Thermal aspects of sea-floor spreading and the nature of the oceanic crust

Tectonophysics,

18 (1973) l-17. 0 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

Research Articles THERMAL ASPECTS OF SEA-FLOOR SPREADING AND THE NATURE OF THE OCEANIC CRUST*

Y. BOTTINGA and C.J. ALLEGRE Institut de Physique du Globe, Universitide

Paris, Paris (France)

(Accepted for publication August 31, 1972)

ABSTRACT Bottinga, Y. and Allegre, C.J., 1973. Thermal aspects of sea-floor spreading and the nature of the oceanic crust. Tectonophysics, 18: l- 17. By means of a plate-tectonics model we have computed radial temperature profiles for various spreading velocities for the region bounded by the bottom of oceanic layer two, the top of the lowvelocity zone, the centre of the ridge, and a vertical plane at 1000 km away from the ridge centre. The model we have used differs from previous models in that certain petrological aspects of basalt formation, partial melting, and latent heat effects have been taken into account. Oceanic heat flow was calculated from the ridge crest to 1000 km away. The thermal relationships in this region seem to rule out a gabbroic or amphibolitic third layer in the oceanic crust. INTRODUCTION

The concept of sea-floor spreading and its generalization have been extremely successful in explaining quantitatively morphological

in terms of plate tectonics various kinematic and geo-

aspects of the earth. Because of this, plate tectonics is no longer a hypotl e-

sis but a theory. Attempts

to use this new theory to explain dynamic or petrological

problems have been at best only qualitatively tectonics theory to arrive at certain conclusions and to calculate oceanic geothermal

successful. In this paper we use plateabout the nature of the oceanic crust

gradients at various distances from a spreading center.

Numerous papers have been published on the nature of the second and third layer of the oceanic crust. While a consensus of opinion has been reached on the constitution of the second layer, the nature of the third layer is still controversial (Le Pichon, 1969). The third layer is best known by being seismically distinct from the overlying second layer and the underlying upper mantle, but the acoustic velocities characteristic for layer thre: do not allow a petrological identification. Unequivocal direct observations of layer three are non-existent. At present most experimental petrologists use one or another version of the Clark and Ringwood oceanic geothermal gradient (Clark and Ringwood, 1964; Ringwood, 1966) to relate the results of their experiments to the real world. It is well *Contribution

I.P.G. NS 43.

2

Y. BOTTINGA AND C.J. ALLEGRE

known, however, that in the calculation in the upper mantle was overestimated

of this geotherm the radiative transfer of energy (Fukao et al., 1968; Fukao, 1969; Shankland,

1970; Pitt and Tozer, 1970). Also, convection

was ignored and the importance

of sea-

floor spreading was generally not realized in 1964. For these reasons this temperature distribution

has little to recommend

is required to understand

it. A knowledge of the oceanic geothermal

the genesis of submarine

gradient

basalts and to put some limits on the

possible nature of the third layer. Many mode1 calculations

of oceanic heat flow have been published

during the last five

years, and one may wonder whether it is necessary to repeat this type of computation yet again. Our answer to this rhetorical question is yes, because most of these models are unrealistic

in several aspects. For instance McKenzie (1967) and Lee (1970) would

like to build lithospheric

plates by dike intrusion

at 500°C. In contrast with previously

published models we have tried to incorporate in our model some petrological information, such as the melting relations of basalt and peridotite. It is a geological fact that basalts are emplaced in the liquid state. However, in no mode1 of processes near the ridge centre, has melting or partial melting been allowed, i.e., the presence of a liquid phase and concomitant latent heat effects have been neglected. It is in these aspects that our model differs from previous ones. Our use of the terms “rise” and “ridge” is synonymic. We make no distinction between plate velocity, spreading velocity, and spreading rate; whenever these words are used we mean the velocity of the plate motion with respect to the ridge centre. MODEL

To calculate an oceanic geothermal

gradient at the spreading centre, we use a kinematic

sea-floor spreading model (Fig. 1) conforming to the plate-tectonics theory. This type of mode1 has been used by various authors (Langseth et al., 1966; McKenzie, 1967; McKenzie and Sclater, 1969; Sleep, 1969; Le Pichon and Langseth, Francheteau,

1970; &later and

1970; Lee, 1970) to explain observed oceanic heat-flow patterns

bottom elevation. We believe that the mechanical

properties

or oceanic

of silicates, together with a

reasonable temperature distribution in the upper mantle and the inferred nature of the low-velocity zone (L.V.Z.), make it plausible that the decoupling between the moving lithospheric plate and the underlying upper mantle takes place in the top layers of the L.V.Z. We agree with the conclusions of Anderson and Sammis (1970) and Lambert and Wyllie ( 1970), that the presence of the L.V.Z. in the upper mantle is most likely due to a small degree of partial melting. This may be caused by the breakdown erals under the pressure and temperatures

of hydrous min-

at the top of the L.V.Z., giving rise to an

aqueous phase (WylIie, 1970). The velocity field for our mode1 is given in Fig. 1. As plate thickness we have taken 75 km, this has been suggested by the analyses of Press ( 1970) Kanamori ( 1970) and Wang ( 1970). We have estimated the temperature at the lower boundary of the plate to be about 133O’C. This is in reasonable agreement with the breakdown temperature of phlogopite at 25 kbar [P(HaO) less than P (total)] according to

THERMAL

ASPECTS

OF SEA-FLOOR

3

SPREADING

MODEL

PLATE

s? :: !!

2nd

LAYER

Ikrn _-------_4krn______.

DIRECTION OF PLATE MOTION

I 1

UPPER

’ 1

tokm’

_

T = 132Q°C

1

T=133Q°C

LOW-VELOCITY

7sm 1500

.

