Plate Tectonics & Isostasy

CE3A8 SMJ Geology for Engineers 1

Plate vs Crust

The crust is a compositional layer. Crust = ‘Light Scum’. When the mantle melts, the magma rises and solidiﬁes to form crust.

The plate is defined in terms of temperature and hence strength. Plate = ‘Cold Skin’. Heat is supplied to the base of the plate by the convecting mantle, and heat is lost to the atmosphere from the top of the plate. Plates have an equilibrium thickness (around 120 km) when the heatflux supplied to the bottom balances the heatflux lost at the top.

The Plate is composed of the crust and the part of the mantle rigidly attached to it.

Constructive plate boundaries

1. Plate Spreading As the oceanic plates spread apart at a mid-ocean ridge, the hot convecting mantle beneath the plates is drawn upwards to fill the gap. 2. Melting The hot mantle melts as it rises because the confining pressure decreases. 3. Formation of crust The magma rises, cools and solidifies to form oceanic crust of basaltic/gabbroic composition. 4. Young plate is thin Since hot, convecting mantle has been drawn upwards to lie directly beneath the crust, the plate at the mid-ocean ridge is no thicker than the crust. 5. Plate cools to equilibrium As the plate spreads away from the mid-ocean ridge, it cools and thickens towards its equilibrium thickness. The principle of isostasy means that because the plate’s thickness and average density increase with age, the plate sinks with respect to the mid-ocean ridge crest.

Destructive plate boundaries

1. Subduction The old, cold, thick oceanic plate dives down into the mantle beneath either a CE3A8 SMJ Geology for Engineers 2

continental or another oceanic plate. Bending of the plate results in a deep trench.

2. Water Sea water subducted down into the mantle along with the oceanic plate decreases the melting temperature of the mantle, so magma begins to form.

3. Volcanoes The magma rises and adds to the overlying crust. The magma is more granitic in composition than that which forms oceanic crust. This compositional diﬀerence makes the magma more explosive, and a chain of volcanoes forms behind the oceanic trench and above the subducting plate. CE3A8 SMJ Geology for Engineers 3

Isostasy Practical

A. Why do only oceans get subducted?

The stability of the continents and the tendency for old oceanic plates to subduct back into the mantle can be explained by calculating the average density of each plate. The density, ρ, of rock is related to temperature, T , according to

ρ = ρ0(1 − αT ) (1)

where ρ0 is the rock density at surface temperature and pressure (S.T.P.) and α is the thermal expansion coeﬃcient of the rock. Equation 1 says that rocks become less dense as they are heated because they expand. In the following questions, refer to the template sketched in Figure 1 and use the values listed in Table 1.

1. Determine the average density of an old oceanic plate using the following procedure.

(a) First, calculate the average temperatures of both the crust and the mantle part of the plate (i.e. the lithospheric mantle). Assume a linear geothermal gradient ◦ from 0 C at the surface to temperature TB at the base of the plate. (b) Use equation 1 to calculate the average densities of the crust and the lithospheric mantle from their temperatures. (c) Calculate the average density of the oceanic plate from the two densities you determined in part (b), bearing in mind the relative thicknesses of the crust and lithospheric mantle.

2. Now calculate the average density of a continental plate by repeating the procedure in part (1).

3. Thirdly, calculate the density of the convecting mantle immediately below the plate (i.e. the asthenosphere) using equation 1.

4. Compare the average densities you have just calculated for an oceanic plate, a continental plate and the asthenosphere. You should ﬁnd that the old oceanic plate is denser than the convecting mantle beneath, whilst continental plates are less dense than the convecting mantle beneath. Thus oceanic plates are unstable and will sink back down into the mantle, given a chance. Continental plates ﬂoat stably on top of the convecting mantle. CE3A8 SMJ Geology for Engineers 4

B. Why are oceans deep?

The difference in elevation between continents and oceans can be explained using the principle of isostasy. Isostasy says that if we consider two blocks of different density and thickness floating in a fluid, the pressure at some reference depth below both blocks must be equal. The pressure, P , at the base of a unit column of rock is given by

P = ρgh (2)

where ρ is the density and h is the column thickness. The aim of the following calculations is to ﬁnd the diﬀerence in height between continents and oceans, termed ∆H in Figure 2.

5. Using equation 2, write down an expression for the pressure at the reference depth beneath an oceanic plate. The pressures generated by the water column and the rock column can be added. Use the average density for the oceanic plate you calculated in part A(1).

6. Similarly, write down an expression for the pressure at the reference depth beneath the continental plate illustrated in Figure 2.

7. Set the two expressions for pressure at the reference depth equal. You should ﬁnd that ∆H is the only unknown in the resulting equation. Rearrange your equation and calculate ∆H.

8. You should ﬁnd that the diﬀerence in height between continents and oceans is just over 6 km. In fact, oceanic abyssal plains lie at a depth of between 5 and 6 km and the average height of the continents above sea-level is 0.8 km.

Symbol Meaning Value Unit 3 ρM0 Density of mantle rock (S.T.P.) 3330 kg/m 3 ρC0 Density of crustal rock (S.T.P.) 2800 kg/m 3 ρW Density of seawater 1030 kg/m α Thermal expansion coeﬃcient of rock 3.3 × 10−5 /◦C CO Average thickness of oceanic crust 7 km CC Average thickness of continental crust 35 km L Average thickness of lithospheric plate 120 km ◦ TB Temperature at base of plate 1300 C Table 1: Information required for calculations CE3A8 SMJ Geology for Engineers 5

Ocean Continent Surface Temperature = 0 C Crust 7 km Crust

Lithospheric Mantle Lithospheric Mantle

120 km 120 km Convecting mantle: Temperature = 1300 C

Figure 1 Average densities of continental and oceanic plates

Ocean Continent Sea level ∆ H Sea water

Plate 120 km

120 km Plate

Convecting mantle ∆ H Reference depth: Isostasy says that pressures here are equal when the columns are in equilibrium

Figure 2 Calculating depth of oceans