Download The Volume and Composition of Melt Generated

The Volume and Composition of Melt Generated by
Extension of the Lithosphere
by D. McKENZIE AND M. J. BICKLE
Department of Earth Sciences, Bullard Laboratories, Madingley Road, Cambridge CB3 OEZ
(Received 21 July 1987; revised typescript accepted 14 January 1988)
ABSTRACT
Calculation of the volume and composition of magma generated by lithospheric extension requires
an accurate initial geotherm, and knowledge of the variation and composition of the melt fraction as a
function of pressure and temperature. The relevant geophysical observations are outlined, and
geotherms then obtained from parameterized convective models. Experimental observations which
constrain the solidus and liquidus at various pressures are described by simple empirical functions. The
variation in melt fraction is then parameterized by requiring a variation from 0 on the solidus to 1 on
the liquidus.
The composition of the melts is principally controlled by the melt fraction, though those of FeO,
MgO, and SiO2 in addition vary with pressure. Another simple parameterization allows the observed
compositions of major elements in 91 experiments to be calculated with a mean error of 11%, and
those of TiO 2 and Na 2 O to 0 3 % . These expressions are then used to calculate the expected
compositions of magma produced by adiabatic upwelling. The mean major element composition of the
most magnesium-rich MORB glasses resemble the mean composition calculated for a mantle potential
temperature Tf of 1280°C. Adiabatic melting during upwelling of mantle of this temperature generates
a melt thickness of 7 km. The observed variations of the MgO and TiO 2 concentrations in a large
collection of MORB glass compositions suggest that extensive low pressure fractional crystallization
occurs, but that its effect on the concentrations of SiOj, A12O3, and CaO is small. There is no evidence
that normal oceanic crust is produced from magmas containing more than 11% MgO. The mantle
potential temperature within hot rising jets is about 1480°C and can generate 27 km of magma
containing 17% MgO.
Extension of the continental lithosphere generates little melt unless /?>2 and Tr> 138O°C. The
melts generated by larger values offtor of Tr are alkali basalts, and change to tholeiites as the amount
of melting increases. Large quantities of melt can be generated, especially at continental margins,
where estimates of ft obtained from changes in crustal thickness will in general be too small.
1. I N T R O D U C T I O N
"In summary, then, the formation of magma remains a geophysical enigma, and much
work, particularly experimental work, on the melting behaviour of possible mantle materials
remains to be done. . . . What is there in the thermal regions of the earth that makes it
impossible for magma to reach the surface at temperatures greater than about 1200°C?
Geophysical and geochemical implications of this observation have, to our knowledge,
never been fully explored, even though they could provide important constraints on
temperature distribution in the mantle and on the very mechanism of magma formation"
(Carmichael et al., 1974, p. 359). Though there is now an extensive body of experimental
work on the melting of mantle materials, and the existence of peridotitic komatiites as lava
flows suggests that some melts at some times reach the surface at temperatures considerably
higher than 1200°C, the physical processes associated with magma formation within the
earth are not much better understood now than they were in 1974. The principal purpose of
[Journal of Petrology, Vol 29, P«rt 3, pp. 623-679, 1988]
© Oxford Umvcrsty Pros 1988
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D. McKENZIE AND M. J. BICKLE
this paper is to combine ideas derived from the geophysical observation of spreading ridges
and of extension of the continental lithosphere to determine the P, T paths of mantle
material in such environments, and hence to calculate the volume and composition of the
magma generated. Magma is also produced beneath island arcs, and by hot jets rising
beneath plate interiors which need not cause extension. But the thermal structure of both
these regions is less well known than is that of ridges and for this reason they will not be
considered further. Furthermore all such sources of magma are small compared with
spreading ridges, which produce about 20 km 3 of melt a year. Though the aim of this
investigation is simple and few of the ideas original, a number of the arguments on which it
rests are either controversial, or not widely known, or spread across the rather extensive
relevant literature or suffer from all three problems! It therefore seemed to us worthwhile to
provide non-technical explanations, illustrated by sketches, of some of the more important
of these arguments where necessary. The new results will be found in section 4 which is
concerned with spreading ridges and the origin of oceanic basalts, especially tholeiitic
basalts, and in section 5 which is concerned with extension in continental areas and the
origin of alkaline melts.
2. PRELIMINARIES
Geotherms
Figure l(a) illustrates two commonly used geotherms, taken from Green & Ringwood
(1967a), together with the dry solidus of garnet peridotite. Many authors illustrate the
melting process with isothermal upwelling lines from the geotherm to the solidus, followed
by melt separation and isothermal upwelling to the surface. As Verhoogen (1973) has
remarked, it is essential to take into account the latent heat of melting. The effect of doing so
and of the adiabatic gradient in the solid and melt considerably decreases the melt
temperature. Another problem concerns the geotherms themselves, which must be the result
of physical processes within the mantle. Many of the geotherms which are commonly drawn
predate our understanding of mantle convection and do not consider the processes by which
FIG. 1. (a) Geotherms proposed by Green & Ringwood (1967a) for ocean basins and shields, principally on the
basis of pressure and temperature estimates from experimental petrology, (b) Convective geotherms with a potential
temperature of I28O°C and a viscosity of 4x 1 0 " m 2 s ~ ' , calculated for old ocean basins with mechanical
boundary layer thicknesses of 100 km and 200 km respectively. The temperature of the ridge axis does not take into
account melting
MELT GENERATED BY LITHOSPHERIC EXTENSION
627
they are maintained. Those shown in Fig. l(b) are obtained from the expressions in
Appendix B for a vigorously convecting constant viscosity fluid overlain by a solid slab
100 km thick if melting is ignored. The solidus is that obtained below, and differs little from
Green & Ringwood's. But the geotherms are different because they all tend to the same
adiabatic curve in the convecting interior. Beneath a ridge axis the upwelling of material is
rapid and dominates the geotherm, because the solid carries heat with it as it moves
upwards. Heat transport of this type is known as advective (or convective) transport, as
distinct from the conductive heat transport, which occurs in the absence of movement. The
question of which type of transport dominates in any region is controlled by the thermal
Peclet number Pex
/*
(1)
where v is the material velocity, / a length scale and K the thermal diffusivity. If Pel»\
advective transport of heat dominates, whereas if Pet« 1 conduction dominates. Beneath a
spreading ridge i>~ 10 mm a" 1 and therefore
Pet^3xl0-4/
(2)
5
where / is in metres. The lithosphere is about 100 km or 10 m thick, giving Pet = 30.
Therefore the temperature beneath a spreading ridge will be dominated by the advection of
heat and conduction can be ignored. Equation (2) can also be used to discover how thick the
conductive layer will be beneath the ridge axis by finding the value of / which satisfies (2)
when Pet = 1. This value is 3 km, or less than the thickness of the oceanic crust. Therefore the
temperature variation which controls melting beneath ridges is entirely governed by
advection.
The same argument can also be used to discover how small must v be before the melting
processes are affected by heat loss to the earth's surface. As we shall show most of the melting
occurs within 30 km of the surface. Setting / = 30 km and Pet =1 in (1) gives v ~ 1 mm a ~ '.
This velocity is smaller than the spreading rate on most ridge axes, and is less than the
upwelling rate beneath many (though not all) continental regions where the lithosphere is
stretching. Therefore it is clearly a good first approximation to neglect the conduction of
heat when considering melting. It is then necessary to determine both the geotherm and melt
fraction which is generated as part of the same calculation. Geotherms cannot be imposed,
since they are entirely controlled by the melting process itself.
One important result follows at once from these arguments. Because the interior of the
mantle is everywhere hotter than the mantle solidus at atmospheric pressure, mantle
material will always melt when it is brought up to depths shallower than about 40 km. The
only exceptions will be regions both whose size is small and where the material moves
slowly, such as the upwelling regions on slowly spreading ridges within a few kilometres of
the older cold plate, where a ridge abuts a fracture zone. Samples of mantle undepleted by
melting will therefore reach the surface only rarely and in special tectonic situations.
The second problem concerns the temperature of the magma as it upwells. If it does so
quickly (Pe,»l) then it will neither gain nor lose heat to its surroundings as it moves to
regions of lower pressure. It therefore undergoes adiabatic decompression, and will do so at
constant entropy to a good approximation. Then the adiabatic temperature gradient
(dT/dz)s is
628
D. McKENZIE AND M. J. BICKLE
where g is the acceleration due to gravity, af the thermal expansion coefficient of the magma,
7" the absolute temperature and CF the specific heat at constant pressure. Using the values of
af and CP given by McKenzie (1984a) and 7 = 1500 K gives
'.
(4)
Therefore if magma is generated near the base of the lithosphere it may cool by as much as
100 °C as it travels to the surface, even though it loses no heat. The corresponding gradient in
the solid material below the melting zone is also adiabatic, and given by (3) but with the
thermal expansion coefficient of the solid not the magma. The gradient in the solid region is
smaller, and is about CH^Ckm" 1 .
It is commonly necessary to compare the heat content of material at different depths. Such
a comparison is straightforward if the material is incompressible, since the difference in heat
content is then simply proportional to the difference in temperature. But this simple result
fails when the material is compressible. Those who ascend mountains are well aware of the
adiabatic temperature gradient which exists because air is compressible. The heat content of
two air masses is only proportional to the temperature difference between them if they have
been brought to the same pressure, which must be done reversibly to conserve entropy. In
meteorology and oceanography this problem has been well understood for many years.
Rather than using the entropy of a mass of fluid to define its heat content, it is common
practice in these subjects to define a new temperature, called the potential temperature,
which is the temperature the fluid mass would have (hence the term 'potential') if it were
compressed or expanded to some constant reference pressure. A similar concept is very
useful in discussion of mantle dynamics, and the relationship between the actual temperature T at a depth z and the potential temperature Tf is easily obtained by integrating (3)
where a = a, within the solid part of the mantle. The reference depth at which T= TP is the
earth's surface. Adiabatic upwelling leaves TP unchanged. TP only changes when the entropy
of the material changes. Though there is a simple relationship between the change in entropy
AS and the associated change in potential temperature, the concept of entropy is less familiar
than that of temperature: hence the usefulness of the potential temperature.
The reason why it is necessary to take account of the compressibility of the mantle is that
the horizontal temperature differences within the convecting mantle are not likely to exceed
200 CC. The interior of the upper mantle is likely to have a temperature gradient which differs
little from the adiabatic gradient and hence material will increase in temperature by 200 °C
on sinking 300 km (equivalent to a change in pressure of about lOGPa). Hence, if
substantial vertical movements occur, the temperature differences are not a good guide to
differences in heat content. Such differences are, however, clearly reflected in differences of
the potential temperatures which are therefore used throughout this paper.
For the same reason it is necessary to use potential temperature when discussing mantle
convection if the lateral temperature differences within the convecting system are comparable to those produced by adiabatic compression between the top and bottom of the
convecting layer. In the mantle the two temperature differences are of similar magnitude.
Interestingly such compressibility has little effect on the dynamics of the convection. The
reason why it concerns us here is that we are interested in the actual temperature variations
which exist within the convecting system, and because the temperature, not the potential
temperature, is measured in the laboratory.
MELT GENERATED BY LITHOSPHERIC EXTENSION
<•)
Axis
1400" 1500°
1500° 1400°
(b)
Axis
200
100
1
Zone of extensive
silicate melting
/
okm
Ml
/100
n£-
•-—
200
'/////////ft///"////,
p-___
Trace amounts of melting
100
1350°
km
1400°
200
Tp =1280°C
FIG. 2. (a) A sketch of the temperature distribution beneath a spreading ridge axis (from Oxburgh, 1980) when it
coincides with a hot rising jet in the mantle For reasons discussed in the text few spreading ndges are now believed
to coincide with such jets, and must instead be passive features underlain by mantle of constant potential
temperature, (b) Shows a sketch of the resulting temperature structure.
Mantle circulation beneath ridges
Most textbook illustrations of spreading ridges, such as that shown in Fig. 2(a) from
Oxburgh (1980), show a hot rising jet in the convecting mantle below. Such a close
association between the convective geometry of the mantle and the movement of plates was
a feature of much of the early work on continental drift and sea floor spreading (see for
instance, Hess, 1962), and caused major conceptual problems. It was difficult to understand
how Africa and Antarctica could be surrounded by spreading ridges. Where did the
upwelling material go, and, if the ridges migrated, how did the convective system below
move with them? What happens where a ridge is offset by a transform fault? Is the convective
630
D. McKENZIE AND M J. BICKLE
system offset in the same way and if so how? What happens when a ridge jumps and leaving a
fossil ridge and starting a new one, sometimes thousands of kilometres away? Does the hot
sheet move also, and if so how? These and other problems with the ideas in Fig. 2(a)
suggested that they should be examined carefully. In particular all these difficulties
disappear if ridges are simply passive features where two plates are separating, and mantle
material upwells simply because of this separation, rather than because there is a hot jet in
the deeper convecting part of the mantle. This line of argument suggested that the logical
consequences of the most extreme model, in which the ridge is underlain by a horizontal
isotherm at some depth (Fig. 2(b)), should be examined carefully.
This reasoning was the motivation behind the simple model of plate creation (McKenzie,
1967), which has successfully accounted for the variation of depth and oceanic heat flow with
age (see Sclater & Francheteau, 1970; Parsons & Sclater, 1977; Sclater et al., 1980). This
success has diverted attention from the original motivation, which is what is of concern here.
The important result from the point of view of magma generation is that the simple model in
Fig. 2(b) succeeds in accounting for the observations in considerable detail, and yet it
contains a horizontal isotherm beneath the lithosphere. It was the high heat flow and
shallow bathymetry of ridges which led to the idea that they were underlain by a hot rising
sheet below the lithosphere. The success of the model in Fig. 2(b) in accounting for these
phenomena shows clearly that no such sheet is required by the observations. The resulting
freedom to move ridges, irrespective of convective geometries in the mantle below, removed
one of the major difficulties faced by the early concepts of sea floor spreading. From the
point of view of magma generation on ridges these results are of great importance because
they lead to a natural explanation of why the oceanic crust is of such a uniform thickness (see
section 3).
Two more subtle questions have recently been raised about the relationship between
ridges and the convective circulation of the upper mantle below. Though for the reasons
discussed above there is in general no observational evidence for an association between
mantle circulation and spreading ridges, under some circumstances it is possible that the
movement of the plates may trap an upwelling hot jet or sheet in the mantle below simply
because the plates are moving apart. The question of whether such trapping can occur is
controlled by how fast the plates and the ridge are moving. Houseman (1983) carried out a
number of numerical experiments and showed that attachment was only possible if the ridge
was moving at a velocity of less than a few millimetres a year.