Fig. 1. Plate

70km

MANTLE

ZONE

km

.

model. Arrows indicate the directions of the movements.

Yoder and Kushiro (1969). At this pressure and temperature we are still in the solidus field of anhydrous tholeiite (Cohen et al., 1967), but partial melting will occur if some water is present (Hill and Boettcher, 1970). Taking the mantle to consist of material which will yield about 25% basaltic liquid upon partial melting, we can calculate the radioactive energy release in the upper mantle from the data of Tatsumoto et al. (1965), for oceanic tholeiite. rived at an estimate of 4.9 . 10-l 5 cal. g-’ set-’ . The thermal conductivity

of probable upper-mantle

In this way we have ar-

materials is about 0.007 cal. sec..’

cm-’ degr-’ according to the measurements of Kawada (1964 and 1966). Fukao (1969) has argued that under upper-mantle conditions at temperatures less than 1400°C no great variations in the thermal conductivity temperature,

should be anticipated;

of olivines, as a result of changing pressure and Shankland

concurs with this opinion (Shankland,

1970). We have therefore assumed that the thermal conductivity

in our plate is constan.:.

As an average density for the upper-mantle material above the L.V.Z., we have taken 3.3 g/cm3 (Wang, 1970). We have taken the specific heat of the upper-mantle material* to be 0.3 cal. g-’ degr.- ‘. From the above figures one may calculate a steady-state heat flow in the quiet ocean basins, far away from the spreading centers, of about 1.25 HFU,* which agrees well with the observations

(Sclater and Francheteau,

1970). The motions

and dimensions of our model plate are given in Fig. 1. We have assumed that the liquidus and solidus of our upper-mantle material to be parallel in P-T space, with a slope of 4°C per km depth, and a zero-pressure solidus tem*The specific

heat of diopside.

l

* 1 HFU=

1 * 10m6 cal. cmw2 set-’

4

Y. BOTTINCA AND C.J. ALLEGRE

perature of IO35”C and a melting interval of 760°C. The work reported by Cohen et al. (1967), and Ito and Kennedy (1967, 1968) indicates that our simplifications are not necessarily poor approximations, Also we have assumed that the degree of melting of this upper-mantle material is proportional to the fraction of the melting interval which has been traversed. Eq. 1 gives the melting behaviour of our hypothetical upper-mantle material. T= Ts +z2+F(q-Ts)

(1)

T = temperature of partially melted material

where:

T, = solidus temperature at I atm.

z = depth, positive z-direction is downward = solidus gradient F = fraction of molten material T, = liquidus temperature at 1 atm. A roughly similar proportionality has been observed by Wright and Weiblen (1967) and Peck et al. (1966) for the crystallization of a Hawaiian tholeiite. We do not know of any laboratory experiments which have provided quantitative information on this point. At 75 km depth and 1329”C, our upper-mantle material is at its melting point. Hence when this material rises, partial melting wil occur as a result of pressure decrease and the poor thermal conducting qualities of silicates. An important quantity in these considerations is the latent heat of fusion of our material. We have assumed that the latent heat of fusion is independent of the degree of melting. Moreover its variation with temperature and pressure, as given by the Planck equation, will be negligible in comparison with our ignorance about the actual value of this quantity. We do not know of any measurements of the latent heat of fusion of possible upper-mantle materials. For a few minerals the latent heat of fusion is known, these values suggest that 100 cal./g should not be unreasonable. In our calculations we have neglected density differences between solid and liquid phases. An average thermal expansion of 3.5 . lo- degr.-’ was assumed. If the temperature at point (xx,z) in our moving plate is less than the solidus temperature at that point, its variation with time will be given by: aT$lz

where:

T = temperature at point (x, z)

t = time x = horizontal distance V,, V, = horizontal and vertical plate velocities; I V, I = I V, I k = thermal conductivity p = density CP= specific heat at constant pressure

THERMAL ASPECTS OF SEA-FLOOR

4 = energy production

5

SPREADING

by radioative decay per unit time and unit mass

dT = adiabatic temperature variation with depth ( aZ 1s The first term at the right hand side (RHS) of eq. 2 gives the temperature variation per unit time due to conduction, and the third term at the RHS of eq. 2 is the adiabatic correction to the first term.

where: g = gravitational

acceleration

(Y= coefficient of thermal expansion The second term at the RHS of eq. 2 gives the variation

in temperature

with time,

being caused by the motion of the plate, and the fourth term is the adiabatic correction to the vertical plate motion term. The two adiabatic corrections are discussed in the appendix. When the temperature at point (x, z) is higher than the solidus temperature, melting or freezing will accompany

temperature

changes. In this case the term L/c,

should be added to the left hand side of eq. 2 and a term V,(_L/c,)(aF/az) The partial differentials modified to:

This equation

involving Fare obtained

aF/ilt

to the RHS.

from eq. 1. As a result eq. 2 should be

takes care of latent heat effects when the fraction molten material changes

and of the transfer of energy due to latent heat stored in moving molten material. The term A represents the RHS of eq. 2. Eq. 2 and eq. 4 were solved numerically by means of an explicit finite-difference method. Temperatures were calculated at the nodes of a square grid, with 5km sides; time intervals ranged from 12,500 to 25,000 years, and the calculation was carried on for a total period of 50 million years. No signs of unstable behaviour were noticed. An explicit method was used instead of an implicit one, because one needs to know at every grid point whether or not a change of phase occurs, before the temperature

at the next grid point can be calculated.

