Oceanography 540--Marine Geological Processes--Winter Quarter 2001

Framework for Heat and Mass Transfer Through the Oceanic Crust

In the next several lectures we will consider a variety of interlinked phenomena that create the oceanic crust, supply heat and basaltic magma to the zone of crustal accretion, and sustain hydrothermal activity along the mid-ocean ridge. This lecture sets a framework for considering in more detail:

Mantle Circulation

This schematic of mantle convection provides a plate scale view of the system:


schematic of mantle circulation

(Figure 7-1, from (17))


Melt that reaches the crust has its origin in the mantle, with melting occurring as ascending mantle material adiabatically decompresses. In this model

  1. asthenospheric material upwells beneath the ridge axis
  2. melting is supported by solid material undergoing adiabatic decompression, crossing the solidus at depth zsub ssub osub l. (The solidus is the P/T condition at which melting begins for a material of a given composition).
  3. crustal formation occurs
  4. melt is supplied to form the crust in a narrow zone near to the axis of spreading; on a time-averaged basis this supply must support Vsub szsub c of crustal generation
  5. the chemistry of basalts suggests that melting is incomplete, that the magmas are differentiated from their mantle source. The degree of melting that can be accommodated is Fsub tsub osub t=20 (+/-10) %
  6. The variables which are poorly constrained are the velocity of the upwelling mantle, Vsub u, and the width of the zone of upwelling, xsub u.
The rate of melting has to balance crustal formation (all melt rises to the surface, because only cooling will stop it), and so:

Eq 7-1: eq 7-1

Eq 7-2: eq 7-2

The simplest model for mantle convection involves a diverging plate overlying a semi-infinite medium of constant viscosity. This model predicts that Vsub s~Vsub u. Thus the zone of upwelling is predicted to be rather wide, about 30 km. One of the central issues in contemporary studies of mantle circulation and its relationship to crustal construction is how to focus the melt from this wide zone of melting into a narrow zone of volcanism.

To understand the parameter zsol, we can examine the relationship of an adiabat to the solidus for mantle rock. As a function of temperature and pressure:


melting of mantle as function of temperature and pressure

Figure 7-2, from (18))


The solidus for mantle material has a slope of about 12°C/kbar while an adibat in the mantle has a slope of about 1°C/kbar, hence these eventually cross and melting begins. Once within the field of melting, the effect of the negative heat of melting is to cause the temperature decrease with decreasing pressure to be steeper than the adiabat. The temperature of the mantle controls both the depth at which melting begins and the fraction of melt generated.

These thermodynamic relationships can be superimposed on the physical model:


mantle circulation showing melting relationships

Figure 7-3, from (18))


When the mantle is cold, melting is initiated at shallower depth and over a narrower zone. A thin crust is generated and the depletion in the residual mantle is minimal. When the mantle is hot, melting is initiated at greater depth and over a wider zone. A thick crust is created and there are greater chemical changes in the residual mantle which extend to greater depth.

Crustal Magma Chambers

Melted material migrates upward from the mantle to form the oceanic crust. When cooled sufficiently from above, this melt will pond and for a liquid pool or magma chamber. Cracking of overlying rock will open conduits (usually axis-parallel planar dikes) to feed extrusive basalt flows at the seafloor. Whether a magma chamber is usually present beneath the seafloor is thought to be strongly dependent on spreading rate. On the fast spreading East Pacific Rise there is extensive evidence from multichannel seismic studies for an axial magma chamber.


seismic image and interpretative section of crustal magma chamber

Figure 7-4, from (19))


This is thought to be a steady state feature, found on 60% of the ridge between the Siqueiros Fracture Zone at 8°30'N and 13°30'N. Its width across axis is 1-1.5 km and height 100-500 m. The low velocity zone surrounding this body is thought to be material with at least 3% melt. In contrast there is no evidence of the existence of persistent magma chambers on the Mid-Atlantic Ridge, although such bodies are likely present episodically.

Heat Transfer at a Mid-Ocean Ridge

Convective cooling occurs because of movement of fluid in the upper crust--through fractures and cracks in basaltic rock, along grain boundaries with the rock mass, and in the pore spaces of sedimentary materials. Thus the depth to which convective circulation occurs is closely tied to existence of pore space. Pore space exists because rock has cooled, so understanding the overall process involves not only the mechanics of fluid transport but knowledge of the heat source (cooling magma and solid rock), how pore space is developed as rock cools and how heat is transferred from solid to liquid.

We can sketch the scales involved:


[large scale geometry]

Figure 10-1


The basaltic crust is emplaced as melt in a narrow zone at the ridge axis, at a temperature near 1300 °C. At the ridge axis, high temperature circulation of fluid is established, with fluid temperatures reaching 350-400 °C. Thus as the crust leaves the zone of generation, it is cooler than it would be by conduction alone. As we will see, a reasonable estimate of the mean temperature of the crust a few kilometers off axis is 200 °C. Thus on a time scale of 100 ky (5 km distance with 5 cm/y spreading), the melt has both solidified and cooled considerably. The heat to be lost in this zone includes both the latent heat of crystallization of the melt and the cooling of the solid rock mass, so that the total heat loss is:

Eq 10-1: eq 8-1

On a global scale, the rate at which ocean crust is generated is 5.4 x 10^1^6 g/y so the convected heat is about 2.3 x 10^1^9 cal/y. This is about 1/2 the deficit in observed conductive heat flow relative to the conductive plate model. (Note that this calculation does not account for conductive heat transfer in this zone.)

On a local scale, we can consider as an example the Endeavour Segment, northern Juan de Fuca Ridge on which the spacing of major sites of hydrothermal discharge is of order 2 km. The heat loss from a 2 km section of ridge should be of order 1.6 x 1015 cal/y:

(crustal depth) x (cell spacing) x (full spreading rate) x (density) x (heat transfer)
6 km x 2 km x (2x5 cm/y) x 3 g/cm^3 x 433 cal/g

while individual vent fields here discharge 0.6 GW = 4.5x1015 cal/y, i.e. the instantaneous flux is 3 times as great as the long term geological average. This implies that venting must be short-lived and episodic.

Magma bodies can serve as a source of heat for hydrothermal circulation. Schematically:


schematic of permeable layer underlain by heat

Figure 10-2


But how quickly does this molten material solidify?

To resolve this question we will need to compare the convectively driven flux of heat in hydrothermal fluids discharging from the seafloor with heat transfer from the upper surface of the magma body. We will find that it is difficult to rationalize observed rates of convective heat transfer with a persistent magma chamber and so we will continue on to examine the character of the boundary between cracked and uncracked rock in terms of its thermal characteristics.
With this background as a framework we can ask a series of questions to consider:

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