The question of whether ridges are underlain by hot rising sheets can now be examined
directly by using satellite altimeters to map the gravity field with wavelengths between 500
and 4000 km (Watts et al, 1985). These signals are the direct expression of the mantle
circulation, and, though a variety of rising and sinking jets have now been mapped in
oceanic regions, they have no obvious association with spreading ridges, which in places lie
above regions where the mantle below is sinking.
The lithosphere
Exactly what different authors mean by the word 'lithosphere' is of central importance to
igneous petrology. At present the most commonly used definition is that obtained from the
thermal model of plate formation: the depth to the horizontal isotherm. Though this depth
can now be determined with considerable accuracy, it is not obvious that the thickness of the
lithosphere defined in this way has any significance for igneous processes. From the point of
view of isotopic studies what is of concern is that part of the plate which is isolated from
mantle convection, which vigorously stirs the upper mantle. Only in this part of the upper
MELT G E N E R A T E D BY L I T H O S P H E R I C EXTENSION
631
mantle can radioactive decay produce distinctive isotopic anomalies. It is not obvious that
these two definitions of the lithosphere are the same. To understand why they need not be,
and why the thermal thickness is in general greater than that of interest to petrologists, it is
necessary to examine the processes which control the temperature structure of old plate far
from plate boundaries.
Near spreading ridges the temperature of the upper mantle is controlled by the upwelling
temperature and the thermal conductivity of rock, and is independent of the depth of the
horizontal isotherm (Parsons & Sclater, 1977). However as the plate ages its thermal
structure becomes more and more dependent on the depth / and temperature 7\, of this
isotherm, until in steady state it becomes independent of all other parameters. The time x
taken to approach the steady state is given by
T
(6)
^
n
K
and can be estimated directly from the observations of ocean depth (Parsons & Sclater,
1977). Because T depends on the square of the depth to the horizontal isotherm, equation (6)
provides the most accurate estimate available for /. Parsons & Sclater obtained a value of
125 km. Recent studies of Pacific bathymetry (Watts et al., 1985) suggest that this value is
slightly too large, though the depth is not likely to be less than 100 km. The plate model
assumes that heat is transported by conduction only above this isotherm. If the same is true
below it then this isotherm will not remain at constant depth, but continue to become
deeper. Parsons & Sclater (1977) demonstrated that the horizontal isotherm did not
continue to deepen with age, and estimated that Tx = 1333°C and / = 125 km.
For some time this explanation of the depth-age curve was controversial and a variety of
other suggestions were offered. Recently, however, a new test of these ideas has been
provided by the satellite altimeters. The magnitude of the geoid step across fracture zones
depends principally on the thermal structure of the plate, and the observations have strongly
confirmed the plate model (Cazenave et al., 1983). There are, however, still some technical
difficulties in the data reduction which cause the estimates of / obtained from such
observations to be less accurate than those from the bathymetry.
Unfortunately the success of the plate model has obscured its fundamental weakness: it
provides no mechanism by which the horizontal isotherm can be maintained at constant
depth. Conductive heat loss to the earth's surface will cause all isotherms to move downward
unless heat is supplied by some means, and this means will in turn affect the temperature
structure. This problem lead to the suggestion that trfere was a convective instability which
removed cold material from the base of old plate and replaced it with hotter material
(Parsons & McKenzie, 1978). A considerable amount of theoretical work has now been
carried out on this suggestion, and no obvious inconsistencies have yet been discovered. The
major virtue of this scheme is that it provides a natural explanation for the constant depth of
the horizontal isotherm.
Unlike the plate model, this model provides no natural definition of the lithosphere. The
boundary layer at the earth's surface consists of two parts. The upper part is rigidly attached
to the surface, and moves with the magnetic lineations. This part is referred to as the
mechanical boundary layer, and in steady state is perhaps 100 km thick. Only its upper part
can maintain elastic stresses for geological times, so estimates of the elastic thickness of old
oceanic plate are even smaller. The mechanical boundary layer is underlain by a thermal
boundary layer, which loses heat by conduction to the earth's surface. It episodically
becomes unstable and is replaced by hotter mantle material.
632
D. McKENZIE AND M. J. BICKLE
fi
Depth km
Depth km
FIG. 3. (a) The horizontally averaged temperature for a potential temperature of I28O°C, a thickness of the
mechanical boundary layer of 100 km and a viscosity o f 2 x l 0 1 7 m 2 s ~ ' , obtained from the expression in Appendix
B. The corresponding adiabatic upwelling curve is shown dashed. The elevation of ridge axes above the surface of
old plate is controlled by the area between the geotherm and the dashed line. The 'lithospheric' thickness is obtained
by requiring the corresponding area for the plate model to be the same as that obtained from the convective model.
The temperature gradients at the surface in the two cases are not identical, though they are indistinguishable in (a)
(b), (c) Enlargements of the geotherm at the base of the thermal boundary layer for two geotherms with interior
viscosities of 2x 1017 m 2 s ~ \ (b), and 4 x 1 0 " m2 s " ' , (c), both with mechanical boundary layer thicknesses of
100 km and potential temperatures of 1280°C.
It is clear that the thickness of the iithosphere' in Fig. 3 will depend on the method used to
obtain the estimate. The oceanic bathymetry will provide an estimate of the mean
temperature difference between the ridge axis and old plate, or the area between the
geotherm and the adiabatic upwelling curve in Fig. 3(a). The corresponding 'lithospheric'
thickness is obtained by calculating a depth on the adiabatic geotherm with the same area.
The lower boundary of the 'Iithosphere' defined in this way is within the convecting region,
and is therefore not simply related to the thickness of the mechanical boundary layer in
which isotopic anomalies can be generated on time scales of 10 8 -10 9 y.
The convective geotherms in Figs. 1 and 3 from the expressions in Appendix B are
everywhere within 100°C of those from the plate model (Fig. 3(b) and (c)), and only differ by
this value at the base of the 'Iithosphere'. It is presumably for this reason that the plate
models are so useful. Though the upper part of the thermal boundary layer has a linear
MELT GENERATED BY LITHOSPHERIC EXTENSION
633
temperature gradient because it is moving slowly relative to the mechanical boundary layer,
it is nonetheless moving and will not accumulate isotopic variations.
In studies of melting by lithospheric extension it is of considerable importance to use an
accurate initial temperature profile because most of the melting occurs in material which
initially is within or just above the thermal boundary layer. The total volume of melt
generated and the amount of melt produced within the mechanical boundary layer are
sensitive to small changes in the temperature structure.
All the discussion in this section has been concerned with the oceanic lithosphere, which,
in contrast to that of the continents, is now relatively well understood. The question of
whether the continental lithosphere is thicker than that of the oceans is still controversial.
There seems no reason to believe that all continental crust is underlain by thick lithosphere.
A powerful argument against such a proposal is the thermal subsidence of sedimentary
basins such as the Michigan Basin (Sleep, 1971) and the North Sea (Barton & Wood, 1984)
and its explanation in terms of lithospheric extension (McKenzie, 1978). The thermal time
constant derived from the subsidence is indistinguishable from that obtained from ridge
subsidence, and therefore requires the same lithospheric thickness. In continental areas
which have not undergone extension the thermal structure must be estimated from the
surface heat flux, which is a very uncertain enterprise. Sclater et al. (1980), argue that the
continental lithospheric thickness need be no thicker than that of old oceans. Pollack &
Chapman (1977) disagree, and believe the lithospheric thickness beneath shields is considerably greater.
The other type of observation which can be used is seismic velocity profiles, though it is
not straightforward to relate either VP or Vs to the temperature. A variety of studies over the
last 20 y have concluded that lateral velocity variations exist which extend to depths of at
least 200 km and which correlate with the surface geology of continents. Convincing lateral
variations at depths greater than 100 km are confined to shields, which have higher V? and
Vs velocities than surrounding regions (Grand & Helmberger, 1984; Rial et al., 1984). It is
not yet clear whether the mantle velocity structure of Archaean and Proterozoic Shields are
the same. There is no doubt that lateral variations of velocity exist throughout the upper
mantle to depths of 700 km. Jordan (1978) has repeatedly argued that these require the
existence of a lithosphere as thick as 400 km beneath some continental regions. In the light of
the thermal evolution of sedimentary basins it seems improbable that such a thickness is
associated with all continental areas. Even beneath shields such a great thickness is not
easily reconciled with conductive heat transport. The best evidence for a thickness of at least
180 km for the mechanical boundary layer beneath Archaean Shields comes from isotopic
studies on diamond inclusions (Richardson et al., 1984).
Mantle convection
As already explained, the principal aspect of mantle convection which is of concern to us is
the magnitude and length scale of the variations of potential temperature within the
convecting upper mantle. More complicated questions, such as the planform of the
circulation, certainly affect the distribution of intraplate vulcanism. Our need here is,
however, simpler, because we are concerned only with melting resulting from plate tectonics.
The convecting mantle can then be regarded as a large source of material of constant
potential temperature. The length scale of the variations is not of interest for ridge upwelling.
Beneath old lithosphere, however, the vertical length scale of the potential temperature
variations within the convecting region is the thickness of the thermal boundary layer, which
must be estimated if accurate initial temperature profiles are to be calculated.
634
D. McKENZIE AND M. J. BICKLE
The magnitude Ad and length scale <5 of variations of potential temperature can be
estimated using a modification of the convective boundary layer theory of Turcotte &
Oxburgh (1967).
2=AR-v*
(7)
where the Rayleigh number R is
(9)
A and B are constants which are best determined by numerical experiments. In these
expressions d is the thickness of the convecting layer, K the thermal diffusivity, k the thermal
conductivity, v the viscosity of the solid material of the upper mantle. F is the heat flux/unit
area through the layer. Substitution of (9) into (7) and (8) shows that both d and Ad are
independent of d. With the exception of v, the appropriate values of the variables in
equations (7)-(9) are reasonably well known. It is therefore useful to rewrite (7) and (8) as
/v Y
A0=F (11)
V'o/
where vo = 2x 1017 m2 s~' and A and B'do not depend on v. Though (10) and (11) show that
the dependence of <5 and AQ on v is weak, estimates for the value of v vary between
2 x 1017 and 4 x 1015 m2 s~' and correspond to a variation in v1/4 of about a factor of 3.
Furthermore (7) and (8) are only valid if the viscosity within the convecting region is
constant: a condition which is certainly not satisfied. Unfortunately, despite several
attempts, no satisfactory theory yet exist which can be used to obtain expressions like (7) and
(8) when the viscosity is a function of temperature.
A variety of arguments suggest that the viscosity of the thermal boundary layer is at least
two orders of magnitude less than that of the principal part of the upper mantle (see Craig &
McKenzie, 1986). A reasonable estimate for this viscosity is 4 x 1 0 " m 2 s ~ ' leading to values
of <5 and A9 of about 30 km and 200°C respectively. These are probably appropriate for the
thermal boundary layer at the upper boundary of the upper mantle. The viscosity of the bulk
of the upper mantle must be considerably greater and there has been general agreement for
more than 50 y that a value of around 2 x 1017 m 2 s~' is more appropriate. Substitution into
(7) and (8) leads to estimates of S and Ad of 80 km and 400 °C. These values are sufficient to
account for the magnitude and extent of the bathymetric and gravity anomalies associated
with features such as the Hawaiian Swell and the Cape Verde rise (Courtney & White, 1986),
which are believed to be the surface expression of a hot jet of rising mantle material. Such jets
will control the potential temperature of mantle material entering the upwelling region
beneath spreading ridges as ridges pass across the convecting system. These variations of
potential temperature then produce variations in the quantity of magma generated by the
upwelling.
In the case of sedimentary basins the quantity of melt generated is determined by the
initial geotherm. The principal region of interest lies within the thermal boundary layer,
MELT GENERATED BY LITHOSPHERIC EXTENSION
635
which, as Fig. 3(b) shows, will be the first to reach the solidus. A suitable parameterization of
the temperature structure of the thermal boundary layer was proposed by Richter &
McKenzie (1981). The modifications required to match this parameterization to the rigid
mechanical boundary layer above and the adiabatic interior are described in Appendix B.
Average melt composition
O'Hara (1985) in particular has emphasized that the composition of magma erupted at the
surface is a rather complicated weighted average of the melt produced at depth. A useful
approximation is to imagine the melting and extraction processes beneath a ridge as
occurring in two steps. A vertical prism of mantle of the same thickness as the oceanic
lithosphere is first brought up beneath a ridge so that its top is at the sea floor. During this
step the material is allowed to melt, but no movement is allowed between the melt and
matrix. Then all the melt is removed to make the oceanic crust. This scheme is not realistic,
because the melt fraction present in the mantle is never likely to exceed 2 or 3%. But it is the
only scheme which allows the melt composition to be calculated from the laboratory
experiments.
To understand the approximations involved in such a scheme requires certain quantities
to be defined. The most basic of these is the composition of the melt which is added to
increase the fraction of melt from X to X + dX by transfer of material from the solid to the
melt phase. This composition will be referred to as the instantaneous melt composition and
will be written c. If c(X, P) is known, the average composition C of all the melt which has
been generated from any particular element of solid can be obtained by integration along the
melting path
C(*) = i | c(X')dX'
A
Jo
(12)
or
c = ~(XC).
(13)
dX
When melting occurs at constant pressure C will be referred to as the point average
composition, because it is the average composition of the melt generated from any point as
the temperature increases (Fig. 4{a)). Finally the average composition of all the melt
generated depends on the weighted average of C over the melting interval 0->h
V=\
XCdzl I Xdz
= \ dz\
Jo
ciX')dX'
Jo
Xdz.
(14)
/ Jo
# will be referred to as the point and depth average composition. Any average constructed
using (12) will be referred to as the point average, and using (14) as the point and depth
average. The relationship between these compositions for the melting scheme described
above are illustrated in Fig. 4(a).
The compositions <<?, C, and c all depend on the way in which melting occurs. The
difference between them can be examined using the standard expressions for the trace
element concentration in the melt for a material undergoing batch or Rayleigh melting
CB=
DD(\+X(}r-l))2
°5)
(b)
(a)
0-3
c
c
\
n
_g 0-2
a
Na,0
\
c
2
-c
0-1
a
2
n
50
Depth km
100
m
Z
N
m
40%
z
a
2
30%
22%
X
0-2
CD
20%
o
rm
18%
0-1
16%
40
60
SO
100
Depth km
FlG. 4. (a) The instantaneous melt composition c(X, z) is that of the melt which is added to increase the melt fraction from X to X + dX. The point average
C(z) is the average melt composition produced from one element of solid at a depth z. The point and depth average is the average melt composition
generated in the melting region, (b) The instantaneous melt composition for Na 2 O calculated using D = 0169 and c 0 = 0-547 from Table A1 (a) for Rayleigh
and batch melting, (c) Contours of cB(X, z) for MgO calculated using Table Al(a), with Xt(z) for two potential temperatures, (d) A sketch of contours of
c(X, z) for MgO for Rayleigh melting with 7"P= 1480°C. Both the contours and X(z) assume cst = cB and Xt = XB and are therefore not accurate. Typical
regions from which melt is extracted are shown dotted.