The lower boundary of our plate is at a constant temperature of 1329”C, and of 1334°C in the region where upwelling takes place underneath the spreading centre. One end of the plate coincides with the vertical plane of symmetry containing the axis of the spreading centre, and the other end is at 1500 km from this axis. The boundary conditions here are that the horizontal temperature gradients vanish. The bottom of layer two is th,: upper boundary of the calculation. The temperature at this boundary can be calculated once one knows the heat flow at the top of layer two, the thickness of layer two, the temperature at its top, and one assumes that layer two is in thermal equilibrium. The temperature at the top of layer two is O”C, the approximate temperature of ocean-bcttom water. Initially we assume a l-km thickness for layer two, although later we will calculate a thickness of layer two from the amount of basalt which is produced at the ridge crest.

6

Y. BOTTINGA AND C-l. ALLEGRE

The thermal conductivity

of layer two was approximated

by 1.5 X the thermal conduc-

tivity of basalt. The factor 1.5 is suggested by the studies of Cermak (1967), who compared the conductivity of dry and water-saturated sediments. OCEANIC HEAT FLOW

In Fig. 2, we have plotted the calculated heat flow for various spreading velocities versus the distance from the ridge axis. It was noticed by Le Pichon and Langseth (1970), that oceanic crust of the same age should have approximately the same heat flow; our curves show this relationship. For a spreading velocity of 4 cm/year we have also calculated a heat-flow profile for a model in which the upper-mantle material does not have a melting range, but a melting point of 1200°C at 1 atm., and 1250°C at 23 kbar. The heat flow for this model is nearly identical

to the one plotted in Fig. 2 for 4 cm/year.

Also are plotted the averages of heat-flow observations for parts of the Pacific plate of the same age range versus distance from the rise crest; the averages and the standard deviations were calculated by Sclater and Francheteau

(1970). The spreading velocity for the

Pacific plate is about 4 cm/year. Our calculated curve does not coincide with these averages but the agreement is to within one standard deviation. We do not think that great significance

should be attached to this agreement, because we are not convinced

these averages are physically meaningful quantities. The difference between our calculated values and the Sclater and Francheteau

that averages

I

I

1

-!

15 \ :\

OCEANIC HEAT FLOW IN THE WCWITY

,

,

,

OF sl’RtSD%

,

,

=NT=

,

,

,

Kloo DISTANCE

FROM RlD’3E CENTER (KM)

Fig. 2. Oceanic heat flow in the vicinity of spreadingcenters for 1 (bottom), 4 (middle) and g (top) cm/year plate velocities. VerticaI arrows indicate averagss and standard deviations for observations for regions of the same age, in the Pacitic Ocean, as given by Sclater and Francheteau (1970).

THERMAL ASPECTS OF SEA-FLOOR SPREADING OBSERVED AND CALCULATED

HEAT FLDW CLOSE TD A SPREADING CENTER

1

1

1

. 0

I Km

.

r..

.

;

0

50

AGE

OF CRUST

(YRS)

I

I

50

aJ

x 10’

EAST

Fig. 3. Observed and calculated heat flow in the vicinity of three different spreading centers plotted versus age of oceanic crust. Bold lines denote calculated heat flow, in this paper. A. Reykjanes ridge, V = 1 cm/year. X = Horai et al. (1970); O= Talwani et al. (1971). B. Mid-Atlantic Ridge, 12S”N-ISSoN, V= 2 cm/year. l = Von Herzen et al. (1970). C. Juan de Fuca ridge, V = 2.9 cm/year. o = Lister (1970).

is greatest close to the spreading centre, this is true for all model calculations

which have

any pretension of representing the real world, such as those by Sleep (1969), &later and Francheteau (1970), and Hanks (1971). Far from the spreading centre, all model calculations show a good agreement with the observations, because this is invariably a built-in feature. In Fig. 3, we have plotted measured heat-flow profiles across the Reykjanes ridge (Horai et al., 1970; Talwani et al., 1971), the Mid-Atlantic Ridge between 12.5” and 15 5” N (Von Herzen et al., 1970), and the Juan de Fuca ridge (Lister, 1970). The spreading velocities for these ridges are respectively 1, 2 and 2.9 cm/year. Inspection of Fig. 3 will reveal that these three profiles have little in common, except for the scatter and the disagreement with the calculated profile. Actually the disagreement between the calculations and the observations is worse than is indicated in Fig. 2 and 3, when one takes into account the heat associated with the production of layer two.

8

Y. BOTTINGA AND C.J. ALLEGRE

The ocean-bottom magnetic-anomaly pattern produced while layer two is extruded, according to the Vine and Matthews ( 1963) hypothesis, has as a necessary corollary that Iayer two is produced in a narrow zone at the ridge centre (Harrison, 1968). Assuming that approximately a 1 km-thick layer of basalts is erupted in a 10 km-wide zone at the ridge centre, one should observe an additional heat flow of 10 X V HFU for this region; I’ is the spreading velocity in cm/year. This additional heat flow is the result of the solidification and cooling to 0°C of the erupted basalt. (In the section “‘Nature of the oceanic crust” we will discuss this point further.) The disagreement between the calculations and the observations is serious and is not understood in a quantitative way at present. The same is true for the scatter in the heat-flow measurements. Fig. 3 shows also a disagreement between the observations of Talwani et al. (197 1) and those of Horai et al. (1970). Most observers have discussed possible reasons for the scatter in their measurements, and Talwani et al. (1971) have also noticed the disagreement between model calculations and the observations. Talwani et al. f 197 1) have suggested that the low heat flow they observed over the centre of the Reykjanes ridge is due to water circulation in the top of layer two. Elder (1965) has pointed out that this phenomenon could be of importance in regions with submarine vulcanism, i.e., ‘where one could anticipate porous layers. However, as far as we know, no anomalous water temperatures close to the ocean floor in the mid-ocean ridge regions or at the center of the oceanic ridges have been observed, see for instance Garner and Ford (1969). Of course there is the possibility that the measuring techniques were not sensitive enough. We think that in regions where layer two has sufficient permeability, oceanic bottom water may be absorbed by the initially dry layer three, and this could be another reason for the disagreement between the calculations and the observations as well as for the scatter in the obse~ations in the vicinity of the ridge centre. In the section “Nature of the oceanic crust“ this point will be further discussed. OCEANIC GEOTHERMAL

