Framework for Heat and Mass Transfer Through the Oceanic Crust

• melting of mantle rock
• heat transfer from magma bodies
• convection in liquids and in porous rock
• fluxes of hydrothermally-derived heat and material

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 z. (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 Vz 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 F=20 (+/-10) %
6. The variables which are poorly constrained are the velocity of the upwelling mantle, V, and the width of the zone of upwelling, x.

Eq 7-1:

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 V~V. 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 z_sol, we can examine the relationship of an adiabat to the solidus for mantle rock. As a 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:

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

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

We can sketch the scales involved:

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:

On a global scale, the rate at which ocean crust is generated is 5.4 x 10 g/y so the convected heat is about 2.3 x 10 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 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:

Figure 10-2

But how quickly does this molten material solidify?

• Is there a persistent magma chamber that continues to provide heat to fluid flowing by it?
• Or is there a cycle of magma injection and solidification with the heat transfer from rock to fluid by penetration of the fluid into uncooled cracking rock?

• Why is the extent of melting of rising mantle not complete? Why does it produce basalts of a narrow range of chemical composition?
• What is the nature of convective heat transport and what roles does it play in heat transfer from magma chambers and through hydrothermal systems?
• What are the fluxes of heat and of chemicals, how do these vary in space and time, and how do they interact with the overlying ocean?