MELT GENERATED BY LITHOSPHERIC EXTENSION
637
and
„
0/,
v\(i/D~D
i\a\
where c 0 is the bulk concentration of the trace element and D is the distribution coefficient. A
subscript B denotes batch and R denotes Rayleigh melting. The usual expression for CB can
be obtained by integrating (15). Curves for cB and cR are illustrated in Fig. 4{b) for Na 2 O. The
melting processes beneath ridges are not likely to leave more than 2-3% melt in contact with
the residue at any time (Ahern & Turcotte, 1979; McKenzie, 1985), and therefore resemble
Rayleigh rather than batch melting. Because cR # cB, batch melting experiments will not in
general provide accurate estimates of the melt composition.
A further difficulty concerns the calculation of (€. No problem arises for the scheme in
which batch melting occurs with no separation, followed by separation with no interaction
with the matrix. Then, as Fig. 4(c) shows for MgO, cB = cB(X, z), where z is the depth, and is
independent of the melting path. Two curves are shown for X(z) for two potential
temperatures, and calculation of l€B is straightforward. If, however, extraction of melt occurs
during the melting process, the problem of calculating "<f is more difficult because the integral
(14) must be carried out along each matrix stream line. This difference is illustrated in
Fig. 4(d) where cR has been assumed equal to cB in Fig. 4(c). The dotted regions show typical
regions from which melt is extracted. Clearly the point average is now unrelated to any melt
which might be produced.
The last difficulty concerns X{z). The discussion in the next section is concerned with
estimating XB(P, T). It is, however, likely that the melt fraction produced will be strongly
affected by whether or not the melt is extracted, since the change of the activity of some
component in the melt produced by the addition of a fixed mass of solid must depend on the
melt fraction present. It is therefore unlikely that
(xB-xR)<<L
(17)
But it is not obvious how XR can be estimated from existing batch melting experiments.
Parameterization
All the calculations described below require continuous descriptions of temperature, melt
fraction and composition, and considerable effort is involved in obtaining suitable functions.
The most obvious and least useful method of proceeding is to use linear interpolation
between experimental results. To obtain a general description of any physical process it is
important to use an understanding of the physics of the problem to suggest a functional form
for the parameterization, and that the function used should contain some free parameters
which can be adjusted to fit the experiments. A well known example of this process is the use
of an activation energy and a frequency factor to describe the rate of a chemical reaction. The
functional form is soundly based on statistical mechanics, but, except in the simplest cases,
the two constants must be obtained from experiments.
A similar approach is adopted here. For instance the variation of melt fraction X with
temperature and pressure must clearly change from 0 on the solidus to 1 on the liquidus. Any
functional form must satisfy these conditions. Imposing this constraint leads to a polynominal form for X{P, T) and all the experiments at different pressures and temperatures can be
fitted with the simple polynominal with only two constants. In all cases the constants were
determined by minimizing the absolute value of the difference between the observed and
638
D. McKENZIE AND M. J. BICKLE
calculated values, rather than its square. Minimization of the square gives greatest weight to
the most discrepant, and therefore least relevant, experimental results. The implementation
of Powell's algorithm given by Press et al. (1986) was used throughout.
The main results of this section
Much of the previous discussion is only indirectly relevant to the melting problem beneath
regions undergoing extension, and it therefore is worthwhile to collect the results we need
later. Perhaps the principal one is that upwelling is generally sufficiently fast for heat
conduction to be neglected. It is therefore essential to calculate both the melt fraction and
the geotherm together. To a good approximation this can be achieved by maintaining the
entropy of the melting system constant during the upwelling. This approximation reduces
the somewhat intractable general problem to the integration of a nonlinear ordinary
differential equation, which can be integrated by standard methods (see Appendix D of
McKenzie, 1984a). The melt fraction generated is then controlled by the heat content of the
solid mantle entering the upwelling zone. Because the solid mantle is slightly compressible its
temperature is not uniquely related to its heat content. It is therefore convenient to define a
potential temperature, the temperature the material would have at the surface if melting does
not occur, which does satisfy this condition.
Variations in potential temperature are controlled by convection and are probably as
large as 200 °C between the hot rising jets and the surrounding upper mantle. These
variations must be reflected in variations in the amount of melting produced by the
upwelling as ridges wander across the convecting system. The ridge motion has little
influence on the convective geometry and ridges are not geometrically related to convective
upwellings.
The melt generated during continental extension depends on the initial temperature
distribution, established over hundreds of millions of years. Like that beneath ridges, the
upwelling is often adiabatic to a good approximation. Hence it is important to start with the
best possible estimate of the initial temperature variation. It is therefore necessary to
understand the physical processes which control steady state continental geotherm, and in
particular the distinction between the mechanical boundary layer, in which large scale
isotopic heterogeneities can be produced over geologic time, and the thermal boundary
layer, where they cannot. The combined thickness of both boundary layers is about 100 km
beneath the North Sea and Michigan Basins, whereas the thickness of the mechanical
boundary layer alone must be more than 180 km beneath Archaean Shields. This variability
must influence the melting processes. Finally the average composition of the magma
produced in any environment is a complicated function of the melt compositions which exist
at depth.
3. MELTING UNDER PRESSURE
Calculations of the volume and composition of melt require knowledge of the variation of
the melt fraction with pressure and temperature. The simple functional forms used by
McKenzie (1984a) were not based on a detailed analysis of the experimental results, and such
a study is required if detailed comparisons are to be carried out.
No general theory of melting exists which can be applied to the melting of a multiphase
multicomponent mantle material at variable pressure in the presence of variable amounts of
solid solution between different phases. The traditional approach to such problems uses
chemical thermodynamics and the concept of activity, and represents the results in terms of
MELT GENERATED BY LITHOSPHERIC EXTENSION
639
multidimensional phase diagrams. A great effort has been devoted to this problem, but the
information required to deal with a system as complicated as the mantle does not yet exist.
We therefore adopted a different approach which is both more empirical and more
quantitative than that commonly used, since we needed to be able to calculate both the
quantity of melt produced and its composition. For numerical convenience we wished to use
analytical expressions wherever possible. In the absence of any general theory of melting all
we could hope to do was to parameterize the results of experiments carried out on rocks of
given compositions. The approach was only possible because of the number of careful
experiments which have now been carried out on ocean ridge basalts, garnet peridotites and
rocks of similar composition. Though the expressions obtained in Appendix A are restricted
to the melting of peridotites, the approach is more general, and can be used wherever
suitable experimental results of sufficient quality are available.
The approach we adopted consists of three steps. We first obtained analytic expressions
for the variation of the solidus T, and liquidus TY temperatures with pressure which agreed
with the experimental observations to within reasonable estimates of the likely experimental
errors (Fig. 5). We then obtained the melt fraction, X, as a function of pressure and
temperature. Finally we parameterized the melt composition as a function of X and
pressure.
utdus
1900
1700
T
° C 1500
A liquid
o solid & liquid
• »olld
1300
1100
4
PGPa
FIG. 5 Experimental determinations of the solidus and liquidus of garnet peridotite. The curves were determined
by minimizing | rob> — Talc| and are generated from equations (18) and (19). The data points for the solidus are from
Ito& Kennedy (1967), (0,—, 1150), (2.04, 1300, 1350), (218, 1200,—), (2-31, 1320,— \ (2-58, 1350,—I (2-99, 1400,
1500), (408,1550,1600), Green & Ringwood( 19676), (1-8,1300,1360), (2-25, 1400,15OO),(2-7,1450,1500), (2-9,1500,
—),(31, 1500, 1550), (3-6, 1570, 1660) Jaques & Green (1980), (0, —, 1170), (0-25,—, 1100), (0-2, —, 1150), (0-5, —,
1200), (0-675,—, 1200), (0-9,—, 1200), (1,—, 1250), (15,—, 1350), (0-2,—, 1200), (0-5,—, 1200), (1,—, 1250), (1-5,—,
1350), Stolper (1980), (1, —, 1250), (1-5, —, 1350), (2, —, 1400), Harrison (1981), (3 5, 1575, 1580), Takahashi &
Kushiro(1983),(0, 1100, 115OX(O-5, 1175, 1200), (0-8, 1200, 1225), (11, 1200, 123OH15, 1275, 1300), (2-, 1350,1375),
(2-5, 1375, 1400), (3, 1475, 1500), and Takahashi (1986), (0, 1100, 1150), (0-5, 1175, 1200), (1, 1250, 1275), (1-25, —,
135O),(l-5, 1350,1400U2,1350,1400M3,1500,1550), (3-5,1600,—),(5,1600,1700),(6,1750,1850), (7,—, 1800), (7-5,
1800, 1900). The first entry inside the brackets is the pressure in GPa, the second the highest temperature in °C at
which no melt was present, and the third the lowest temperature at which melt was present. If either the second or
the third entry is marked with —, the appropriate temperature bound cannot be determined from the experiment.
The data points for the liquidus are from Takahashi (1986) (0,1600, —), (1 -5,1800,1850), (3,1900,1950), (5,2000, —),
(7-5, 1900, 2000), where the second entry is the highest temperature at which solid was still present, and the third
entry the lowest temperature at which there was no solid.
640
D. McKENZIE AND M. J. BICKLE
The solidus temperature is both better known and more important than 7j, and different
groups have obtained results which agree well. The expression used was
-968xl(T4exp(l-2xl(r2(7;-1100))
(18)
C
where P is the pressure in GPa and T, the solidus temperature in C. Because the expression
gives P(T,\ T,(P) is obtained by numerical iteration. This expression fits the observations
reported by the authors listed in the caption to Fig. 5 with a mean error of 6°C, and it is not
likely that the temperature measurements themselves are of this accuracy. The expression
used for the liquidus temperature Tt in °C was
T, = 1736-2 + 4-343P + 180 tan-'(P/2-2169).
(19)
This expression fits the liquidus temperatures with a mean error of 7°C. The observations
and empirical expressions are shown in Fig. 5.
The next question concerns the fraction by weight A" of a rock which melts at a given
pressure and temperature. To determine X{ T, P) directly is difficult. It is easier first to use the
requirement that X = 0 when T=T, and =1 when 7"= 7j, by defining a dimensionless
temperature 7"
r
Then from the definitions T, and Tt, X(T') must pass through ( - 0 5 , 0 ) and (0-5,1). The
general polynominal which satisfies these conditions is
X-0-5 = T + {T'2-0-25)(ao
+ a,7" + a2T'2. . .).
(21)
The observed values are plotted in Fig. 6.
With the exception of Mysen & Kushiro's (1977) results, which were affected by quench
overgrowth (Takahashi & Kushiro, 1983) and were not used or plotted, there is good
agreement between different authors. What is surprising is that there is no evidence of any
variation of X(T') with pressure. Using two coefficients only gave
ao= 0-4256
a, =2-988
(22)
with a mean error of 3%. The inclusion of more coefficients and linear variation with
pressure did not produce an appreciable improvement. Since it is not likely that the
observations themselves are accurate to 3 % no such improvement would be expected.
The curve calculated from equation (21) using the constants (22) illustrated in Fig. 6 has
the general form expected for the melting of garnet peridotite. The rapid increase of X with
increasing T near A" = 0 corresponds to the cotectic melting of olivine and two pyroxenes.
As will be shown below, the clinopyroxene is exhausted when X ~0-25. The rapid increase as
7" ->0-5 corresponds to the melting of olivine. The absence of any pressure effect means that
X depends only on 7". Of course X = X(T, P) because the solidus and liquidus temperatures
are pressure dependent. The parameterization of T,(P), Tt(P) and X(T') are simple and
convenient, and easily included in calculations like those of McKenzie (1984a) and Furlong
& Fountain (1986).
The results obtained by integrating the equations in Appendix D of McKenzie (1984a) are
illustrated in Fig. 7, but are labelled with the potential temperature of the geotherms rather
than with the solidus intersection temperature used in McKenzie (1984a). The principal
uncertainty in these calculations is still the entropy change AS on melting. A value of
250 J k g " ' °C~' was used to generate the curves in Fig. 7. The principal difference between
MELT GENERATED BY LITHOSPHERIC EXTENSION
641
10r
0-8
0-6
0-4
+ 0<SP Z 0-5
0-2
O 0 - 5 < P « 1-5
* 1-5 < P
0-0
-0-5
-0-3
00
0-3
0-5
r
FIG. 6. Melt fractions of a rock with the composition of a garnet peridotite plotted as a function of
T =
T,-T,
where 7J and T, are the hquidus and sohdus temperatures. Data points are from Bickle et al. (1977), Arndt (1977),
Bickle (1978), Green et al. 1(979), Stolper (1980), and Jaques & Green (1980). The melt fractions corresponding to
Stolper's experiments were calculated from the composition of the olivine and orthopyroxene by requiring the bulk
composition to contain 44-48% SiO 2 and 39-22% MgO. Where the bulk composition differed from this
composition in the other experiments olivine and orthopyroxene were added or subtracted to adjust the MgO and
SiOj compositions to these values. The curve was obtained by minimizing \Xalc — Xob, | and calculated using
equation (21) with the constants (22).
Fig. 7 and the earlier results of McKenzie (1984a) concerns the behaviour between X = 0-3
and X = O6 (see his Fig. 13). This difference has little effect on the total amount of melt
generated below a given depth, shown in Fig. 7(b), which therefore is now well determined.
In order to generate a melt thickness of 7 km, corresponding to the average thickness of the
oceanic crust, the potential temperature must be 1280°C. This calculation assumes that all
the melt is extracted, and that adiabatic melting continues to the surface rather than to the
Moho. Once AS is better known more accurate calculations will be possible. The
temperatures of the melt generated in this way range from 1300°C on the solidus at a depth
of 45 km to 1200°C at the surface, and average 1232°C. The average depth of generation is
15 km and melt fraction is 0135. These numbers are somewhat dependent on the choice of
AS. A value of 400 J k g " ' °C~' requires a potential temperature of 1300°C to generate 7 km
of melt and the melt temperatures range from 1325°Cat 51 km to 1191 °C at the surface, and
the average melt fraction is 0114. These estimates are in general agreement with experimental determinations of the Hquidus temperatures of oceanic basalts (Tilley et al, 1972;
Bender et al, 1978; Fujii & Bougault 1983).