GRADIENTS

In Fig. 4 we have plotted steady-state oceanic upper-mantle tempera~re profiles for spreading velocities of 1,4 and 8 cm/year, at 0, 200, and 1000 km from the ridge centre. The gradients at the ridge centre are very steep and do not depend much on the spreading velocity. Hence differences in the mechanical properties of rocks underneath ridge crests with different spreading rates should be minimal. We have also plotted an equilibrium gradient at a distance sufficiently far away from the ridge axis to be independent of the plate velocity and the distance from the ridge centre. This gradient resembles the oceanic geothetm as given by Ringwood (1966). The difference between the equilibrium gradient and the steady-state gradients is quite appreciable, even at 1000 km from the ridge crest. Because of this we think that the use of equilibrium gradients in discussions about the genesis of oceanic basalts is inappropriate. Our calculated ocean-ridge temperature profiles intersect the solidus tem~rature of our hypothetical upper-mantle material at rather shallow depth (4-8 km). The consequent reduction of material strength at this depth is in good agreement with the obser-

THERMAL ASPECTS OF SEA-FLOOR SPREADING

TEMPERATURE

9

(*C t

24 28 ;; Y -

3236-

f 4aB Q 4448 s256-

OCEANIC GEOTHERMAL GRADIENTS

60 64 68 12 -

Fig. 4. Oceanic geothermal gradients at 0, 200 and 1000 km from a spreading center, and phase relations for the basalt system. Data for the basalt-ecfogite transition from Ringwood and Green (1966). -.- = spreading rate 1 cm/year; -..- = spreading rate 4 cm/year; -_- = spreading rate 8 cm/year. A = basalt-eclogite transition for high-aluminum basalt, D = basalt-eclogite transition for low-potassium tholeiite, E = equilibrium geothermal gradient far away from a ridge center, S = soiidus tempera ture of the upper-mantle material in our model.

vation that ocean-ridge earthquakes are characterized by epicenters close to the surface [Ward et al., 1969; Sykes, 1970;Thatcher and Brune, 1971). Thatcher and Brune (1971) found that the only acceptable fit to their seismic data, from an earth-quake the crest of the East Pacific Rise near the northern

swarm on

tip of the Gulf of California,

demanded

a focal depth of only 7 km into the crust. These authors have also reported anomalous low seismic velocities in the upper mantle underneath

the ridge crest. Molnar and Oliver

(1969) have reported high seismic-wave attenuation for paths which cross a spreading centre. These observations may be explained by the presence of a partially melted zone in the upper mantle under the ridge crest. In Fig. 5, zones of 1 and 1% partial fusion in the upper mantle under the ridge have been plotted versus the distance from the ridge axis, for spreading rates of 1,4 and 8 cm/year. The shape of the top lo-km part of the 4 and 8 cm/year curves, and the top 20.km part of the 1 cm/year curve, is due to the depth at which magma release takes place. For the 4 and 8 cm/year spreading-rate calculations, magma release occurred between 40 and 10 km, while for the 1 cm/year case the corresponding figures are 40 and 20 km. This point will be further discussed in the next section. Because the thermal conductivity of the upper mantle is very small, the temperatures inside the plate not far from the ridge axis are

10

Y. BOTTINGA AND C.J. ALLEGRE

5s

Dmmce low

7%

f,m u&e

cente, j Lm !

MmIO -

_

PARTIAL YELTW IN WKR MANTLE WXlJS OWANCE FROM RIDGE CENTER

52 -

“\

i

“1

56: i 60

-

64

-

68

-

Y r 72:

“\

i i

I

i /’ =::i..c”~_..-...-.,.~.‘.-

,. _..-*._.‘--

dl_‘.-..-‘+.,,_,..

76

..i’ -*I.-..*-.**-

1Y. LVL C

Fig. 5. Partialmelted zones in the upper mantle. 1 and fC@partial meit contours for spread@ rates of 1 cm/year (-.-),

4 cm/year (-..-),

and 8 cm/year f-...-).

almost completely determined by the spreading velocity. For the same reason that oceanic crust of the same age should have the same heat flow, we observe that at constant depth the contours in Fig. 5 should run at distances from the spreading center which are proportional to the plate velocity. These contours agree qualitatively with the anomalous uppermantle zones beneath the oceanic rises, which were outlined by Talwani et al. (1965a and b). Unfortunately this work was done apparently before the ridge sections that the authors discuss were well defined. The East Pacific Rise section (Talwani et al., 1965b) is across a portion of the rise known as the Juan de Fuca ridge; it is not perpendicular to the ridge and appears to transect a small ridge offset. Similar, but more important ridge offsets by transform faults occur in the Mid-Atlantic region, also discussed by Talwani et al. (1965a). Therefore, the lateral extent of the anomalous upper-mantle zones reported by these authors is probably not correct. The density contrast which these authors have choosen, normal mantle p = 3.4, and anomalous mantle p = 3.15, is larger than one would expect to be caused by an average partial fuoion of 15%. A density contrast of about 3% of the normal mantle density could be expected in such a case. Hence one should not look for a quantitative agreement in lateral and vertical extent between the Talwani et al. (1965a and b) anomalous mantle zones and the contours of Fig. 5.

