

aT a2T a2T 41ax = K, + KS ax-

This equation has been solved for various boundary conditions in previous plate models (e.g., McKenzie, 1967; Sclater and Francheteau, 1970; Davis and Lister, 1974; Lubimova and Nikitina, 1975; Oldenburg, 1975) and in each case it was concluded that the first term on the right-hand side plays a minor role. Thus to simplify the present analysis, and to avoid repetition, the standard boundary layer approximation is made at the outset and horizontal quently, through a transformation of coordinates: t’=t-t,=(x-

diffusion

is neglected.

w)/u,

(8)

where t, is the time at which a particle Lagrangian

Conse-

passes the point x = W, eq. 7 can be re-cast in

form as:

aT

aT2

atf

az2

-=K-

Equation 9 is the standard solution can be expressed T(z,

t’)=T,(a-z)+

f u, exp( - n2m2Kt’/a2) n-l

The coefficients between an=-

initial

2 aTI /[o

u

one-dimensional thermal diffusion in terms of a Fourier series as:

a, are determined

from Fourier

equation

sin( nrz/a) decomposition

for which the

(10)

of the difference

and final states as: T z, t’=O)-(a-z)T,]

(

where T( z, t’ = 0) is the temperature

sin(nrz/a)dz solution

given by eq. 5.

(11)

115

MODEL RESULTS

In the formulation

above there is only one model parameter

adjust.

This is the dimensionless

plicitly

in eq. 5 and enters eq. 10 implicitly

of mass requires u,W=

gradient through

G’ =

which we are free to

UV,,/K

which

the coefficients

appears

ex-

a,. Conservation

that:

UoU

(12)

so that for given values proportional G’=

velocity

of u,, and a (generally

known

quantities),

to W. Using eq. 12, G’ may be re-expressed

u0 is inversely

as:

U2U,/KW

(13)

Thus assuming u2, u0 and K are known quantities, an alternate (and potentially more useful) independent parameter of the problem is W, the half-width of the zone of horizontal extension and vertical model solutions depends directly been

adjusted

to produce

intrusion below the ridge. Since the form of the upon G’, W is obtained from eq. 13 once G’ has

the best

agreement

between

model

predictions

and

observations. Observations of heat flow and topography in the major ocean basins are normally tabulated as a function of sea floor age (e.g. Parsons and Sclater, 1977). In the outer zone of model III results are computed in terms of t’, with a corresponding age t = t, + t’. However the age t, of the sea floor at x = W can only be estimated. This is because

the surface velocity

in the inner

(stretching)

the range x = [0, W]. The time taken for a particle an initial

position

zone varies from 0 to a0 in

in the inner zone to move from

at x = x0 to x = W is: (14)

Thus material

on the ridge axis will never arrive at x = W, while material

x0 = 0.135W will arrive at x = W after a time Z, = 2W/u,. same as for material

moving

uniformly

This latter

from the ridge crest at 1~1= u,/2,

initially

at

time is the the mean

velocity in the inner zone. Although this ambiguity remains, to = 2W/u, will be used for illustrative purposes. Isotherms from a typical model solution for which G’ = 411 are shown in Fig. lc. Labels on the isotherms indicate the ratio T/T, for each contour. In the central region, the upwelling outer zone diffusive

flow confines the contours close to the surface while in the cooling allows the isotherms to spread out with increasing

distance from the ridge. Parsons and McKenzie (1978) have suggested that the base of the rigid lithosphere may be defined by the isotherm for which T/T, = 0.75. When G’ = 411 this isotherm is found in the inner zone at a depth of 0.0569~ or 7.11 km (if a = 125 km). Models with larger values of G’ predict a larger crestal heat flow,

Fo, a narrower

central

zone of extension,

2W, and a thinner

lithosphere,

L.