The answer to one of the questions posed by Carmichael et al (1974), quoted in the
introduction, is now clear. Magmas are not in general erupted at temperatures much greater
than 1200°C because the average potential temperature of the mantle is 1280°C. Because
the thickness of the oceanic crust varies little, most of the upper mantle apart from the hot
rising jets must have approximately the same temperature. Hence the constancy of the
eruption temperature. The potential temperature of the hot jets is probably about 200 °C
D. McKENZIE AND M J. BICKLE
642
Ib)
Depth km
100
2
4
Pressure GPi
FIG 7 (a) Adiabalic decompression paths calculated using the equations given by McKenzie(l984a) Appendix D,
a fourth order Runge-Kutta scheme and
A5=250Jkg-'°C"'.
The curves are labelled with their potential temperatures, and entropy is conserved to I part in 10* during the
numerical integration. The curves between the solidus and the liquidus are labelled with the melt fraction by weight.
(b)The total thickness of melt present below a given depth plotted as a function of depth, calculated by integrating
the volume of melt present in (a).
greater than tjiat of the mantle interior, or about 148O°C. As Fig. 7(b) shows, the resulting
melt thickness is 27 km, in agreement with the crustal thicknesses of the aseismic ridges.
These structures are produced when a hot jet coincides with a spreading ridge. Iceland is the
best known example of such a coincidence. The measurement of crustal thickness is at
present the most accurate method of mapping variations in mantle potential temperature.
Originally the principal purpose of this project was to use convective geotherms calculated for plate interiors and X = X(T') to calculate the melt volumes generated by
lithospheric stretching. But the unexpectedly simple relationship between X and 7", and the
absence of any pressure effect, suggested that it might be possible to calculate the
composition of the melt as well as its volume. It seemed likely that the melt composition
would be principally controlled by the quantity produced. Since X = X{T'), this suggestion
was easily tested by plotting the abundance of various oxides as functions of 7". The results
of so doing are illustrated in Fig. 8.
The plots labelled (b) are those for which the melt fraction is known, either because it was
determined in the original experiment or could be calculated from the published information. These experiments are the 38 used in Fig. 6. The plots labelled (a) contain results
from the larger number of experiments which determine the melt composition as a function
of T and P. Since 7" can easily be calculated, these experiments can also be used to test
whether the composition is a function only of X and hence of 7". The results are striking.
With the exception of SiO 2 , FeO, and MgO, the melt compositions are functions only of 7"
MELT GENERATED BY LITHOSPHERIC EXTENSION
643
to within experimental error. SiO 2 shows a systematic decrease and both MgO and to a
lesser extent FeO an increase in concentration with increasing pressure. Most experimental
results are available for values of T' between —0-5 and —02, which, as Fig. 7 shows, is the
region of most interest from the point of view of MORB generation.
Despite the obvious variation between the oxide concentrations in the melt and T', the
experimental results were not easily parameterized. Appendix A contains description of how
this was achieved. The melting region O ^ X ^ l was divided into three regions with
boundaries at Xx and X2, where the composition CB (but not cB) of the batch melt was
required to be continuous. In each region the oxide composition of the instantaneous melt
was required to satisfy Rayleigh's Law or to be zero. Hence the total mass of any oxide in the
melt could never decrease with increasing X. For all oxides except FeO, MgO, and SiO 2 , the
concentration in the instantaneous melt was taken to be zero when X > X l and no pressure
dependence was allowed. The concentration of MgO and FeO was required to vary linearly
with pressure at constant A" up to a pressure of 3-5 GPa. The SiO 2 concentration was obtained by subtracting that of all the other oxides from 100. Those oxides, such as
•
o < P < o-s
O 0-5 < P < 1-5
A 15 < P
-0-2
00
0-2
0-4
T'
(b)
*
0 < P « 0-5
O 0-5 < P *
54
» 1-5 < P
50
SIO 2
%
46
-0-4
-0-2
0-0
0-2
T'
0-4
1-5
644
D. McKENZIE AND M. J. BICKLE
MELT GENERATED BY LITHOSPHERIC EXTENSION
CO
CJ
|
S*
O
,
645
646
D. McKENZIE AND M J. BICKLE
2 #
2
a?
o
(-
MELT GENERATED BY LITHOSPHERIC EXTENSION
647
(a)
08
K2O
0-2
-0-4
00
-0-2
0 2
0-4
r
(b)
0-8
0-6
K2O
%
0-4
0-2
00
-0-2
r
FIG. 8. Compositions of melts as functions of 7" given by equation (20). (b) shows the compositions of 38
experiments for which the melt fraction was measured (Fig. 6), with the exception of K 2 O for which only Jaques &
Green's (1980) results are plotted, (a) shows results from these 38 experiments together with those from Takahashi &
Kushiro (1983), Takahashi (1986), and Fujii & Scarfe (1985), for which X was not determined, 91 in total. Crosses
mark compositions from experiments carried out with P<,Q-5GVa-, circles those with Q-5<P<, 1-5 GPa, and
triangles those with P > 1-5 GPa. Where three curves are shown they are the calculated compositions at pressures 0
(not labelled), I and 2 GPa. The parameterization takes C to be a continuous function of pressure and melt fraction
(see Appendix A). All the results for K 2 O are shown in (a). The solid lines are calculated from the two
parameterizations obtained by minimizing \Cob, —C^ | see text and Appendix A. The curve in series (b) for K 2 O
was obtained from fitting Jaques & Green's (1980) results only.
MnO, Cr 2 O 3 , and P 2 O 5 , for which the data were insufficient were included as a single
concentration independent of melt fraction and pressure called 'the rest'. The constants of
the parameterization were then obtained by minimizing G
C = X>JC ob ,.-C c . lc .|
(23)
n
where the sum was taken over SiO 2 , TiO 2 , A12O3, FeO, MgO, CaO, Na 2 O, K 2 O, and 'the
rest'. Values of wH of 1 were used for the major elements, iron and 'the rest', 20 for TiO 2 , 10
648
D. McKENZIE AND M. J. BICKLE
for Na 2 O, and 30 for K 2 O. These weights were used to force the adjustments required to
match the overall concentrations into the parameters of the major elements, and so to fit
those of the minor elements as well as possible. The concentration of TiO 2 in Jaques &
Green's experiments is about a factor of four greater than that of all other experiments
because they used a Hawaiian basalt to construct their pyrolite. Their results for this oxide
were therefore not included (but see Appendix A). Three sets of constants were then
determined (Appendix A, Table Al), two ((a) and (c)) for the experimental results shown in
Fig. 8(a), and one, (b), for the results in Fig. 8(b). Where X was not given it was obtained from
(21) and (22). The minimization run for 8(a) included all the K 2 O observations rather than
just those of Jaques & Green (1980). After some experimentation 22 parameters were used
for the minimizations, and the concentrations calculated for the two cases (a) and (b) are
shown in Fig. 8.
The difference between the two minimisations (a) and (b) is not large, and is most obvious
near T' = —0-5. Few of the experiments in Fig. 8(b) involve small melt fractions, whereas
those in 8(a) include a number of runs made by Takahashi & Kushiro (1983) where the
calculated melt fraction was 10% or less. These results constrain the behaviour as T' -<•
— 0-5, and therefore the parameters from 8(a) are to be preferred. They also involve more
than twice the number of experiments. The values of A^ and X2 were two of the parameters
determined, giving values of 0-245 and 0438. Xt corresponds to the removal of all oxides
except FeO, MgO, and SiO 2 from the residual solid, and hence to the elimination of
clinopyroxene. It is shown as 'cpx-out' on later plots. X2 has no physical significance. It is
required simply to provide enough variables to fit the observations and should not be
interpreted as 'opx-out'. When more experimental results are available with small values of
X it will probably be necessary to add a third boundary X3 at which the aluminous phase
disappears, with X2>X^. However, as Fig. 8 illustrates, the scatter in the observations is
still too large at present for such an effect to be resolved.
The validity of the parameterization does not depend on the assumptions underlying the
derivation of Rayleigh's Law being satisfied. The expressions used are simply convenient
functional forms for parameterization, and their validity should be judged only by how well
they fit the observations. Since 22 parameters were used tofit750 observations, the system is
strongly overdetermined. Formally the bulk distribution coefficient, D, is given by D = n/{n
+ 1), but this expression should only be used as an estimate of D for TiO 2 , Na 2 O, and K 2 O.
The values in Table Al suggest TiO 2 is the least compatible.
Figure 9 shows a detailed comparison of the error distributions for the major and two of
the minor elements (the data for K 2 O are inadequate, see Fig. 8(a)), together with normal
distributions with the same mean absolute error. In the case of the major elements the mean
difference between the observed and calculated compositions is 106%. Since the compositions were determined using electron probes to a relative accuracy of 2%, or 50 ± 1% in the
case of SiO 2 , the difference between the calculated and observed compositions is probably
comparable to the observational error. The agreement is less good for TiO 2 and Na 2 O
because the bulk concentrations of these elements were intentionally varied in some of the
experiments. Nevertheless the mean error was only 027%.
It is also of interest to compare the melt composition obtained from the parameterization
when X = X i with that estimated by Stolper (1980) for cpx-out. His estimates are shown in
Figure 10(b) in the projection onto the Ol-Di-Qz plane from PI suggested by Walker et a\.
(1979). The calculated compositions in Fig. 10(a) agree excellently with those of Stolper, and
confirm his argument that cpx-out does not lie within the MORB field at pressures of
between 1 and 2 GPa (see section 4). O'Hara (1968a,b) argued that cpx-out would reenter
the tholeiitic field in Fig. 10 as the pressure increased beyond 3 GPa. No such tendency is
MELT GENERATED BY LITHOSPHERIC EXTENSION
649
9 O 2 , AI 2 O 3 , FeO,
MgO, CaO
mean error 1-06%
'•xp*
(b)
•
TK> 2 , Na2O
30
mean error 0-27%
20
•
•
10
•
•
•
n
0-2
0-4
0-6
08
FIG. 9. Distribution of errors for major and minor elements obtained from the parameterization (a) and
experiments shown in 8(a). 399 observations were used in (a) and 26 were outside the range of the plot. The
corresponding figures for (b) were 145 and 4. The bin sizes s were 0 2 % for (a) and 006% for (b). The Gaussian
distributions were calculated from
Aexp(-x2f2o2)
where
A = INsjnx
F
and N is the number of points used whose mean value is x. The values of .x were 1-06% for (a) and 0 2 7 % for (b).
observed in the experiments discussed here, but few of them were carried out at such high
pressures.
Tliese tests show that the parameterization is a compact and accurate description of the
experimental data. However we wish to use it to calculate mantle melt compositions, and
D. M c K E N Z I E A N D M. J. B I C K L E
650
a
FIG. 10. (a) Experimental results for which the observed or calculated A'^A r 1 =O245 (cpx-out) plotted in the
manner proposed by Walker et al. (1979, caption to their fig. 2). When the points fall inside the triangle this plot is
identical to one produced from the CIPW norm if Or, Ab, and An are plotted as PI. The curves are calculated from
the parameterization (a) and are marked with the pressure in GPa and end at X =0-35. (b) is taken from Stolper
(1980) for comparison. The symbols correspond to ranges of pressure in GPa The ellipses show the projections of
the 2<r 8 dimensional ellipse of the error of the mean for the parameterization, (oblique lines), and for an individual
electron probe analysis of the Smithsonian data set (Presnall & Hoover, 1984).
therefore desire to test whether the parameterization is also satisfactory for this purpose.
Though the most convincing test is the agreement between the MORB compositions and
those calculated from the parameterization which is discussed in detail in the next section, a
simpler test can also be used for CaO, A1 2 O 3 and TiO 2 whose abundance ratios can be
estimated using cosmochemical arguments (Ganapathy & Anders 1974; O'Nions et al, 1981)
to be
CaO
= 0-806
A12O3
and
CaO
= 15 9.
TiO 2
These oxides are all in the melt when X> Xu and their concentration ratios then are
CaO
= 0781
A12O3
and
CaO
= 15-2.
TiO 2
Since these element oxides are among the least volatile, their abundances are believed to be
constant in meteorites and the silica rich planets. Because A12O3 and CaO are very
abundant in the mantle, and TiO 2 is not concentrated in the continents, their abundance in
the mantle has scarcely been affected by continent formation. Another test of the
parameterization is the ratio (MgO/FeOJi^^MgO/FeO),^,,, which lies between 0 2 and
0-3 for the conditions under which the experiments were conducted.
M E L T G E N E R A T E D BY L I T H O S P H E R I C E X T E N S I O N
651
We did not expect to be able to produce a single set set of parameters that agreed with all
experimental observations. Since we have made little use of the conventional phase diagram
approach to such problems, solid solution and other difficulties which complicate its use do
not affect our parameterization. We will now use this approach to calculate the expected
compositions of MORBs.
4. MELTING BENEATH RIDGES
Adiabatic decompression
Seafloor spreading generates about 20 km 3 a" 1 of MORB, which is the dominant
volcanic rock type on the earth. The most obvious interpretation of the observations is that
this melt is a primary melt generated directly from the mantle by adiabatic decompression,
and only modified by fractional crystallization within the crust. We demonstrate below that
this model can account for almost all the observations, and discuss the problems with the
views of O'Hara and others below. The term 'primary' will be used here to describe any melt
that is in chemical equilibrium with the solid with which it is in contact. Since melts must
move with respect to the matrix from which they are separating, the distinction between
primary and fractionated melt is only meaningful when melt and solid residue cease to
interact chemically. Such interaction must cease when the melt crosses the Moho, and
therefore only at shallower levels is there necessarily a distinction between primary and
fractionated magmas.
The melting process must be able to generate enough melt to produce the average
thickness of oceanic crust of about 7 km, increasing to about 25 km where the ridge crosses a
hot rising jet. These thicknesses are produced by adiabatic upwelling of the mantle with
potential temperatures of 1280°C and 1480 °C respectively. The mean composition of this
melt should agree with that of the oceanic crust, as should also the range of compositions.