THERMAL ASPECTS OF SEA-FLOOR

In Fig. 4 we have also plotted transition information

11

SPREADING

ranges for the basalt-eclogite

transition.

has been taken from Ringwood and Green (1966). This transition

upon the chemical composition for high-alumina

of the basalt; curves A and L) give the transition

basalt and low-potassium

rocks are frequently

olivine tholeitte,

respectively.

The

depends ranges

Both types of

found near spreading centres on the ocean bottom. These data and

our oceanic geothermal

gradients confirm the conclusions

by Harris and Rowe11 ( 1960),

Bullard and Griggs (196 1) and Wetherill ( 196 1) that the suboceanic be due to the transition eclogite-basalt.

Moho is unlikely

to

NATURE OF THE OCEANIC CRUST

In our model we have assumed that the second layer consists of basalt; in accord with the conclusion

of Le Pichon (1969). We have not noticed a significant

correlation

be-

tween spreading velocity and the observed thickness of layer two. The absence of this correlation is a feature of our model in which layer two is produced by the extrusion of basalt from a 10 km-wide strip at the ridge centre. This basalt is the liquid fraction in an upward-moving 10 km-wide column of partially melted upper-mantle material underneath the ridge crest. The degree of partial melting is nearly independent of the vertical plate velocity; it is determined by the amount of pressure release. The total amount of basait produced per unit time and per unit length of ridge is thus proportional to the spreading velocity, assuming that the release of the basalt does not depend on this velocity. Our calculations show that for spreading rates of 4 and 8 cm/year, the loss of heat by conduction in the rising column under the ridge crest is too small to cause significant soliditi, cation of the partially melted material before extrusion, but for a spreading rate of 1 cm/year this is not true. In order to make the thickness of layer two independent of the spreading rate, basalt has to be released from the upper mantle at a depth greater tha.1 20 km. This is in agreement with the deductions of Green (1970) about the depth at which high-alumina basalt is released from the upper mantle. The melting relation we have chosen causes our upper-mantle

material to be about 20%

partially fused when it has risen from the top of the L.V.Z. to the ridge crest. Hence from our 10 km-wide column, 2 km of basalt can be extracted,

producing

a 1 km-thick layer

two, moving in both directions laterally away from the spreading center. Upon solidifying and cooling to O”C, this 1 km-thick layer of basalt should cause an additional average he2.t fIow of 10 X V HFU, where Y is the spreading velocity, in the 10 km-wide zone in which layer two is extruded. In our model it has been assumed that the cooling of layer two occurs nearly instantaneously, which is suggested by the texture of the oceanic-ridge basalt!;, as a result of the good thermal contact between the basalt and the ocean-bottom water. Opinions on the nature of layer three seem to sway forward and backward. At present the two leading hypotheses are that layer three consists predominantly of serpentinite (Hess, 1962) or that it is made up of gabbro or gabbro derivatives (Cann, 1968). Hess envisioned an upward-moving column of peridotite underneath the axis of the ridge which upon passing the 500°C isotherm in the upper mantle, would partially autohydrate to

12

Y. BOTTINGA

AND C.J. ALLEGRE

serpentinite. Hess predicted that the 500°C isotherm would be at 4.7 km depth; this is equal to the presumed constant thickness of layer three. According to Cahn ( 1968), see also Miyashiro et al. ( t970), layer three is made up of amphibolite. Christensen’s (1970) measurements of the acoustic velocities in amphibolite are in agreement with the Cann hypothesis. The thermal predictions of the Hess model are in disagreement with our calculations, see Fig. 4. Our 500°C isotherm is at about 2 km below the ridge crest for spreading rates of 4 and 8 cm/year, while for the 1 cm/year rate it is at 3 km. If wrong predictions are a reason to reject a theory, the Cann model should also be rejected. According to the Cann model the Mid-Atlantic Ridge spreading rate has considerably slowed down over the last few million years. This prediction is incorrect according to the results of Phillips and Luyendyk (1970), Williams and McKenzie (197 1), and Pittman et al. (197 1). Most arguments pro or contra any hypothesis for the composition of layer three, have been based on the supposed unifo~ seismic velocity of this layer, the supposed constant thickness of this layer, or on an anticipated correlation between heat flow and the thickness of layer three. The large scatter in the oceanic heat-flow values make these values useless as an analytical tool. Consultation of the original literature on observed seismic velocities and inferred thicknesses for layer three, makes clear that there is a considerable spread in these values. For instance Le Pichon et al. (196.5) have determined seismic velocities and thicknesses for layer three, which range from 6.21 to 7.63 km/set, and from 1.8 1 to 4.05 km, respectively. Other arguments, for or against any hypothetical layer-three composition have been based on the igneous rocks which have been dredged from the ocean-bottom. In our opinion not much can be concluded from these samples which usually turn out to be gabbroic or basaltic, frequently displaying signs of low-grade metamorphic, because the area1 dredge-s~pIe density is far too low. Serpentinites are rarely found among these samples and amphibolites even more infrequently. The hypothesis that layer three consists mainly of gabbro or one of its metamorphic derivatives, raises a serious difficulty if the upper-mantle material is predominantly peridotitic. In this case, layer three must have originated as a liquid intrusion, making the di~greement between calculated and observed heat flow near the ridge center catastrophic, because of the latent heat of fusion which has to be dissipated. Also there exists no seismic evidence for completely melted regions near ridge crests. An eclogitic upper mantle would be a way out of these difficulties. However, we have already pointed out in the preceding section that the arguments against such an upper mantle are just as strong to day as they were in the early sixties. Further, the rare-earth element fractionation observed in oceanic-ridge basalts (Kay et al., 1970) and the lack of evidence for magma pools under ridge crests argue strongly against an eclogitic upper mantle. We therefore favor a sepentinized layer three. Hess ( 1962) has assumed that the water needed to serpentinize layer three came from the upper mantle. This, we think, is impossible. One of the most important cont~bu~ons of stable-isotope geochemistry to earth science has been the demonstratian by Craig et al. (1956) that juvenile water is exceedingly scarce. Moreover the work by Moore (1970) has established beyond doubt that the water Hess needs for serpentinization, is not to

