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GEO 5/6690 Geodynamics 08 Sep 2014 Last Time: Conduction; Radiogenic Heating; Critical Thinking Skills Material Properties of Rocks: • Thermal Conductivity k: - Temperature sensitive; composition dependent - Mafic rocks have lower k at low T but higher k at high T than granitic rocks • Heat Production A: (In T&S, H) - Radioactive decay of crustal K, Th, U adds to surface heat flow; heat production A (W/m3) is a source - Only composition-dependent - A(granites) >> A(mafics) >> A(mantle rocks) - Normal crustal fractionation processes ~exponential decay of A with depth Read for Wed 10 Sep: T&S 132-149 © A.R. Lowry 2014 Roy et al. “wrap-up”: Food for thought: • If elevation increased by heating after Laramide, where should it have risen? • And what should it have looked like before flat-slab subduction? He isotope ratio figure provided by Crossey et al. for the EarthScope 2010-2020 Science Plan… Black dots are travertines; color contour is P-velocity at 100 km depth. Recall surface heat flow… > 50 mW/m2 requires advection; For advection by rifting alone, >90 mW/m2 requires a strain rate in excess of 3x10-15 s-1. Eastern Basin-Range is ~1x10-15 s-1; Rio Grande Rift is much less than that! 13C suggests ~1/3 total CO2 is deep-derived, with ~1/4 of that from “mantle” and 3/4 from “crust”; 3He/4He also suggests a contribution from the mantle coupled with an important contribution from the crust. So important questions include: • What is the transfer mechanism across the ductile lower crust? • Does the combination of “crustal” and “mantle” signatures reflect mixing, or residence time? • What are the flux rates? • How much heat was lost along the way? We derived our equation relating heat flow q and the geothermal gradient assuming no heat dT sources… q k dz More realistically in the Earth, expect that all rock acts as a heat source due to radioactive decay of U, Th,K etc. For a material with heat production A (W/m3), q A and the 1D solution becomes: T A 2 k z 2 Material Properties of Rocks: Similarly can measure A of rock from U, Th, K concentrations (inferred by measuring radioactive decay products). A is high in granitic rocks (particularly near top of intrusions), lower in lower crustal rocks, very low in the mantle. Brady et al Lithos 2005 K Th U Surface radiogenic element concentrations (averaged over 10-km scales) US Geological Survey has flown aero-spectral gamma at relatively high resolution (<1 km pixel) over the entire conterminous United States… Measurements are integrative so are representative of properties of surface rocks. Can these be used to draw inferences about deeper rocks also? Combined radiogenic heat production can be estimated from (T&S eqn 4-8): If heat production truly decays exponentially with depth, i.e., A A0 explrad z for some length-scale parameter lrad, then if heat flux at the base of the lithosphere q0 is constant, we would expect: qs q0 lrad A0 Here solved for slope & intercept of line fit averaged within 500X500 km windows. Other complications: What about topography? T h Two effects: • Temperature depends on altitude per “lapse rate” • Heat flow “refracts” toward heat sinks (i.e., surface) For periodic boundary, first effect is attenuated as 2 x 2 z T cos e xp Second expresses in temperature as: 2x 2 z q0 A0 lrad h0 cos e xp k Other complications: What about topography? So can Fourier transform observed topography and surface T variations and solve!