The calculated compositions of the point averages for a potential temperature of 1280°C
are shown as stereographic pairs in Fig. 11, together with a variety of dredged glass
compositions which are either ne-normative or have an MgO concentration > 9 % . These
glasses are least likely to have undergone low pressure fractional crystallization. Figures 12
and 13 show projections from the plagioclase and diopside apices of the point averages
corresponding to several potential temperatures, together with those of the glass compositions selected by Elthon. The ellipses are projections of the error ellipses for the observations and for the mean composition from the parameterization in Fig. 8(a). Curves from
the parameterization in Fig. 8(a) are shown in Fig. 12(a) and 13(a), those from 8(b) in 12(b)
and 13(b). The agreement between the curves for a potential temperature of 128O°C in 12(a)
and 13(a) and the glass compositions is good. Indeed it is probably better than would be
expected from the size of the error ellipses. No extensive olivine fractional crystallization is
required to generate these glass compositions from the point average melt compositions. An
important feature of the 1280°C melting curves is that they do not quite exhaust the
clinopyroxene in the matrix. The result is in excellent agreement with Dick & Fisher's (1984)
work on abyssal peridotites. They found that the enstatite in these rocks was saturated with
diopside, but that there was little free diopside. They argued that calcium had been removed
by melt separation. Since the potential temperature of 1280°C was chosen to generate 7 km
of melt, it is encouraging that the resultant depletion is in agreement with Dick & Fisher's
observations.
Table 1 shows the point and depth average for a potential temperature of 1280°C,
together with various average compositions.
652
D. M c K E N Z l E AND M. J. BICKLE
(a)
(b)
n
t
(C)
FIG. 11. Stereographic pairs with rotation angles of 6°, showing Elthon's glass analyses (1987 and pers. comm, 108
analyses) and those from Melson et al. (1977 and pers. comm.) that either have MgO>9% or are ne-normative,
plotted (a) using Walker et al.'s (1979) projection with tetrahedron faces being 01=0, Di = 0, Pl = 0, and Si = O,
(b) using O'Hara's (1968a) CM AS with faces C = 0-15, M = 0-10, A = 0-15, and S = 0-45, and (c) Walker el al.'s (1972)
projection, equation (4.1), with faces An =0-20, Di = 0, Ol = 0-20, and Si = 0-30. The line is calculated for adiabatic
melting with Tr= 128O°C. These plots were produced by M. Spiegelman.
653
M E L T G E N E R A T E D BY L I T H O S P H E R I C E X T E N S I O N
GlasMs
FIG. 12. Projections from PI into the Ol-Di-Qz plane of Walker el a/'s (1979) tetrahedron, using molar
concentrations. The crosses represent glass compositions collected by Elthon (1987) with MgO>9-0 %. The curves
in (a) are point average compositions calculated from the parametenzation shown in Table Al(a), whereas those in
(b) are from that in Table Al(b). The dashed line marks a line of constant melt fraction corresponding to 0245 (cpxout). In (b) cpx-out occurs at X = 0265. The small open circles on the curves mark melt fractions of 005, O15, and
035, with the arrows pointing in the direction of increasing X. The solid dots inside larger circles show the point and
depth averages. The ellipses are as in Fig. 10.
FIG 13. As for Fig. 12 but projected from Di.
TABLE
1280°C
Mean Elthon's glasses
SAVE (Pallister, 1984)
Mean Melson el al.'s glasses, M g O > 8 %
Mean of all of Melson et al.'s glasses
Mean IGCP basalts
Cumulus gabbro (Pallister, 1984)
SiO2
TIO2
51-89
49-37
511
49-87
5113
49-64
49-9
O92
084
060
1-01
1 69
1-44
031
1
14-57
16-31
16-6
1617
1508
15-48
16-9
FeO
MgO
CaO
Na20
K20
8-53
8-85
7-2
9-23
1050
9-77
6-0
1027
9-50
9-2
8-78
7-09
7-65
105
11O1
12-38
12-8
12-20
I1O8
11-67
14-6
216
2-15
2-3
2-26
2-67
2-62
1-5
025
O08
012
009
022
021
003
654
D. McKENZIE AND M. J. BICKLE
The average composition of the glasses analysed by Melson et al. (1977) and the mean
IGCP oceanic basalt composition probably contain more FeO and TiO 2 and less MgO than
does the 1280°C point and depth average because considerable quantities of the primary
magma have been removed by fractional crystallization. Pallister's (1984) estimate of the
average composition of the Semail Ophiolite, SAVE, and the average of Elthon's (1987)
MgO-rich glass compositions are more similar to the 1280 °C point and depth average. The
observed MgO concentrations are, however, about 1 % less than that calculated. The
removal of about 2% olivine from the melt by fractional crystallization could account for
this difference. The observed concentrations of SiO 2 , A12O3, and CaO differ from those
calculated by between 1 and 2%. The differences are probably just greater than the
experimental and parameterization errors.
A simpler comparison between the observed and calculated compositions than those
illustrated in Fig. 11-13 is obtained by using oxide-oxide plots. Five of these are illustrated
in Fig. 14 for Melson et al.'s glasses containing more than 8% MgO. All oxides except K 2 O
are plotted as functions of Na 2 O, which varies inversely with the melt fraction. The listed
concentrations of K 2 O are not accurate enough to be useful. The usual 1280°C reference
line shows that the concentrations of FeO and TiO 2 vary in the way expected from the
melting experiments, but the concentration of A12O3 is approximately constant, that of CaO
increases as the melt fraction increases and that of Na 2 O decreases. This behaviour suggests
that the aluminous phase is the first to melt, followed by diopside. A more complicated
parameterization was tried in which the concentration of CaO and A12O3 in the experiments
was modeled in the same way as that of FeO and MgO by allowing the compositions to
depend on pressure (Table Al(c)). The fit was scarcely improved, with the mean error for
major elements remaining at 106% and that for Na 2 O and TiO 2 decreasing to 0-26%. The
pressure dependence introduced was, however, considerable and agrees with that discussed
by Jaques & Green (1980). Curves calculated from this parameterization are illustrated in
Fig. 14 as dashed lines, and agree better with the observed trends.
Instead of excluding the glass analyses which have been affected by fractional crystallization, Klein & Langmuir (1987) have taken account of such effects by estimating the
composition that a parental magma would have had when the concentration of MgO was
8%. They argued that the observed regional variations in the parental composition result
from variations in the mantle potential temperature, and correspond to variations in the
residual depth of the ridge axis. Figure 15 shows their estimates of the composition when
MgO = 8%, together with curves showing the point and depth averages calculated from the
parameterization (a) in Table A1, except in the case of CaO/Al 2 O 3 , where both (a) and (c)are
shown. The depths in Fig. 15 were calculated by isostatic compensation of a column 150 km
deep against a standard ridge axis with a water depth of 2-8 km, a crustal thickness of 7 km
and a mantle potential temperature of 1280 °C. The density of the crust was calculated from
the CIPW norm of the point and depth average, with the opx distributed between olivine
and quartz. If the orthopyroxene is not distributed in this way the calculated water depth
decreases by 100m for r P =1160°C and increases by 270m when r P =1480°C. The
agreement between the calculated and observed variations is in general good, even though
the point and depth average contains considerably more than 8% MgO when TP is greater
than 1280 c C. However Fig. 15(d) suggests that the observed concentration of Na 2 O may
increase more rapidly than would be expected as the potential temperature decreases below
1250°C and the crustal thickness below 5 km. This difference could result from errors in the
calculated melt compositions, since the accuracy of the parameterization becomes poor
when the melt fraction is small. It is, however, also possible that it is caused by the generation
of Na 2 O-rich melts at temperatures below the onset of extensive silicate melting at Ts.
MELT GENERATED BY LITHOSPHERIC EXTENSION
655
o
o
co
CM
2
o
o
*
*
D. McKENZIE AND M. J. BICKLE
656
15
O
MgO
10
NB2O %
FIG. 14 (aH e ) oxide-oxide plots for all Elthon's glasses, and those of Melson et al. (1977) with MgO > 8%. The
l280°C lines are calculated from the parameters in Fig. 8(a). The arrows show the direction in which X increases,
with open circles marking values of 0-05 and Ol5 The dot inside a circle shows the point and depth average. The
ellipses show estimates of the 2a error ellipses for individual probe analyses and for the error in the mean from the
parameterization. The ellipse for the parameterization is marked with oblique lines. The dashed lines in (b) and (d)
show compositions calculated with Tr = 128O°C and a parameterization of the CaO and AI 2 O 3 experimental
compositions with C o = C0(P) (Table Al(c)).
A further condition which must be satisfied is that the primary melt from the mantle must
be able to generate the observed range of compositions of oceanic basalts and gabbros by
low pressure fractional crystallization. The most sensitive measure of fractional crystallization available from the major and minor oxide compositions is the MgO/TiO 2 ratio, since
MgO is the most and TiO 2 the least compatible oxide. Three plots showing oxide
concentrations as a function of TiO 2 are shown in Fig. 16. Plots of MgO and FeO against
TiO 2 are to be preferred to one of TiO 2 against m#-number because they do not confuse
MgO depletion with FeO enrichment.
Also plotted in Fig. 16 are the 0 GPa fractional crystallization trends given by Biggar
(1983), obtained from the experiments of Shibata et al. (1979), Walker et al. (1979) and of
Biggar & Kadik (1981). There is good agreement between the trends shown by the glass data
and those derived from the experimental results. Furthermore it is clear that the removal of
the cumulus gabbro can in a general way account for the observed trends. As Biggar (1983)
has pointed out, the point average melt compositions first produce olivine as they cool. After
the loss of a few percent olivine, plagioclase, and clinopyroxene join olivine and thereafter
the removal of large melt fractions have little effect on the major element compositions. This
behaviour is clearly illustrated by the small change in MgO concentration which is
associated with a change in TiO 2 concentration by a factor of 3 in Fig. 16(b).
Pallister(1984) gives the mean composition of the Semail cumulus gabbros as containing
105% MgO and 0 3 % TiO 2 (Table 1). This point is marked in Fig. 16 by a cross inside a
circle. If MORBs result from the removal of this gabbro from the primary melt, then the
mean gabbro composition, the point and depth average, and the average MORB composition should all lie on a straight line in Fig. 16, and the amount of crystallization calculated
from the point and depth average should be the same for all oxides. This calculation gives the
MELT GENERATED BY LITHOSPHERIC EXTENSION
657
fraction of gabbro required as 057 and 044 for TiO 2 and FeO respectively to produce the
mean glass composition, and 0-80 and 078 to produce the mean of the basalts from the
Galapagos which are particularly rich in FeO and TiO 2 , the so-called Fe-Ti basalts.
Cumulus gabbros make up a fraction of 066 of Pallister's (1984) measured section. If about
half of the primary melt crystallizes as gabbro to make the oceanic layer 3, its expected
thickness is between 3 and 4 km. The thickness of the dykes and pillow lavas which make
layer 2 should also be between 3 and 4 km. These numbers are in satisfactory agreement with
each other and with the geophysical observations. The Fe-Ti basalts are the extreme
products of fractional crystallization, requiring as they do removal of 80% of the primary
melt by crystallization. If the oceanic crust was usually produced in this way, many of the
(a)
Na2O
%
(b)
0 8 -
CaO
0 7 -
0 6 2
4
Depth km '
(c)
FeO
%
FIG. 15. (aHc).
658
D M c K E N Z I E A N D M J. B I C K L E
3-5
FIG. 15. Estimates of the Na 2 O, (a), CaO/Al 2 O 3 , (b), and FeO, (c), concentrations in basalts containing 8% MgO
plotted against the average depth to the ndge axis, (d) Seismically determined crustal thickness as a function of the
Na 2 O concentration in basalts with 8% MgO. The curves show the point and depth average compositions for the
potential temperatures marked in (a) and (d), obtained from the parameterization in Table Al(a), shown as
continuous curves, and from Al(c), shown as the dashed curve in (b). The depths were calculated by isostatic
compensation against a ridge axis depth of 2-8 km, a crustal thickness of 7 km and TP = 1280 °C with a 'lithospheric'
thickness of 150 km (see text). The points are taken from Klein & Langmuir (1987), but the point corresponding to
the Cayman Trough in (d) is not plotted.
erupted magmas would have this composition. Mass balance would then require the
production of 5-6 km of gabbro to every 1 -4 km of Fe-Ti basalts. Their rarity in Melson et
al.'s data set implies that the proportion of the oceanic crust which consists of gabbro is on
average closer to 50 than to 80%. This conclusion is also in agreement with the seismically
determined thickness of about 4 km for the oceanic layer 3, which is believed to consist of
gabbro (White, 1984).
The same calculation is not successful for MgO. Though the crystallization trend is clear,
and is consistent with Pallister's mean and with Biggar's (1983) experimental estimates, the
point and depth average contains about 0-8% more MgO than is required by the gabbro and
MORB compositions. It is not clear whether this difference is due to errors in the
calculations, or is an indication of some physical process which has not been taken into
account. If, for instance, the value of the entropy of melting is increased from 250 to
400 J ° C ~ ' k g " 1 , a change which is within the present experimental uncertainty, the
difference between the required and calculated MgO concentrations is reduced to 0-4%.
The case of Na 2 O is more complicated. Pallister's (1984) estimate of the mean composition of the cumulus gabbro contains less Na 2 O than does the point and depth average, and
removal of 45% of this gabbro from the primary melt produces a melt with the mean
composition of Melson et a/.'s glasses. Biggar's (1983) estimates of the Na 2 O concentration
in the residual melts illustrated in Fig. 16 are not likely to be as accurate as are those for
MgO, FeO, and TiO 2 because Shibata et al.'s (1979) experiments produced zoned, nonequilibrated feldspars. Biggar & Kadik's (1981) experiments suffered from the same problem
and in addition their charges lost Na through evaporation (Biggar, 1983). Nonetheless there
is reasonable agreement between the expected and observed trends in Fig. 16(c). Though the
removal of the cumulus gabbros can account for the average Na 2 O concentrations in
MELT GENERATED BY LITHOSPHERIC EXTENSION
MORB glasses, it cannot account for the absence of any continued Na 2 O enrichment at the
larger degrees of fractional crystallization required to produce the Fe-Ti basalts.
Mass balance calculations are less useful for CaO and A12O3 because the changes in
composition produced by fractional crystallization are so small, as Biggar (1983) has
remarked.
The complementary relationship between the MORB glass compositions and that of the
gabbro of the Semail Ophiolite supports the commonly held view that at least this ophiolite
is a reasonably representative piece of oceanic crust.