THERMAL ASPECTS OF SEA-FLOOR

13

SPREADING

be found in the oceanic upper mantle. If water for serpentinization upper mantle, it would have the upper-mantle another embarrassing

contribution

local temperature,

to the mid-oceanic

were available in the and one would have

ridge heat flow, because of the

heat of reaction liberated when the peridotite is serpentinized. In our model we have assumed that layer three is formed by serpentinization of the material remaining in the 10 km-wide column underneath

the ridge crest after layer two has been extruded.

This

10 km-wide column was reduced to 8 km after the extrusion of 2 km of basalt, and these remaining 8 km split in two, producing 4 km-thick layers moving laterally away from thr spreading centre in either direction (see Fig. 1). Assuming that at this moment rial in this layer is equivalent and 14 weight% enstatite.

to lherzolite,

the mate-

it will contain about 6 1 weight% forsterite

Using the thermodynamic

data of Kitahara and Kennedy

(1967)

one can calculate that per gram of rock about 64.5 cal. will be liberated in the process of’ serpentinization if the water is upper-mantle water. However, if the water needed for thi; serpentinization

process originates as 0°C ocean-bottom

water, 57.3 cal. per gram of rock

are needed to bring the water to the required P and T conditions.

In this case the net

amount of heat liberated per gram of rock is only 7.2 cal. In our model we have shown that the thickness of layers two and three is virtually independent of the spreading rate. Layer three will become thicker as a result of progressive serpentinization, the rate of this process will depend on the cooling rate and the availability of water. The latter will be controlled by the permeability of layer two; the progressive thickening of layer three has been pointed out by Le Pichon (1969). The erratic heat flow in the ridge-crest area may be caused in part by the uneven distribution of permeability in layer two. The serpentinites described by Miyashiro et al. (1969), from the Mid-Atlan tic Ridge contain about 11 weight% water, this is equivalent to what is needed to serpen tinize our lherzolite. Serpentinites from St. Paul’s Rock are different, their origin we hope to discuss in a future paper. SUMMARY

From our numerical

experiments

we have drawn the following conclusions:

(1) Realistic heat-flow model calculations,

within the framework of plate tectonics

fail to reproduce the available observations for the oceanic ridge regions. Further the observations of heat flow in regions close to a spreading center do not confirm the conclusion, based on plate-tectonics theory, of Le Pichon and Langseth (1970) that they should be the same for regions of the same age. A way out of this dilemma would be an ad-hoc postulate of different upper-mantle compositions beneath the different regions which have been investigated. The similarity of ocean-ridge basalts (Kay et al., 1970) argues strongly against such a postulate. We would like to attribute the discrepancy between calculations and observations, at least in part, to circulating water in layer two (Elder, 1965) and the absorption of oceanic water by layer three in the vicinity of the oceanic rise crests. (2) Energy considerations indicate to us that a basaltic or a basalt-derived (amphibolitic)

14

Y. BOTTINGA AND C.J. ALLEGRE

layer three is highly unlikely.

The only undisputable

evidence in favour of an amphibolitic

layer three, the agreement between observed and measured seismic velocities (Christensen, 1970) according to us does not rule out a serpentinized or partially serpentinized layer three, particularly

because the seismic velocities of layer three show a con-

siderable spread. (3) In discussions about the genesis of ocean-ridge basalts, equilibrium temperature distributions, such as the different versions of Clark and Ringwood are not consistent with mass movements

in the submarine

upper mantle.

(4) There is no reason to postulate

greatly different geothermal

gradients beneath the

crests of slow (1 cm/year) and fast (8 cm/year) spreading ridges. (5) Ocean-ridge basalts should be released from the upper mantle at depths greater than 20 km beneath the ridge crests, in order to give rise to a second layer whose thickness does not depend on the spreading rate.

ACKNOWLEDGEMENTS

We would like to acknowledge J. Francheteau,

discussions with Drs. T. Van Andel, X. Le Pichon,

B. Velde, and R. Albarbde.

APPENDIX Imagine a one-phase, one-component, closed system surrounded by adiabatic walls. Along the z-direction there is a pressure gradient as result of the presence of a gravitational field. Thermal equilibrium in this system will be attained when the internal entropy production (d$) vanishes. Because the system has adiabatic walls, no entropy enters the system from the exterior; i.e., deS = 0. Considering entropy to be a function of temperature and pressure we may write: dS= (aSfaT)p dT+ (as/aP)TdP=cpjTdT-crVdP also ds = diS + de.S. Hence when our system is in equilibrium, di.9 = 0, it will display in the z-direction an adiabatic variation of temperature (aT/aP), = QV T/cp. Of course if our medium did not have a pressure gradient, the dp term in the above equation would be zero and the equilibrium state would be isothermal. If one applies the classical Fourier Law of heat conduction J = -k a T/az to our system with its pressure gradient, one would arrive at the contradiction that in our system, which is in equilibrhrm, a heat flux would occur because of the adiabatic variation of temperature with pressure. Hence in this case one has to write the Fourier law asJ(z) = -k @T/at-(aT/az)& where (aT/az)s is the adiabatic gradient at level z. Because silicates behave Like thermal insulators, we think that to a fist approximation one should use the amended Fourier Law for heat conduction in the upper mantle, rather than the classical version of this Law. The third term at the RHS of eq. 2 results from these considerations.

