Temperature at the Base of the Mantle

A constraint on the temperature at the base of the mantle is the seismic evidence that the outer core is liquid. This evidence consists mainly of the inability of shear waves to propagate through the outer core. Measured velocities of seismic compressional waves in the outer core indicate that, although the outer core is primarily composed of iron, it must also contain significant concentrations of one or more other constituents, the most likely of which is sulfur. The melting temperature for the iron–sulfur eutectic mixture at the core–mantle boundary is estimated to be 3200 K. This is an approximate minimum value for the temperature at the core–mantle boundary. The adiabatic lower mantle geotherm in Figure 4–57 is in approximate agreement with this constraint.

Just as an upper mantle thermal boundary layer, the lithosphere, inter-venes between the surface and the interior adiabatic state of the mantle, a lower mantle thermal boundary layer is expected to exist just above the core–mantle boundary. Seismic studies have confirmed the existence of this boundary layer, which is referred to as the D′′-layer. The D′′-layer has a complex structure with a thickness of 150 to 300 km. Laboratory studies indicate that the solidus temperature of a perovskite–magnesiowüstite assemblage at the core–mantle boundary would be about 4300 K. In addition to showing the two geotherms associated with whole mantle convection a and layered mantle convection b, Figure 4–57 gives the range of values for the mantle solidus as well as the temperature increases associated with the

D′′-layer. Although the required heat flux through the D′′-layer can be estimated,the stability of the layer which would give its thickness is difficult to determine. There may also be compositional stratification in this layer.

How much heat is conducted along the adiabat of Figure4–57 at depths of 1000 and 2000 km? At the core–mantle interface? Use k = 4 W m−1 K−1, αv = 1.5 × 10−5 K−1, g = 10 m s−2, cp = 1 kJ kg−1 K−1.

If the rate at which heat flows out of the core (J s−1) is 10% of the rate at which heat is lost at the Earth’s surface, how large is the mean temperature drop across the lower mantle thermal boundary layer in terms of the mean temperature drop across the upper mantle thermal boundary layer? Assume that the heat transport across a boundary layer can be calculated from Fourier’s law of heat conduction in the simple form 4.29 Thermal Structure of the Subducted Lithosphere 345 Figure 4.58 Isotherms (◦C) in a typical descending lithosphere. The 410- km phase change is elevated in the subducted lithosphere. The position of the slip zone is also shown. of Equation (4–3). Also assume that the upper and lower mantle boundary layers have the same thicknesses.