The simple model of primary melt segregation followed by low pressure fractional
crystallization which accounts for the major and minor element concentrations in MORB
can also account for those of some compatible trace elements like Ni. The point and depth
average Ni concentration calculated from Hart & Davis's (1978) distribution coefficient is
245 ppm for a bulk Ni concentration of 0-23%, and is little changed if the distribution
coefficient of Takahashi (1978) is used instead. Hart & Davis's (1978) distribution coefficient
£>(ol/melt) depends inversely on the MgO concentration in the melt, and may be too large
(a)
15
FeO
©
10
20% 40%
.1
1
60%
80%
2
TiO 2 %
(bi
15
1280°
MgO
%
1
2
TK> 2 %
Fio. 16. (a>-(b)
I
D McKENZIE AND M. J. BICKLE
:6«Ci
Ic)
Na,0
1280
'-#<>>
0
1
2
3
4
TiO 2 %
FIG. 16. Oxide-oxide plots of all of Elthon's and Melson et a/.'s (1977 and pers comm., 1092 analyses) glass data.
The solid dots inside circles mark the point and depth averages, solid circles the compositions of the basalts nch in
Fe and Ti from the Galapagos Spreading Centre at 0-71 °N, 85-5O°W, and heavy crosses within circles the average
composition of layered cumulus gabbro from the Semail Ophiohte (see Table 1, taken from Pallister, 1984). The
heavy dashed lines show the 0 GPa fractional crystallization trends from Biggar (1983, Table 1), with an initial
MgO concentration decreasing in the direction of the arrow from 9%, 7% where the lines intersect, to 5% at the
end. The percentage of crystallization required to generate a particular TiO 2 concentration by the separation of
cumulus gabbro from the point and depth average is marked in (a) along the .x-axis. See Fig. 14 for the meaning of
the error ellipses.
(Clarke & O'Hara, 1979; Elthon & Ridley, 1979). But Fig. 17 shows that the fractional
crystallisation of 5% olivine from the 1280°C point and depth average can produce the
average observed Ni concentration in the IGCP basalts in which the Ni concentration was
determined. The only other trace elements for which a clear trend was visible in the IGCP
data when their concentration was plotted as a function of MgO were Cr and V. The first
behaves like Ni, presumably because chrome spinel crystallises at the same time as does
olivine. The V concentration, like that of TiO 2 , increases by a factor of 2 as the MgO
concentration decreases from 10 to 5%.
The MORB primary magma debate
The calculations above show that the compositions of the most MgO-rich glasses closely
resemble that of the primary point average compositions generated by adiabatic decompression. These calculations therefore support the views of Green & Ringwood (1967a), Kushiro
(1973), Presnall et al. (1979), Fujii & Bougault (1983), and Takahashi & Kushiro (1983). The
depthaverageofthepressure(equation(14))for7 P =1280 o CisO48GPaandfor^isl3-5%.
The point average magnesium concentration ranges from 9-3 to 10-4%, and the maximum
amount of melt is not quite sufficient to eliminate clinopyroxene. The calculated MgO
composition of the instantaneous melt is illustrated in Fig. 4, but it is not clear that there is
any relationship between the instantaneous batch melting and the instantaneous Rayleigh
melting compositions.
A quite different origin for MORB has been proposed by O'Hara (1968a, b), Green et at.
(1979), Jaques & Green (1980), Stolper (1980), and Elthon & Scarfe (1980, 1984), who have
argued that a major fraction of the primary magma from which MORB is generated is
MELT GENERATED BY LITHOSPHERIC EXTENSION
661
(a)
1380°
Melting
400
1330
200
. * •
•••
5
(b)
10
15
MgO%
400
1380°
Fractional crystallisation
200
10
15
Mgo %
FIG. 17 Ni concentration as a function of MgO in the basalt of the IGCP data set resulting from batch melting
during adiabatic upwelling, (a), and fractional crystallization of olivine, (b) The solid dots in (a) and (b) mark the
point and depth averages for the potential temperatures shown, and the dashed line shows the melt composition
after the separation of 5% olivine. The large circle enclosing a cross in (b) shows the mean composition of the basalt
analyses in (a).
produced at pressures of between 2 and 3 GPa, and contains 15% or more MgO. The
following arguments have been used to support this view.
The composition of some MgO-rich glasses is not in equilibrium with orthopyroxene and
olivine at any pressure (O'Hara 1968a, b; Green el al., 1979; Elthon & Scarfe, 1984; Elthon,
1987). One method of producing such compositions is to generate picritic melts with MgO
concentrations of 15-20% at pressures of 2-3 GPa, then to remove olivine by fractional
crystallization. But this proposal suffers from major geophysical difficulties. If a large
quantity of the melt which is to form the oceanic crust is produced at a depth of at least
45 km then extensive melting must occur at such depths. Reference to Fig. 7(b) shows that
662
D. McKENZIE AND M. J. BICK.LE
the potential temperature required is about 1480cC, or 1600°C at a depth of 200 km
(Fig. 7(a)). This temperature is hotter, though probably not much hotter, than most
proposed geotherms. A more serious problem is how melting at depths shallower than
45 km can be prevented. As was shown in section 2, conductive cooling is quite unable to
remove heat from such great depths. Unless the heat is removed, another 20 km of melt will
be added on the way to the surface, and the composition of the MORB which forms the
oceanic crust will be dominated by this melt generated at lower pressure. The only escape
seems to be to circulate sea water to depths of 40 km, even beneath rapidly spreading ridges
like the East Pacific Rise. Such a proposal generates more problems than it solves.
A possible solution to these difficulties was proposed by Klein & Langmuir (1987), who
remarked that there was no reason why a melt generated from a range of depths should be in
equilibrium with opx at any particular depth. Only if the compositions generated by
adiabatic decompression lie on straight lines will mixtures between melts from different
depths also lie on the same lines, and thus remain on the opx-bearing cotectic. (see Walker et
al., 1979). This condition is, however, approximately satisfied during adiabatic decompression at melt fractions less than cpx-out at 24-5%, and is therefore probably not the
explanation. The point and depth average in Table 1 also does not support Klein &
Langmuir's suggestion. It is constructed by averaging point averages, all of which are in
equilibrium with opx, and is about 2% richer in SiO 2 than is the mean of Elthon's MgO-rich
glasses. Presnall & Hoover (1984) have argued that such differences may result from
analytical errors. But there is no evidence from the present study that their argument is
correct, since the parameterization of a large number of different experiments agrees
excellently with the results from individual laboratories. Therefore, though the difference
between the calculated SiO 2 concentration and the average from MgO-rich glasses is small,
it appears to be real. It is, however, not clear how representative the compositions of the rare
MgO-rich glasses are of the mean composition of the primary magma. A better estimate of
the mean composition of the oceanic crust may be Pallister's (1984) estimate, SAVE, from
Oman, and it has essentially the same SiO 2 concentration as the point and depth average
(Table 1).
Another argument used by O'Hara (1968a, b), Jaques & Green (1980) and Stolper (1980) in
favour of a picritic parent for MORB is concerned with the trend in Figs. 11-13. Walker el
al. (1979) argued that low pressure fractional crystallization of olivine, diopside and
plagioclase moves the residual melt composition towards the quartz apex. This behaviour is
illustrated in Fig. 10. If it is to account for the trend in Figs. 11-13 then the initial
composition should be close to the olivine-diopside-plagioclase plane, which is a thermal
divide. Fractional crystallization of olivine from a melt generated at the cpx-out point at
2 G P a in Fig. 10 can generate such a melt. But is the trend due only to fractional
crystallization? Its presence in the MgO-rich glasses, which can only have crystallized
olivine, suggests that it is not. Plots of m^-number and TiO 2 concentration should decrease
and increase respectively as the normative quartz increases. Elthon (1983) found no such
tendency in projections of MORB compositions using Walker et a/.'s (1979) projection, and
therefore modified the method of projection. Presnall & Hoover (1984) plotted the mgnumber against normative quartz and only found a clear decrease when Q z > 2 5 % .
An alternative explanation of the trend in Figs. 11-13 is that it results from different
amounts of melting. This explanation can account for the good agreement between the
observed trend and that of the calculated point average compositions, and the extension of
both across the thermal divide into the ne-normative region. 1-3% of the analyses of Melson
et al. (1977) and 10% of those of Elthon (1987) are ne-normative. As was recognized by
Elthon (1983), Takahashi & Kushiro (1983), and Fujii & Scarfe (1985), the observed trend
MELT GENERATED BY LITHOSPHERIC EXTENSION
661
results from variations in the concentration of Na 2 O, not SiO 2 . This proposal is easily tested
by recalculating the locations of the points within the tetrahedron of Walker et al. (1979)
without the contributions from the alkali metal oxides.
An = Al 2 O 3
Di = C a O - A l 2 O 3
Ol = (FeO + MgO + A12O3 - CaO)/2
Qz = SiO 2 - (A12O3 + FeO + MgO + 3CaO)/2
(24)
where the symbols on the right hand side of equations (24) refer to the molar concentrations.
This tetrahedron was used by Walker et al. (1972) in their discussion of lunar basalts. The
resulting plots are simple and straightforward to interpret. Figure 18 shows the calculated
and experimental compositions at various pressures. What was before a dispersed cloud of
points in Fig. 10 has concentrated in a small region whose composition moves towards the
Ol corner as the pressure increases.
Figure 19 shows the data sets projected onto two planes, with the 1280°C curve and
Biggar's (1983) fractional crystallization lines for reference. Crystallization has little effect in
these plots because the concentration of MgO + FeO is scarcely changed by the removal of
as much as 80% of the melt as cumulate. The trend observed in Figs. 11-13 is no longer
present, and therefore it was indeed produced by variations in the alkali oxide concentrations. The compositions now cluster about the 0 GPa cotectic. The plots show several other
Major Element Oxides only
(a)
FIG . 18. The normative projection of Walker et al. (1972) using only the major element concentrations expressed in
mol. % (see equation (24)). (a) is a projection from An, (b) from Di. The upper triangles show the paths calculated
from the parameterization shown in Fig. 8(a), with the circles in (b) and 5% and 15% melting by weight. Diopside
disappears at 24-5% melt, shown as a dashed line. The arrows point in the direction of increased melting, and the
numbers show the pressure in GPa. The lower triangles show the experimental observations, with crosses for
experiments between 0 and 0 5 GPa, open circles O5 to 1-5 GPaand filled tnangles for higher pressures. Only those
results for which the observed or calculated melt fraction was less than 24-5% are plotted. The ellipses show the
projections of the la errors for the mean composition from the parameterization (oblique lines) and the probe
analyses (open).
664
D. McKENZIE AND M. J BICKLE
interesting features. The plots of glasses with MgO greater than the average value of 7 1 %
are clearly more dispersed than are those with MgO < 7-1 %. This behaviour is that expected
if the initial differences in melt composition are removed by low pressure fractional
crystallization which concentrates all compositions at the cotectic, where olivine, clinopyroxene and plagioclase all crystallize together.
The ne-normative melts are shown separately as crosses in Fig. 19 because they are the
most extreme representatives of the trends in Figs. 11-13. Therefore, if they plot in the same
group as do the other analyses, the observed trend is entirely produced by the alkali oxides.
In Fig. 19(b) it is clear that this condition is satisfied. In 19(a) however the ne-normative
points are all below the 1280 °C reference line whereas most of the glasses with MgO > 7-1 %
lie above it. This observation suggests that the melt fraction formed by small degrees of
partial melting is depleted in CaO relative to MORB. The resulting variation in the
CaO/Al 2 O 3 ratio leads to a dispersion in the plane containing the diopside corner and the
cotectic. It is this dispersion which causes the trend to be less clear in Fig. 12 than it is in
Fig. 13.
It is now straightforward to understand how the trends in Figs. 11-13 arise. The initial
melt fraction generated by small amounts of melting is a ne-normative basalt which plots
well to the left of the Ol-Di-Pl join in Fig. 20 and contains a large concentration of Na 2 O.
As the melt fraction increases it is diluted by melt which contains less Na 2 O. As the melt
fraction increases, the path of the melt composition in any tetrahedron is a straight line if the
distribution coefficient of Na 2 O between melt and solid is constant. The composition of the
melt therefore lies on the line joining the initial melt composition to that of the cotectic. The
trend is clearer in the projection from Di than from PI because the CaO content of the initial
melt differs from that of the cotectic. This simple explanation of the observations is
consistent with physical models of ridge axis processes, with modern ideas of melt extraction
and with the geochemical observations.
FIG.
19. (a)
M E L T G E N E R A T E D BY L I T H O S P H E R I C E X T E N S I O N
FIG. 19. Projections from An (a) and Di (b) of the tetrahedron calculated from the major elements using equation
(24). The points from Elthon's collection are shown in the centre, with the data set of Melson el at. arbitrarily
separated into two parts, depending on whether the MgO concentration was greater or less than the average of all
the analyses. Those analyses which are ne-normative and the Fe-Ti rich basalts from the Galapagos Ridge are also
shown below the central triangle as crosses and solid dots respectively. The boundaries of the enlarged triangles are
(a) 20% Ol, 0% Di, 50% Qz giving a variation of 30% from apex to base, and (b) 20% Ol, 20% An, 38% Qz giving a
variation of 22% from apex to base. The heavy cross within a circle marks the average composition of layered
cumulus gabbro from the Semail Ophiolite (Pallister, 1984). The heavy dashed lines show the OGPa fractional
crystallization trend in the direction of the arrows from Biggar( 1983, table 1), starting from an MgO concentration
of 9%, decreasing to 7% where the lines intersect and to 5% at their ends. The large ellipses show the errors for the
enlarged triangles, the small ellipses those for the full triangle, using the same convention as in Fig. 18.
Picritic basalts and ophiolites
If the primary melts which generate typical oceanic crust are not strongly picritic, what is
the origin of those picritic magmas which are produced, and of the thick olivine accumulations commonly found in ophiolites, both of which have been used to support O'Hara's
ideas? Picritic magmas are not common, and some of those that do occur are related to hot
jets in the mantle. A potential temperature of 1480°C produces 27 km of a melt whose point
and depth average contains 17% MgO. The composition of two well known picritic basalts
from Baffin Bay analysed by Clarke (1970) are listed in Table 2, together with the 1480°C
point and depth average. The agreement is good. The existence of a hot jet in the mantle
beneath Baffin Bay at the time of eruption is also suggested by the shallowness of the region
between Disko and Baffin Islands. It is important to determine whether other examples of
picritic magmas are also the surface expression of mantle upwelling. Melts of such extreme
composition are not likely to be common because the thickness of the oceanic crust rarely
exceeds 10 km.