REFERENCES Anderson, D.L. and Sammis, C., 1970. Partial melting in the upper mantle. Phys. Eurth Planet. Inter., 3: 41-50. Bullard, E.C. and Griggs, D.T., 196 1. The nature of the Mohorovicic discontinuity. Geophys. J., 6: 118-123.

THERMAL ASPECTS OF SEA-FLOOR SPREADING

15

Cann, J.R., 1968. Geological processes at mid-ocean ridge crests. Geophys. J., 15: 331-341. Cermak, V., 1967. Coefficient of thermal conductivity of some sediments, its dependence on density and on water content of rocks. Chem. Erde, 26: 271-278. Christensen, N.I., 1970. Composition and evolution of the oceanic crust. Mar. Geol., 8: 139-154. Clark Jr., S.P. and Ringwood, A.E., 1964. Density distribution and constitution of the mantle. Rev. Geophys., 2: 35-88. Cohen, L.H., Ito, K. and Kennedy, G.C., 1967. Melting and phase relations in an anhydrous basalt to 40 kbar. Am. J. Sci., 265: 475-518. Craig, H., Boato, G. and White, D.E., 1956. Isotopic chemistry of thermal waters. Proc. 2nd Conf Nucl Processes Geol. Settings. Publ. 400 NAS-NRC.

Elder, J.W., 1965. Physical processes in geothermal areas. In: W.H.K. Lee (Editor), Terrestrial Heat Flow, Geophys. Monogr., 8. Am. Geophys. Union, Washington, DC., pp. 211-239. Fukao, Y., Mizutani, H. and Uyeda, S., 1968. Optical absorption spectra at high temperatures and radiative thermal conductivity of olivines. Phys. Earth Planet. Inter., 1: 57-62. Fukao, Y., 1969. On radiative heat transfer and thermal conductivity in the upper mantle. Bull. Earthquake Res. Inst., Tokyo Univ., 47: 549-569. Garner, D.M. and Ford, WI., 1969. Mid-Atlantic Ridge near 45”N., IV. Water properties in the median valley. Can. J. Earth Sci., 6: 1359-1363. Green, D.H., 1970. A review of experimental evidence on the origin of basaltic and nephelinitic magmas. Phys. Earth Planet. Inter., 3: 221-235. Green, D.H. and Ringwood, A.E., 1970. Mineralogy of peridotitic compositions under mantle conditions. Phys. Earth Planet. Inter., 3: 359-371. Hanks, T.C., 1971. Model relating heat flow values near, and vertical velocities of mass transport beneath oceanic rises. J. Geophys. Res., 76: 537-544. Harris, P.G. and Rowell, J.A., 1960. Some geochemical aspects of the MohoroviEic’ discontinuity. J. Geophys. Res., 65: 2443-2459. Harrison, C.G.A., 1968. Formation of magmatic anomaly patterns by dike injection. J. Geophys. Rex, 73: 2137-2142. Hess, N.H., 1962. History of the ocean basins. In: A.E.J. Engel et al. (Editors), Petrological Studies, Buddington Memorial Volume. Geol. Sot. Am., Boulder, Colo., pp. 599-620. Hill, R.E.T. and Boettcher, A.L., 1970. Water in the earth’s mantle: melting curves of basalt-water and basalt-water carbon dioxide. Science, 167: 980-982. Horai, K., Chessman, M. and Simmons, G., 1970. Heat-flow measurements on the Reykjanes ridge. Nature, 225: 264-265.

Ito, K. and Kennedy, G.C., 1967. Melting and phase relation in a natural peridotite to 40 kilobars. Am. J. Sci., 265: 211-217.

Ito, K. and Kennedy, G.C., 1968. Melting and phase relations in the plane tholeiite-lherzolitenepheline basanite to 40 kilobars with geological implications. Contrib. Mineral. Petrol., 19: 177211. Kanamori, H., 1970. Velocity and Q of mantle waves. Phys. Earth Planet. Inter., 2: 259-275. Kawada, K., 1964. Studies of the thermal state of the earth, 15. Variation of thermal conductivity of rocks. Bull. Earthquake Res. Inst., Tokyo Univ., 42: 631-641. Kawada, K., 1966. Studies of the thermal state of the earth, 17. Variation of thermal conductivity of rocks, 2. Bull. Earthquake Res. Inst., Tokyo Univ., 44: 1071-1091. Kay, R., Hubbard, N.J. and Gast, P.W., 1970. Chemical characteristics and origin of oceanic ridge volcanic rocks. J. Geophys. Res., 75: 1585-1613. Kitahara, S. and Kennedy, G.C., 1967. The calculated equilibrium in the system MgO-SiO,-H,O at pressures up to 30 kbar. Am. J. Sci., 265: 211-217. Lambert, I.B. and Wyllie, P.J., 1970. Low-velocity zone of the earth’s mantle: Incipient melting caused by water. Science, 169: 764-766. Langseth Jr., M.G., Le Pichon, X. and Ewing, M., 1966. Crustal structure of the mid-ocean ridges. J. Geophys. Rex, 71: 5321-5355. Lee, W.H.K., 1970. On the global variations of terrestial heat-flow. Phys. Earth Planet. Inter., 2: 332-341.