Fig. 3. Predicted

values of F,, the surface

zone of model III and the corresponding function

of the model parameter

from eq. 6, F, = 0.638@

0

20

IO

0

G’. (Note:

H.F.U..

model

10

heat flow. and L. the lithospheric values of W, the half-width F, was computed

and, from eq. 5. erf( LJG’/2

assuming /a)

thickness

within

the inner

of the inner zone, ail plotted F, = 0.8 H.F.U.)

as a

For G’>_ 8.

= 0.75 or L = (144.07/G-)

km.

I

20

2

20

10

0

10

?O

18 2 I -9 I.!_

,/-' L

0

20

10

0

10

20

t(my)

Fig. 4. Profiles across a mid-ocean H.F.U.

= 10e6 cal cm-2

in kilometres, measured represent

\

.iII20 10

10

t pm, 1

rift of F, the surface

20 heat flow measured

in heat flow units (where

set-’

as predicted

in millions

AT\,

1

), and S, the subsidence of the sea floor relative to the ridge crest measured by (a) model I, (b) model II and (c) model III. I is the age of the sea floor

of years

the range of “reliable”

(m.y.)

The rectangular

heat flow measurements

boxes

superimposed

at various

sea-floor

on the heat-flow ages.

curves

117

Corresponding

values of these variables

all reasonable

values of G’, F, (YJG’

are plotted

as a function

of G’ in Fig. 3. For

and L a l/ @.

Figure 4 compares variations of surface heat flow and topography as a function of ocean floor age as predicted by the three models shown in Fig. 1. Superimposed on the heat flow curves for each model are rectangular (at the centre

of the boxes) and standard

tions from well sedimented measurements

represent

ducted

the conducted

observations

It would therefore

of reliable

heat flow observa-

ocean floor (Sclater

et al., 1976). These

portion

of the total heat flow through

the total heat flow. The large scatter

at young ages indicates

the

amongst

that this is not always the case.

seem likely that the mean values of these data are underestimates

of the total heat flow. The tops of the rectangular more reliable indications as large as 16 H.F.U. at the Galapagos

the means

areas it is usually presumed that the relatively low seals off hydrothermal circulation so that the con-

heat flow in fact represents

even “reliable”

deviations

areas of young

sediments. In well sedimented permeability of the sediment

boxes representing

regions

on Fig. 4 may provide

of the total heat flow at these young ages. Individual

at an age of 2 Ma and 18 M.F.U.

spreading

centre (Anderson

values

at 0 Ma have been measured

and Hobart,

1976). Unless topographic

focussing has influenced heat flow in these areas, such measurements lower bounds to the total heat flow at M.O.R.‘s.

may also be

Interpreting the “reliable” means as underestimates of heat flow at young ages, it is clear from Fig. 4 that close to the ridge axis model I becomes untenable. Predictions of heat flow are infinite at the ridge axis but as much as 30% too low at sea-floor ages of 4 Ma and 5 Ma. In other words the central anomaly is too narrow as well as too high. This is because the upwelling mantle, in model I, is injected along the axial plane only, and at infinite velocity. However, since the extensional model introduced here assumes upwelling over a broad region at finite velocities, it predicts

both finite

values

for the axial heat flow and a broader

Larger axial heat flow values are obtained the central becomes

heat flow anomaly

indistinguishable

The predicted

elevation

Fig. 4. (Topography described

central

anomaly.

in model III at the expense of the width of

(Figs. 3 and 5). Beyond

ages of 20 Ma model

III

from model I. of the ocean floor with decreasing

was computed

by Jarvis and McKenzie,

assuming

isostatic

age is also shown in

compensation

1980.) Profiles from models

at z = 0 as

I and II are similar

except that less elevation is predicted by model II due to its artificially reduced central thermal anomaly. The M.O.R. profile predicted by model III differs in a qualitative manner from the previous models in that a flat top is predicted across the width of the inner zone. Although this would appear to be an undesirable feature of the uniform stretching model it may, through comparisons with bathymetry profiles over M.O.R.‘s, allow us to constrain W, the one free parameter of the model. Moreover, from an analysis of the slopes of ridge flanks, Davis and Lister (1974) pointed out that the mean elevations of ridge crests in the major ocean basins were about 0.2 km less than that expected on the basis of model I. While their attempts to