D. McKENZIE AND M. J. BICKLE
(a)
(b)
N* normative
initial rrwlt
FIG 20. Sketches to illustrate how the trends in Fig 11—13 arise by mixing variable proportions of the nenormative basalt with the cotectic melt
TABLE
Clarke (1970) no. 3
Clarke (1970) no. 4
1480°
2
SiO2
TiO1
Al>03
FeO
MgO
NiO
CaO
Na2O
K2O
Total
451
44-4
49-34
076
118
065
108
102
11-70
102
109
9-75
197
18-6
17-27
012
013
006
9-2
9-7
9-04
1-04
1-37
1 63
008
013
021
97-0
96-6
99-65
The composition marked 1480° is the point and depth average, the greatest NiO concentration in the instantaneous
melt for TT= 1480° is 0 23%.
Considerable thicknesses of olivine cumulates are often present in ophiolites, which are
widely believed to represent pieces of oceanic crust and lithosphere. But many ophiolites
were generated by some form of back-arc spreading. As Thompson (1987) has pointed out,
the presence of water in such environments is likely to give rise to boninites, and these will
produce large quantities of dunite by fractional crystallization. Thompson also emphasizes
that the mean composition of ophiolites can rarely be determined with confidence.
The main results of this section
Mantle melting by adiabatic upwelling beneath ridges can produce the mean oceanic
crustal thickness of 6-7 km, and the primary melts have the range of concentrations of MgO,
CaO, A12O3, and SiO 2 observed in MgO-rich MORBs. In the basalt tetrahedron the
calculated compositions form a band pointing at the Qz apex of the tetrahedron. This trend
results from variations in the Na 2 O concentration in the melts, not from low pressure
fractional crystallization. About half the melt is removed by low pressure fractional
crystallization to generate the cumulus gabbros. This process accounts for the range in the
observed MORB compositions. The other half is erupted as pillow lavas, or intruded as
dykes. There is no reason to suppose that MORBs are generated by the fractional
crystallization of a picritic parent, as has often been proposed. Picritic magmas are, however,
produced by melting above hot rising jets in the mantle. Variations in the potential
MELT GENERATED BY LITHOSPHERIC EXTENSION
667
temperature of the converting upper mantle can also account for the correlation between
ridge depth and composition discussed by Klein & Langmuir (1987). The results are in
excellent agreement with Thompson's (1987) arguments, who also demonstrated that the
trend seen in MgO-rich glasses in Walker et al.'s (1979) projections must be due to variable
amounts of melting, and not crystal fractionation.
A feature of the method used to calculate the melt compositions is that it makes
comparatively little use of phase diagrams, and so is unaffected by solid solution. The
parameterization allows the composition of the primary magmas to be obtained without
understanding any of the chemistry involved in the melting process! It is, however, only
possible to be so dumb if there is an excellent experimental base. For this reason a similar
approach cannot yet be used when the melt fractions are small or when the pressure is
greater than 4 GPa.
In one way the success of the batch melting calculations is disappointing. From the
discussion in section 2 it is clear that they cannot be correct, yet they reproduce the melt
compositions very well. Therefore the melt compositions cannot be very sensitive to the fluid
mechanics of the melting process. The small differences between the observed and calculated
compositions of SiO 2 , A12O3, and CaO in Table 1 may result from the naivety of the melting
model, but they could also be caused by errors in the assumed mantle composition and in the
parameterization.
5. MELTING PRODUCED BY EXTENSION OF THE CONTINENTAL
LITHOSPHERE
The original purpose of the work described in this paper was to test the suggestion
(McKenzie 1984£>) that significant volumes of basaltic melt can be generated when the
continental lithosphere is stretched. This question has previously been studied by Foucher et
al. (1982), who used geotherms obtained from the plate model and Ahern & Turcotte's (1979)
expression for X(P, T) to calculate the thicknesses of melt produced. Though the parameterization used here is likely to be the more accurate, in practice the resulting differences
are small. As in the case of ridges, the total melt thickness is not sensitive to the details of the
calculation, and the results obtained below agree with those of Foucher et al. (1982) for
corresponding values of TP. Their calculations were, however, concerned with the northern
margin of the Bay of Biscay, which was underlain by mantle whose potential temperature
was similar to that of the mean mantle temperature at the time of stretching, and produced
little melt. The assumption that crust is conserved during stretching is therefore reasonably
accurate. But the results are very different for a potential temperature of 1480° C. The other
difference arises because Foucher et al. (1982) assumed that about 10% of melt must be
generated before melt and matrix could separate. It now seems likely that this value is nearer
2 than 10%. Therefore for geophysical calculations melt separation can be regarded as
complete and as occurring in times of 1 Ma or less. Because so little melt is present even
during'extension, its influence on the mean density can be neglected. The most important
effect of this melt is therefore the resulting increase in crustal thicknesses. If the melt is
emplaced into the base of the crust (Cox, 1980; Herzberg et al, 1983; McKenzie, 1984b), the
amount of extension will be underestimated if it is determined from the change in the crustal
thickness.
There is an important difference between the behaviour of continental and oceanic
lithosphere when it is stretched. In the oceans stretching leads to a spreading ridge, with very
localized deformation. The same is rarely true of the continents, where the extension is
generally distributed over a considerable region such as the Basin and Range province in the
668
D. McKENZIE AND M J. BICKLE
western U.S.A., or the Aegean Sea. The cause of this difference is not properly understood,
but must be taken into account in any melting calculations.
The amount of extension is determined by the areal extension which some part of the
lithosphere has undergone, and is generally expressed in terms of /?, the ratio of the final to
the initial surface area. In the North Sea the values of P obtained from refraction and thermal
subsidence are less than 1-5 for the Jurassic-Cretaceous stretching event (Barton & Wood,
1984). In the Basin and Range P is probably as large as 2 over considerable regions and may
locally exceed 3 (Gans & Miller, 1983). Even larger values of P have resulted from the
stretching of continental margins (White et al., 1987).
To calculate the amount of melt produced by extension requires an initial geotherm. Since
most of the melt is generated from the material which is initially within and below the
thermal boundary layer, the initial geotherm must be chosen with care. The method used to
calculate the initial temperature variation is described in Appendix B and makes use of a
rather complicated parameterization obtained from numerical experiments.
The behaviour is illustrated in Fig. 21, which closely resembles a sketch of Dixon et al.
(1981) and the calculations of Foucher et al. (1982), and shows the melt volumes generated
for various values of)? when the interior potential temperature of the mantle is 1480°C. Such
high temperatures are probably restricted to hot rising jets. Figure 22 (a) shows that the
amounts of melt generated are considerable. An alternative method (McKenzie, 19846) of
representing the results is in terms of the apparent value of P, p,pp, determined from the
change in crustal thickness resulting from stretching when all the melt thickness tm is
assumed to be added to the crust of thickness tc. Then
Cm + tJ
(25)
Values of P,PP(P) in Fig. 22(b) were calculated for tc = 30 km and show that melting can have
a large influence on estimates of fi made from the change in crustal thickness. For instance
when the mechanical boundary layer is 100 km before extension, and the potential
temperature of the upper mantle is 1480°C, /? app < 14 no matter how large P may be. The
melt thickness generated in this way reaches 7 km when ^ = 2 and, because of its density, it is
likely to be emplaced in the lower crust (Herzberg et al., 1983). Such volumes of melt may
well account for the crustal thickness beneath the Basin and Range province ofthe western
U.S., and may also be the heat source which generated the widespread rhyolites by crustal
melting.
The volume of melt generated by extension depends strongly on both the thickness ofthe
mechanical boundary layer and on the potential temperature of the interior of the upper
mantle. When the potential temperature is 1280°C even a mechanical boundary layer as
thin as 70 km only leads to the production of 2 km of melt when P = 3. Most sedimentary
basins have a value of P<2 and are not above subduction zones or rising jets. Presumably
for this reason changes in crustal thickness often provide satisfactory estimates of p. These
are the conditions which Foucheref al. (1982) used, and they also found the effect of melting
to be small. However the conditions beneath the Basin and Range province are different,
because it is still about 1 km above sea level despite having been stretched by a factor of 2
over large areas. Both its elevation and crustal thickness of 25-30 km are probably caused by
a rising jet in the mantle, which can maintain 1 km of uncompensated topography and add
large volumes of basalt during the extension (Gans, 1987). In contrast little melt has been
added to the crust beneath the North Sea, where changes in crustal thickness provide an
accurate measure of the amount of extension.
MELT GENERATED BY LITHOSPHERIC EXTENSION
669
Depth km
0
50
2100
100
I
•
1S0
1
f-
1800
1700
1500
/
/
1300
i m n
Wftf
2
Thermal
boundary layer
/--
"""
Mechanical
boundary layer
_i
i
3
Pressure GPa
(b)
Ic)
100km
200km
100
50
Depth km
50
100
Depth km
FIG. 21. (a) Adiabatic upwelling due to stretching of convective geotherm generated from a mechanical boundary
layer thickness of 100 km, an interior potential temperature of 1480°C and a viscosity of 4 x 1 0 " m2 s'1. The
numbers against the geotherms give the values of /?, the stretching factor. The curves between the solidus and
liquidus show the melt fraction by weight, and the clashed line marks the path of the lower boundary of the
mechanical boundary layer as 0 increases, (b) The melt fraction as a function of depth generated in (a). The numbers
against the curves give the values of p. (c) as for (b) but with a mechanical boundary layer thickness of 200 km.
670
1480'C
1380 C
2
3
4
STRETCHING FACTOR P
(b)
1280°C
P.pp
» 1380"C
1480"C
Ptrue
FIG. 22. (a) Total melt thicknesses generated by various amounts of extension, /?. The numbers against the curves
give the thickness of the mechanical boundary layer, and the temperatures on the right are the interior potential
temperatures, (b) The apparent extension /), pp as a function of the true extension 0lnit for the examples in (a),
calculated from equation (25).
As is clear from Fig. 22, estimates of p from the change in crustal thickness produced by
the extension are likely to be underestimates, especially if the mechanical boundary layer is
thin and the potential temperature high. This effect may account for the difference between
the values of/? obtained from crustal thinning and from thermal subsidence by Royden &
Keen (1980) and by Royden et al. (1980).
An important difference between the me/t produced by continental extension and that
from ridges is that the former is added to the continental crust. The commonly accepted view
MELT GENERATED BY LITHOSPHERIC EXTENSION
671
is that new continental crust is largely generated at subduction zones by partial melting of
the oceanic crust and overlying mantle. Figure 22 shows that this is not the only possible
mechanism, and that large volumes of new continental crust can be generated by continental
extension. However, unlike island arc vulcanism, this process requires the existence of
continental crust to operate, and generates basaltic, not granitic, crust. Otherwise the
extension and the vulcanism will be confined to a ridge axis. It is therefore more likely to be
important when an appreciable fraction of the earth has already been covered by continental
crust. It will then become an efficient method of increasing the continental volume.
The association of alkali basalts with continental rifting and extension is well known, and
it is of interest to discover the extent to which the observed compositions can be accounted
for by simple extension. It is clear from Figs. 11-13 that melt fractions generated at
considerable depths will have the composition of alkali basalts. Figure 21 shows that the
melt generated during extension does indeed come from the necessary depth, and can be
expected to consist of alkali basalts. This qualitative argument was used by Dixon et al.
(1980) to account for the composition of North Sea basalts, and is strongly supported by the
present calculations. Quantitative estimates of the composition can easily be made from the
empirical expressions. It is important, however, to realize that they are not likely to be as
reliable as those for MORB because the compositions are controlled by those of the small
melt fractions until the thickness of melt generated exceeds a few kilometres. There is little
experimental control on the melt compositions until the melt fraction exceeds about 10%.
The point average compositions for two examples are illustrated in Fig. 23 together with
the point and depth averages. The arrows on the curves show the compositional trend as the
depth of the point averages decreases. The boundaries of the magma types are taken from
Cox et al. (1979,fig.2.2) except for the boundary between alkali basalts and olivine tholeiites
from McDonald & Katsura (1964) (see Carmichael et al., 1974, p. 413). The onset of extensive
silicate melting occurs when /?=l-5 when 7p=l480°C, and produces 2-4 km of alkali
basalts. When the amount of extension exceeds yS = 2 0 the point and depth average
composition crosses into the olivine tholeiite field. As the melt fraction increases further the
melts become picritic. Though Fig. 23 implies that the point average melt fractions produced
when /? = 50 are basaltic andesites, their true composition contains up to 16% MgO. The
effect of increasing potential temperature is to move the curves downwards in the
alkali-silica plot. If the value of ft is kept fixed they also move to the right.
The composition of two North Sea basalts from the most extended region of the basin
(Fig. 23) plot near the extension of the curve for T P = 1280°C. They therefore result from
small amounts of partial melting, probably smaller than can be accurately modelled with the
parameterization discussed here. When the mantle potential temperature is 1480 °C
stretching by a factor of 2 generates 7 km of melt whose composition is on the line separating
alkali basalts from olivine tholeiites, in agreement with the compositions of the large
eruptions of plateau basalts (Norry et al., 1980; Mohr, 1983). As the stretching increases
further the composition of the melt changes to tholeiitic. A detailed comparison of the
crustal structure and vertical motions (White et al., 1987; White & McKenzie, in prep.)
shows that the melt generated by adiabatic decompression can produce the observed lower
crustal velocities of 7-2 k m s ' 1 if the large quantities of hot picritic melt containing an
average of 16% MgO are underplated beneath the original continental crust in the manner
discussed by Herzberg et al. (1983). The P-wave velocities of 7-2 k m s " 1 are then the result of
the increased MgO content, rather than due to phase changes as Foucher et al. (1982) and
Furlong & Fountain (1986) argued. A potential temperature of about 1480 °C is required to
generate the melt volumes observed. Little subsidence then occurs until stretching ceases,
but thereafter the thermal subsidence is very rapid. Figure 21 shows that most of the melt
D. McKENZIE AND M. J. BICKLE
672
/
Basaltic
B A S A L T S
/
and* sites
afcal
/
Ni 2 O
/
thotofitlc
-
(b)
Na2O
/
A*—Hortt\
Sea
,'••
K2O
40
44
48
52
SJOj %
FIG. 23. (a) Various basalt types in an alkali-silica diagram from Cox et al. (1979). (b) and (c) melt compositions
generated by extension of a lithosphere with a mechanical boundary layer thickness of 100 km, a viscosity of 4
x 1 0 " m2 s" ', and the potential -temperature shown. The curves are marked with the value of/? and represented
point averages. The solid dots are point and depth averages. The two points marked 'North Sea' show the
compositions of 9B and 9C from Gibb & Kanans-Sotiriou (1976)
MELT GENERATED BY LITHOSPHERIC EXTENSION
673
comes from below the mechanical boundary layer, and therefore will have the asthenospheric isotopic composition. Any isotopic signature from the mechanical boundary layer is
likely to occur through interaction with melt as it moves upwards.