16

Y. BOTTlNGA AND (‘..I.

ALLWRI:

Le Pi&on, X., 1969. Models and structure of the oceanic crust. Tectonophysies, 7: 385-401. Ix Pichon, X. and Langseth Jr., M.G., 1970. Heat flow from the mid-ocean ridges and sea-floor spreading. Tecton~physics, 8: 319-344. Le Pichon, X., Houtz, R.E., Drake, C.L. and Nafe, J.E., 1965. Crustal structure of mid-ocean ridges, 1. Seismic refraction measurements. J. Geophys. Res., 70: 319-339. Lister, C.R.B., 1970. Heat flow west of Juan de Fuca ridge. J. Geophys. Res., 75: 2648-2654. McKenzie, D.P., 1967. Some remarks on heat flow and gravity anomalies. J. Geophys. Res., 72: 6261-6273. McKenzie, D.P. and Sclater, J.G., 1969. Heat flow in the eastern Pacific and sea-floor spreading. Bull. VolcanoL, 33: 101-117. Miyashiro, A., Shido, F. and Ewing, M., 1969. Composition and origin of serpentinites from the MidAtlantic Ridge near 24” and 30” North latitude. Contrib. Mneral. Petrol., 23: 117-127. Miyashiro, A., Shido, F. and Ewing, M., 1970. Petrologic models for the Mid-Atlantic Ridge, Deep Sea Res., 17: 109-123. Molnar, P. and Oliver, J., 1969. Lateral variations of attenuation in the upper mantle and discontinuities in the lithosphere. J. Geophys. Res., 74: 2648-2682. Moore, J.G., 1970. Water content of basalts erupted in the ocean floor. Contrib. Minerd. Petrol., 28: 272-279.

Peck, D.L., Wright, T.L. and Moore, J.G., 1966. Crystallization of tholeiitic basalt in Alea Lava Lake, Hawaii. Bull. Volcanol., 29: 629-655. Phillips, J.D. and Luyendyk, B.P., 1970. Central North Atlantic plate motions over the last 40 million years. Science, 170: 727-729. Pitt, G.D. and Tozer, DC., 1970. Radiative heat transfer in dense media and its magnitude in olivines and some other ferro-magnesian mine& under typical upper-mantle conditions. Phys. Enrfh Planet. Inter., 2: 189-199. Pittman HI, WC., Talwani, M. and Heitzler, J.R., 1971. Age of the North Atlantic from magnetic anomalies. Earth Planet. Sci. Lett., 11: 195-200. Press, F., 1970. Earth models consistent with geophysicai data. Pbys. Earth Planet. Inter., 3: 3-22. Ringwood, A.E., 1966. Mineralogy of the mantle. In: P.M. Hurley (Editor), Advunces in Earth Science. M.I.T. Press, pp. 357-399. Ringwood, A.E. and Green, D.H., 1966. The gabbro-eclogite ~ansformation. Tectononhysics. 3: 383-427.

Sclater, J.G. and Francheteau, J., 1970. The implications of terrestial heat-flow observations on current tectonic and geochemical models of the crust and upper mantle of the earth. Geophys. J., 20: 509-542. Shankland, T.J., 1970, Pressure shift of infrared absorption bands in minerals and the effect on radiative heat transport. J. Geophys. Res., 75: 409-414. Sleep, N.H., 1969. Sensitivity of heat flow and gravity of the mechanism of sea-floor spreading. J. Geophys. Res., 74: 542-549. Sykes, L.R., 1970. Earthquake swarms and sea-floor spreading. J. Geophys. Res., 75: 6598-6611. Talwani, L.R., Lc Pichon, X. and Ewing, M., 1965a. Crustal structure of mid-ocean ridges, 2. Computed model from gravity and seismic refraction data. J. Geophys. Res., 70: 341-352. Talwani, M., Le Pichon, X. and Heirtzler, J.R., 1%5b. East Pacific Rise: The magnetic pattern and fracture zones. Science, 150: 1109-l 115. Taiwani, M., Windish, C.C. and Langseth, Jr., MC., 1971. Reykjanes ridge crest: A detaikd geophysical study. J. Geophys. Res., 76: 473-517. Tatsumoto, M., Hedge, C.E. and Engel, A.E.J., 1965. Potassium, rubidium, strontium, thorium, uranium and the ratio strontium-87 to strontium-86 in oceanic thokiitic basalt. Science, 150: 886-888. Thatcher, W. and Brune, J.N., 1971. Saismic study of an oceanic ridge earthquake swarm in the Gulf of California. Geophys. J., 22: 473-489. Vine, F.J. and Matthews, D.H., 1963. Magnetic anomalies over oceanic ridges. Natwe, 199: 947-949. Von Ilerzen, R.P., Simmons, G. and Folinsbee, A., 1970. Heat flow between the Caribbean Sea and the Mid-Atlantic Ridge. J. Geophys. Rex, 75: 1973-1984.

THERMAL ASPECTS OF SEA-FLOOR SPREADING

17

Wang, C., 1970. Density and constitution of the mantle. J. Geophys. Rex, 75: 3264-3284. Ward, P.L., Palmason, G. and Drake, C., 1969. Microearthquake survey and the Mid-Atlantic Ridge in Iceland. J. Geophys. Res., 74: 665-684. Wetherill, G.W., 196 1. Steady state calculations bearing on the geological implications of a phase transition MohoroviEic’ discontinuity. J. Geophys. Res., 66: 2983-2993. Williams, C.A. and McKenzie, D.P., 1971. The evolution of the North-East Atlantic. Nature, 232: 168-173. Wright, T.L. and Weiblen, P.W., 1967. Mineral composition and paragenesis in tholeiitic basalt from Makaopuki Lava Lake, Hawaii. Geol. Sot. Am., Progr. Ann. Meeting, p. 242 (abstr.). Wyllie, P.J., 1970. Ultramafic rocks and the upper mantle. Minerul. Sot. Am., Spec. Publ., 3: 3-32. Yoder Jr., H.S. and Kushiro, I., 1969. Melting of a hydrous phase: phlogopite. Ann. Rep. Dir. Geoph_vs Lab., Carnegie Inst. Wash., D.C., pp. 161-167.