GEO 5/6690 Geodynamics 10 Sep 2014 © A.R. Lowry 2014 Read for Wed 10 Sep: T&S Last Time: Radiogenic Heating; Topography Radioactive decay of crustal K, Th, U adds to surface heat flow; heat production A (W/m 3 ) is a source such that: Material Properties of Rocks: Heat Production A : - Only composition-dependent - A (granites) >> A (mafics) >> A (mantle rocks) - Normal crustal fractionation processes  ~ exponential decay of A with depth Topography can be handled in Fourier domain!

Next Journal Article Reading: For Monday Sep 15: Karlstrom et al. (2013) Geology 41(4),

The Geotherm Cont’d: Up to now, we’ve focused on the geotherm in steady-state… However temperature is not always constant! Recall the 1D steady-state heat equation in the absence of radiogenic heating: So, negative conductivity anyone?

If boundary conditions of temperature or heat flow change with time, need to generalize Fourier’s law to include time. This leads to the Heat Equation : where is thermal diffusivity (m 2 /s),  is mass density (kg/m 3 ), c is specific heat (J kg -1 °K -1 ). In 1D:

Example I: Subduction Initiation t = 0 t = 3 t = 2 t = 1

Example II: Subduction Cessation?

Example III: “Instantaneous” Rifting (McKenzie EPSL 1978) Basically a cooling model: crust mantle lithosphere crust mantle lithosphere crust mantle lithosphere Elevation h decays ~ exponentially as where  is stretching factor; characteristic time  is l

How would we measure this? ~1-2 km over Myrs  0.1 mm/yr. You’ll never see this with GPS! Need measurements of elevation change on geological time scales!!! One approach is to look at the sedimentary record, e.g., backstripping: Isostatic balance of water + sediment + crust + mantle. After correcting for sediment compaction (can predict from load) and sea level change, get elevation change!

The Adiabat (the “other” part of the geotherm): approximately describes mean temperature in convecting systems Depth Temperature ºC km Conductive Convective Adiabat: Temperature increases with pressure but energy doesn’t change

The Adiabat: What happens when mantle material moves up or down within a vertical column of flow? Assume: No transfer of heat energy into or out of volumetric elements (constant entropy s ) Compressibility , coefficient of thermal expansion  are independent of pressure P, temperature T Acceleration of gravity, g, is independent of depth No phase changes in the material s

Definition of compressibility: Change in pressure: Change in entropy: Then a change in pressure (i.e. depth) yields a change in temperature: (No heat energy transfer  This is not convection!!!)