All these results are in agreement with the observations. A simple extensional model can
therefore account for the principal geochemical and geophysical features. This agreement
suggests that the melt distribution and composition can be used to map the vertical
movement of the base of the 'lithosphere', in the same way as crustal thinning is used to map
crustal extension. The eruption of alkaline magmas within the area of the North Sea which
has undergone most crustal extension suggests that the stretching of the mantle part of the
'lithosphere' is also greatest beneath the graben.
Further tectonic applications of these ideas depend on understanding what controls the
compositions of small melt fractions. Few relevant experiments have yet been carried out,
but it may be possible to exploit knowledge of the erupted magma compositions to provide
the constraints.
6. DISCUSSION AND CONCLUSIONS
The most important result is the demonstration that the range of composition observed in
MgO-rich MORBs is very similar to that of the primary melts produced during adiabatic
decompression of a rock with the composition of a garnet peridotite. The compositional
variations in these glasses result from differing degrees of melting, and not from either
variations of the source rock composition or fractional crystallization. Beneath a normal
ridge axis the melting starts at a depth of about 40 km and generates a basalt containing
about 10% MgO. The greatest degree of melting occurs at the shallowest depths, and does
not exceed 24%. A small amount of diopside is therefore left in the residue. These results
depend on an accurate parameterization of experimental batch melt compositions in terms
of the melt fraction present. It is surprising that the agreement between the calculated and
observed compositions is so good, because batch melting is likely to be a poor approximation to the melting processes beneath ridges. It is not yet clear whether the small differences
between the calculations and the observations are due to differences in the bulk compositions, errors in the parameterization, or fluid dynamical and chemical processes involved in
the generation and separation of the melt that have not been taken into account in this
discussion.
The trend seen in the MORB compositions when plotted in either Walker et a/.'s (1979) or
O'Hara's (1968a, b) projections has been interpreted as being due to fractional crystallization. But the primary melt compositions calculated from the parameterization of the
experiments show exactly the same trend, which in both cases clearly extends into the nenormative field. That this behaviour is produced by variations in Na 2 O concentrations was
recognised by Elthon (1983), Takahashi & Kushiro (1983), and Fujii & Scarfe (1985). It
results from the dilution of the ne-normative basalts generated by small amounts of melting
by a cotectic melt. This simple result is not evident when all the normative plagioclases are
combined together, but is obvious when the alkalis are omitted from such plots. Comparison
of the calculated FeO, TiO 2 , and Na 2 O concentrations with the mean value of Melson et
a/.'s glasses shows clear evidence of low pressure fractional crystallization, and require on
average about half of the primary melt to be removed as gabbro to produce a cumulus
thickness of between 3 and 4 km. This result agrees well with the measured sections in the
Semail Ophiolite, and with the thickness of layer 3 of the oceanic crust determined by seismic
refraction. These conclusions are in excellent agreement with those of Thompson (1987) and
of Klein & Langmuir (1987).
674
D. McKENZIE AND M. J. BICK.LE
The extension of the calculations to basins formed by stretching supports the arguments
of Dixon et al. (1981) and shows how this process can generate considerable thicknesses of
alkali basalts. The thickness, location, and composition of the melt produced can provide
estimates of the potential temperature of the upper mantle and the shape of the base of the
'lithosphere' resulting from the extension. Such applications are likely to be of considerable
importance, especially when combined with studies of thermal subsidence, but will require
the work discussed here to be extended to allow the accurate calculation of the composition
of melt fractions of less than 10%. The calculations also show that crustal conservation can
be used to estimate the amount of extension ft which has occurred if fl < 2 and TP < 1380 °C,
in agreement with Foucher et a/.'s (1982) results. These conditions are satisfied by many
stretched basins. Many continental margins, however, have undergone larger amounts of
extension, and the value of P estimated from the change in crustal thickness or the initial
subsidence will then be less than the true value. Uniform stretching of the crust and
lithosphere can easily account for Royden and Keen's (1980) observations, and is especially
important where the potential temperature is greater than average.
ACKNOWLEDGEMENTS
This project was only possible because of the generosity of W. Melson, who collected and
supplied the data set on which most of the arguments in this paper depend. We would also
like to thank G. Biggar, P. Browning, K. Cox, J. Durham, D. Elthon, P. England, G. Fitton,
T. Holland, E. Klein, C. Langmuir, R. K. O'Nions, S. Ripper, M. Spiegelman, R. N.
Thompson, G. Turner and D. Walker for their help. This research forms part of a general
investigation of partial melting supported by N.E.R.C. Department of Earth Sciences
contribution 1062.
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APPENDIX A
The compositions of melts generated from a rock with the composition of a garnet peridotite
The functional form chosen for the parameterization was based on Rayleigh's law. The instantaneous melt composition c was required to satisfy
X)ll")
(Al)
M E L T G E N E R A T E D BY L I T H O S P H E R I C E X T E N S I O N
677
in each of the intervals 0<A" <X,, X ,<X <X2 and X2<X <\ denoted by subscripts 1, 2 and 3
respectively for all oxides except SiO 2 , which was calculated by requiring the sum of all concentrations
to equal 100%. The values of a, b, and n(D = nj(n+ 1) where D the distribution coefficient) are required
to be constant in each interval, and c is required to be ^ 0 for all values of X. This condition prevents
any component returning to the residue as X increases. The relationship between c and the batch melt
(or point average) composition C is given by equation (13), and integration gives
C{X) = a+
( l - ( l - X ) ( 1 " " + 1 ) + —.
(A2)
Since C(0) is finite, d must be zero in the first interval for all oxides. Therefore
(A3)
C (but not c) was required to be continuous on X = X,, X2. For the parameterizations (a) and (b), a was
taken to be zero in all intervals, and b to be zero in all except the first interval, for all oxides except FeO,
MgO, SiO 2 , and 'the rest'. Those melt compositions where X had also been determined were then
plotted as functions of 7". For (c) A12O3 and CaO were treated in the same way as FeO and MgO in the
first interval, but a and b were set to zero when X > X t. Now Fig. 6 shows that X = X (7"). Therefore if
a, b, and d are constant in each interval, C = C( 7"') and all points should lie on a single curve if the same
bulk composition was used in all experiments. This condition is approximately satisfied for the major
elements. Of these SiO 2 , FeO and MgO show a pressure dependence, the first decreasing and the
second two increasing with pressure. This behaviour was taken into account by requiring C(0) and
C(X,) to be linear functions of pressure for these oxides. The additional conditions that C(l) must
correspond to the bulk composition, C be continuous on Xu X2, and the value of c(l) should
correspond to the melting of forsterite provides six equations in the six unknowns at, b,, i= 1, 2, 3 for
each of FeO and MgO which were solved analytically, d was set to zero in all intervals for these two
oxides. After a number of numerical experiments it became clear that the values of n for FeO, MgO and
CaO were poorly constrained if 0<X <XU and for FeO and MgO if Jf j <A'<A' 2 . This behaviour
presumably occurs because these oxides are essential components of the phases present. These values
of n were therefore fixed at unity, giving a linear dependence of C on X.
The concentrations of the minor elements TiO 2 , Na 2 O, and K 2 O in the melts were more variable.
Jaques & Green's (1980) pyrolite was produced from a Hawaiian basalt and contained about three
times more TiO 2 than any of the other melts. Their results for this oxide were therefore not used in the
determination of the best parameters. A separate determination of n for this oxide using their results
alone gave a value of 0-114, in excellent agreement with that of 0-115 from all other results. All
measurements of Na 2 O and K 2 O were used together, and those for Na 2 O are likely to be reliable,
though absolute concentration may be too low because of losses due to heating by the electron probe.
Since the same difficulty occurs in the MORB glass analyses it should not affect the comparison
between the two. The tabulated abundance of K 2 O in most of the melts was too low to allow accurate
parameterization. However, because Jaques & Green's (1980) K 2 O concentration was a factor of three
greater than that in most of the other experiments, their results allow the value of n to be determined,
and were best fit with n = 0-200. This value is surprisingly similar to that of 0-203 obtained for Na 2 O.
Since SiO 2 was calculated by subtraction, all oxides present in the melt had to be included in the
parameterization. The concentrations of those other than SiO 2 , TiO 2 , A12O3, FeO, MgO, CaO,
Na 2 O, and K 2 O were lumped together and fit with a single constant independent of melt fraction and
pressure. This constant is included as 'the rest' in Table Al. Though the value obtained by the fitting
program for this constant is only 0-41 %, a considerable reduction in the mean error resulted when it
was included.
The parameters were determined by minimizing the absolute value of the difference between the
observed and calculated concentrations, weighted in the manner described in the text. This procedure
avoids giving undue weight to the observations which fit the worst. It does, however, have one
disadvantage. Any curve which is fitted to two points with the same value of A" (or 7") has the same
value of the misfit, provided it passes between them. This effect leads to the minimum being shallower
than it is for the least squares condition. Twenty-two parameters were determined to produce the fits
shown in Fig. 8(a). Three determinations of the parameters were carried out. The first, shown as (b) in
Table Al and Fig. 8, used only those experiments listed in the caption to Fig. 8 -for which X was
678
D. M c K E N Z I E A N D M. J. B I C K L E
TABLE
C(0)
SiO 2 (a)
(b)
(c)
TiO 2 (a)
(b)
(c)
AI 2 O 3 (a)
(b)
(c)
FeO(a)
(b)
(c)
MgO(a)
(b)
(c)
CaO(a)
(b)
(c)
Na 2 O(a)
(b)
(c)
K,O(a)
(b)
(c)
The rest (a)
(b)
(c)
fdC\
( —)
VdP/,,0
C(XX)
Al
(AC\
Mean
I—)
\dPj . ,
Qi)
"2
error
x t
1-77
1 38
1-77
17-26
1796
18-89
0
0
0
0
0
— 1 65
0-115
0-162
0-116
0-521
0-354
1-0
860
611
7 58
4 61
2-04
361
12-05
12-20
12-02
3 24
518
314
0-26
0-16
0-27
0-41
0-27
0-37
0-59
3-05
1-82
3-01
2-29
4-76
0
0
-1-61
0
0
0
0
0
0
1-0
1-0
1-0
1-0
1-0
10
1-0
0-905
10
0-203
0114
0-227
1-777
0-278
10
1314
818
8O0
7 88
10-53
12-34
11-58
0-36
0-82
0-25
312
2 29
3-20
11 16
10
10
10
10
10
10
1-38
1 45
1-83
0-60
0-60
0-60
45-53
45-35
4412
017
017
018
309
3-23
3 82
8-50
8-50
850
39-20
39-20
39 20
2-59
2-75
3-25
044
050
O49
O06
003
007
041
027
037
1 15
022
118
098
082
1 19
029
023
015
C(X) is given in %. The values of X, and X2 were O245 and 0438 for (a), 0263 and 0438 for (b), and 0291 and
0439 for (c), respectively. c(l) for FeO was taken to be 0%, and for MgO to be 57%. (a) and (b) refer to the plots in
Fig. 8, and the fit labelled (a) is to be preferred, (c) is used in Figs 14 and 15.
measured or could be calculated. It excluded Stolper's (1980) results for AI 2 O 3 because they were
affected by the presence of spinel in the olivine and orthopyroxene, and Jaques & Green's (1980) results
for TiO 2 . The second determination, shown as (a) in Table Al, used a large number of experiments
listed in the caption to Fig. 8 for which 7" but not X was available, and obtained X from T' in these
cases. Stolper's (1980) results for AI 2 O 3 were included but not those for TiO 2 of Jaques & Green (1980).
The distribution of errors for this fit is shown in Fig. 9. In the third determination, (c), the
concentrations of AI 2 O 3 and CaO were allowed to vary with pressure in the interval 0 < X < A", in the
similar way to those of FeO and MgO. Outside this interval c for these elements was taken to be 0.
The care with which the experiments have been carried out is demonstrated by the agreement
between different studies and by the surprising success of the parameterization using the single bulk
composition given in Table Al(a). A listing of the FORTRAN subroutine used to calculate Cand X as
functions of depth for adiabatic upwelling is available on request, or on an IBM PC floppy disc for a
small fee.
APPENDIX B
Steady state geotherms
Richter & McKenzie( 1981) give parameterizations for three types of constant viscosity calculation;
with free boundaries on which the heat flux or the temperature are given, and for rigid boundaries at
constant temperature. To generate geotherms for the thermal boundary layer beneath an old plate the
MELT GENERATED BY LITHOSPHERIC EXTENSION
679
heat flux through the mechanical boundary layer must match that out of the top of the thermal
boundary layer. It is therefore necessary to convert the expressions Richter & McKenzie (1981) give for
constant temperature rigid boundary conditions to constant flux conditions. The Rayleigh number for
fixed temperature boundaries RaT is
RaT=-
gad1 AT
(Bl)
KV
where g is the acceleration due to gravity, a the thermal expansion coefficient, d the depth of the layer,
AT the temperature difference between top and bottom, JC the thermal diffusivity and v the viscosity of
the fluid. The corresponding expression RaT when the heat flux F is given is
RaF=-
gad'F
(B2)
kxv
where k is the thermal conductivity of the fluid. The Nusselt number Nu defined as
Nu=
Fd
(B3)
kAT
and an empirical expression which agrees with laboratory experiments is
Nu = 0-184Ka° 2 8 1
(B4)
substitution of (B3) and (B4) into (B2) gives
Ra F = 0-184Raj 2 8 1
(B5)
RaT = 315Ra%lsl.
(B6)
or
If the origin is taken to be at the base of the mechanical boundary layer and the positive direction is
downwards, the appropriate stretched variable z is
Q
(B7)
and the increase in temperature ATfrom the base of the mechanical boundary is given by
AT= —
Kaf 0 2 1 9 1-84 + e - z £ aj")
(B8)
with
ao=-l-84
a2=-O22
a, = — 1-18
a3
The value given for the thickness of the thermal boundary layer is the value of z for which z = 5.
It is then necessary to find the value of AT(0) from the requirement that the heat transported by
convection and conduction down the adabatic gradient at the top of the thermal boundary layer is the
same as that conducted through the mechanical boundary layer when the interior potential
temperature and the thickness of the mechanical boundary layer are given. The problem is solved by
iteration, the potential temperature ATP(z) then determined from (B8) and converted to the actual
temperature.
The temperature structure depends weakly on the depth of the convecting layer, which was taken to
be 700 km, and strongly on the viscosity through the Rayleigh number. Two geotherms for different
viscosities are illustrated in Fig. 3(b) and (c). The maximum in TP is a feature of all horizontally
averaged convective temperatures, and is produced by the shape of the isotherms in Fig. 2(a).