Fig. 5. Superimposed as a function from model It

model heat flow predictions,

for this observation

this same qualitative M.O.R.

through

the corresponding

(the boxes)

with typical

cases

of model 111 for G’= IOO. 411.

values of G’.

minor variations

feature is an immediate

of model I were unsuccessful,

consequence

of the flat top in model III

profiles.

Various

model heat flow profiles

Fig. 5. In Fig. 5a the differences overlaying profile

heat flow measurements

of model I is compared

(j3 = 16)and model III (G’ = 41 I). b. Heat flow predictions

1600 and co. Labels next to each curve indicate

account

F, and “reliable”

of sea floor age, t. a. The heat flow prediction

in the vicinity between

models

a typical case from each of models

of model

I. Relative

to McKenzie’s

of the ridge are superimposed

in

I, II and III are emphasized

by

II and III on the predicted

(1967) plate model (model

heat flow I), model

II

has a lower heat flux not only on the ridge axis but at all ages of ocean floor. Model III, however, has a lower axial heat flow but a higher heat flow on the ridge flanks out to about 20 Ma. At older ages than 20 Ma heat flow profiles from all three models converge. Figure 5b illustrates a series of heat flow profiles from the extensional model (model III) for various values of G’. At low values of G’ (e.g. G’ = lOO), the central anomaly is too low and too wide. As G’ increases the anomaly increases in magnitude and decreases in breadth, eventually converging with the model I profile (for which G’ = co). An advantage of model III is that even for large G’ the axial heat flow remains finite, and the model itself remains thermally and mechanically self-consistent.

119

DISCUSSION

AND CONCLUSIONS

The extensional differs

from

model

most

incorporated

of rifting

previous

models

at mid-ocean in that

ridges

which

a finite-width

is presented

zone

below the ridge crest. From eq. 13 the half-width

of intrusion

is

of this zone is:

W = u,a2/G’K

(15)

or assuming typical values of u0 = 4 cm/yr, half-width is: W = (24790/G’)

here

a = 125 km and

K =

0.008 cm2/sec,

km

the

(16)

Thus for G’ = 411 the width of the zone of intrusion,

2W, is approximately

120 km,

while for G’ = 1600 the width is approximately 30 km. Heat flow profiles for these two values of G’ are included on Fig. 5b. The corresponding lithospheric thicknesses at the ridge crest are - 7 km and - 3.5 km (see Fig. 3). The model with G’ = 411 is more successful in accounting for the observed high heat flow values, one standard deviation above the mean value, but predicts a relatively low axial heat flow of 13 H.F.U. (heat flow units). When G’ = 1600, the (lower) heat flow predictions on the ridge flanks are very close to the mean values of reliable observation while the (larger) predicted heat flow at the ridge axis has a value of 26 H.F.U. If the reliable mean heat flow data are true measures of the total heat flux at very young sea floor ages, the model with a 30 km wide intrusion zone (G’ = 1600) provides a better estimate of the M.O.R. heat flow than does a model with a 120 km wide intrusion zone. However, if due to hydrothermal circulation even the “reliable” measurements underestimate the total heat flow, then a wider zone of intrusion on the order of 100 km may be required. A more precise fitting of model heat flow profiles to the observations is not attempted here because of the inherent ambiguity, discussed above, concerning the age t, of the ocean floor at the boundary between the stretching and uniform spreading zones (at x = + W). An additional constraint on the width of the intrusion zone below the ridge is provided by the topographic relief of M.O.R.‘s. The extensional model of rifting presented here predicts a ridge topography which is flat across the entire intrusion zone.

