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Geodynamics 456‐556 Problem set #3. Isostasy and Ridge Push (Due in class on May 6) 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 ρo 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 the crust and the average temperature of the sub‐ crustal upper mantle (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. 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 ΔH in Figure 2. 1. 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). 2. Similarly, write down an expression for the pressure at the reference depth beneath the continental plate illustrated in Figure 2. 3. Set the two expressions for pressure at the reference depth equal. You should find that ΔH is the only unknown in the resulting equation. Rearrange your equation and calculate ΔH. 4. 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. C. Isostasy and ice sheets 1. Consider the Laurentide ice sheet that was, at the last glacial maximum (LGM, about 20 Ka), 3 km thick in its center. Calculate the expected subsidence of the crust if this ice sheet was in place long enough for isostatic equilibrium to have been achieved. Assume densities of ice and mantle to be 910 and 3300 kg/m , respectively. Note that the answer is independent of what you assume for the density of the crust. 3 D. Average Continental crustal thickness 1. If the mean altitude of continents is 0.8 km, and the mean oceanic depth is 3.5 km, and the mean oceanic crustal thickness is 6 km, how thick is the mean continental crust? Assume that the densities involved are: seawater (1000 kg/m ), continental and oceanic crust (2700 and 3000 kg/m , respectively) and upper mantle (3300 kg/m ). 3 3 3 E. Isostasy, potential energy, and the forces of ridge‐push For part b/ of the following problem: If you can not integrate, then assume a constant density for the complete lithosphere (similar to the sketches above) to estimate the Gravitational Potential Energy for each column (the area in the triangle). d/ Assuming that lithospheric rocks have a strength of 70 MPa, would the gravitational forces determined in b/ produce lithospheric deformation?