(The

predicted

central

graben

by such a “fluid”

both the assumption neglect of horizontal

characteristic model.)

of slowly

This feature

cannot

be

of the model is a consequence

spreading

ridges

of

that the intrusion velocity o,, does not vary with x, and the diffusion of heat within the stretching zone. The uniform

stretching model can therefore

only approximate the extensional processes at submarine rifts. A more realistic model would have a maximum extension (and hence maximum intrusion velocity) at the ridge axis, grading smoothly to a rigid horizontal motion at x = W. This would require a numerical solution of the temperature equation, since it would no longer be separable in terms of spatial coordinates, but would result in a smoother ridge crest topography. In general the topography about

120

oceanic rifts lies between that predicted by the narrow dyke intrusion of model I and the flat-topped topography predicted by the uniform extension model (Davis and Lister, 1974). Comparisons ions of non-uniform

of detailed

stretching

the width of the intrusion broad

zone of intrusion

the vicinity

profiles with the predict-

models would be extremely

zone. The present is required

of mid-ocean

M.O.R. topographic

valuable

model suggests

to account

in constraining

that the presence

of a

for the heat flow and topography

in

ridges.

If the width of the zone of intrusion is as large as 100 km, it thickness of the lithosphere and thus resembles a mantle plume ridge. Such an upwelling plume is required in models of mantle the moving lithosphere forms the cold upper surface layer of a

is comparable to the upwelling below the convection in which large convection cell

(e.g., Turcotte and Oxburgh, 1967; Peltier, 1980; Jarvis and Peltier, 1980. 1982) but is not an essential feature in any previous plate model. Near-surface isotherms in the

‘\ \

L-

lil -__1

Fig. 6. Near surface

isotherms,

pair of two-dimensional the rising plume horizontal

T, and streamlines,

mantle convection of 120 km and

T are labelled

4, in the vicinity

of the common

rolls. The region for which solutions

axis and lies in a vertical

dimensions

temperature

~-----i-7--l15

plane

normal

to the plane of upwelling.

1500 km respectively.

with values of T/r

are

(Vertical

exaggeration

where T is the mean temperature

upwelling

It has vertical

by the dashed isotherm

for which T is 30% greater

numerical

of five points vertically

and 5 1 horizontally.

interpolation Rayleigh

for this convection

Fig. 7. The variation upwelling

33 x 101

to a refined

number

mantle

conductivity from Parsons

prior to contouring

Values of F are those computed

of the mantle.

F’ as indicated

model temperature

and Sclater.

1977).

of

layer.

than L? The

Fifth order spline

both T and I). The (Benard)

mode1 is 3.9’10”.

of surface heat flow, F, with horizontal

plume.

from the convection

grid was performed

on and

= 7.5) Contours

of the convecting

The centre of the rising plume is indicated grid in the area shown consists

limb of a

shown is centred

distance,

d, away from the central

using an estimated

on the right-hand

ordinate

field using a conductivity

axis of an

value of the mean thermal

scale is the heat flow computed

appropriate

to the lithosphere

(taken

121

vicinity

of an upwelling

vigorous

mantle

mantle

convection

Streamlines

of the convective

qualitative

similarity.

upwelling

plume

as predicted

and

Peltier,

spread

are concentrated

diffusively

again

zone of the convective

shows a qualitative

rifting

model. The convection

which constant

physical

material

of

with Fig. lc shows a

to the surface is swept

in Fig. 7. Comparison

to the heat flow predictions

temperatures

properties

model

in Fig. 6. above

the

horizontally

of surface heat flow across the top of the

plume is plotted

similarity

close

as plume

below the cold upper surface. The variation upwelling

by a numerical

1982), are displayed

flow are also shown. Comparison

Isotherms

but

plume,

(Jarvis

are derived

with Fig. 4c

of the extensional

from a numerical

and simple geometry

prevent

of mantle flow. Nevertheless the qualitative similarity duced actively by a mantle convection cell or passively

model in

an exact simulation

of isotherms, whether proby an extensional mode of

rifting at the mid-ocean ridge, illustrates the difficulty in distinguishing cause and effect with regard to plate formation and motion. In the extensional model unspecified forces, outside the model domain, pull plates apart at the ridge crest. In the convective model diverging flow above the plume axis supplies the necessary forces. At present it is not known whether large mantle plumes are upwelling below mid-ocean ridges. Nor is it established as yet that the intrusion zone below ridge crests is 0 (100 km). It is possible that both of these conditions occur and hence that the convection

and

extensional

plate

models

detailed analyses of sea floor topography may help to resolve these issues.

are not

mutually

about the central

exclusive.

Future

rifts on mid-ocean

ridges

ACKNOWLEDGEMENTS

I am grateful to Dan McKenzie for critical comments and stimulating discussions at the outset of this study and to Dick Peltier for suggesting the comparison of active and passive ridge isotherms. This work was sponsored by the Natural Sciences and Engineering Research Council of Canada and the University of Toronto. REFERENCES

Anderson, eastern

R.N. and Hobart,

M., 1976. The relation

Pacific. J. Geophys.

Davis, E.E. and Lister, C.R.B.,

between

heat flow, sediment

thickness

and age in the

Res., 81: 2968-2989. 1974. Fundamentals

of ridge crest topography.

Earth Planet. Sci. Lett., 21:

405-413. Jarvis,

G.T. and McKenzie,

D.P.,

1980. Sedimentary

basin formation

with finite extension

rates.

Earth

Planet. Sci. Lett., 48: 42-52. Jarvis,

G.T. and Peltier,

convecting

mantle.

W.R.,

Nature,

1980. Oceanic

bathymetry

Jarvis, G.T. and Peltier, W.R., 1982. Mantle convection Astron. Lubimova,

profiles

flattened

by radiogenic

heating

in a

285: 649-651. as a boundary

layer phenomenon.

Geophys.

J. R.

Sot., 68: 389-427. E.A. and Nikitina,

Res.. 80: 232-243.

V.N., 1975. On heat flow singularities

over mid-ocean

ridges. J. Geophys.

McKenzie.

D.P..

1967. Some remarks

on heat flow and gravity

anomahes.

J. Geophya.

Res.. 72(24):

6261-6273. McKenzie,

D.P.. 1978. Some remarks

on the development

of sedimentary

basins.

Earth Planet. Sci. Lett..

40: 25-32. Oldenburg.

D.W.. 1975. A physical

model for the creation

of the lithosphere.

Geophys.

J. R. Astron.

Sot..

43: 4255451. Parsons,

B. and McKenzie.

Geophys. Parsons,

D.P.,

1978. Mantle

B. and Sclater.

with age. J. Geophys.

J.. 1977. An analysis

of the Earth’s

Interior.

North-Holland,

Amsterdam.

J.G. and Francheteau.

tectonic

and the thermal

structure

of the plates.

J.

of the variation

of ocean

floor bathymetrv

and heat flow

Res.. 82: 803-827.

Peltier, W.R., 1980. Mantle convection

Sclater,

convection

Res., 83: 4485-4496.

and geochemical

Proc.

and viscosity.

Enrico

Fermi

In: A. Dziewonski

International

J.. 1970. The implications

of terrestrial

models of the crust and upper

and E. Boschi (Editors).

School

mantle

of Physics

(course

heat flow observations of the earth. Geophys.

Physics

LXXVIII). on current J. R. Astron.

Sot., 20: 5099542. Sclater.

J.G.. Crowe,

Geophys. Turcotte,

J. and Anderson.

R.N.,

1976. On the reliability

of oceanic

heat flow averages.

J.

Res., 81( 17): 2997-3006.

D.L. and Oxburgh.

Mech.. 28: 29-42.

E.R.. 1967. Finite amplitude

convective

cells and continental

drift. J. Fluid