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THE HEAT LOSS OF THE EARTH Claude Jaupart Jean-Claude Mareschal Stéphane Labrosse Institut de Physique du Globe de Paris
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SECULAR COOLING EQUATION M C p = - ∫ q r dA + ∫ H dV + ∫ dV = - heat loss + internal heat production + external energy tranfers (ex: tidal interaction) Note (1) : negligible contribution of contraction, zero contribution of dissipation Note (2) : external energy transfers are negligible dT dt
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Core Mantle Core has no U, Th, K?
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AIMS (1)Evaluate heat loss and uncertainty (2)Constraints on secular cooling (3)Breakdown between core and mantle
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Heat flux ~ (age) -1/2 (Cooling by conduction in upper boundary layer)
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OCEANIC HEAT FLUX
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k T m Q = √ t Cooling model (based on boundary layer theory, consistent with laboratory experiments and numerical simulations) T m = mid-ocean ridge temperature k, = thermal conductivity, diffusivity t = age
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t -1/2 model
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Juan de Fuca ridge
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Well-sedimented areas worldwide
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Check no.1 = depth variations of the ocean floor (contraction due to cooling) Check no.2 = temperature at mid-ocean ridges T m = 1350 ± 50 °C consistent with basalt composition k T m Q = √ t
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Heat flux through old sea floor
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OCEANIC HEAT LOSS = 32 ± 2 TW (includes contributions from “hot spots” (mantle plumes) Main uncertainty : time-variations of age distribution
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CONTINENTAL HEAT FLUX
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CRUST Enriched in U, Th and K Lithospheric mantle (rigid root) Radiogenic heat production in continental lithosphere Q s = Q c + Q LM + Q b QcQc Q LM Basal heat flux Q b
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(Q) (Q) N WORLD All values 79.7 162 14123 Continental Heat Flow
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Scale (Q) (Q) N CANADIAN SHIELD All values 40.6 8.9 316 50 km 39.8 8.8 250 km 39.5 7.3 500 km 39.9 4.3 Continental Heat Flow Averaging over different scales (windows)
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Scale (Q) (Q) N CANADIAN SHIELD All values 40.6 8.9 316 50 km 39.8 8.8 250 km 39.5 7.3 500 km 39.9 4.3 WORLD All values 79.7 162 14123 1°x 1° (≈100 km) 65.3 82 2°x 2° 64.0 57 5°x 5° 63.3 35 Continental Heat Flow Averaging over different scales (windows)
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From Abbott et al. (1994) Earth’s secular cooling rate From the composition of mid-ocean ridge basalts and similar magmas
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50 K Gy - 1 ≈ 50 ± 25 K Gy -1
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Sub-solidus convection. Constraints from phase-diagram
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Solid fraction ≈ 60% @ 1800 ± 100 K
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(1)Assume same secular cooling rate than the mantle. Accounting for latent heat release and potential energy change due to crystallization: 2 - 6 TW (2) Use magnetic field intensity and dynamo efficiency. 5 - 10 TW CORE HEAT LOSS 2 methods (Upper bound preferred because of constraints on boundary layer at the core-mantle boundary)
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M C p = - ∫ q r dA + ∫ H dV Secular cooling rate ≈ 25 - 75 K Gy -1 ≈ 4 - 12 TW (for mantle + crust) Present-day crust + mantle heat loss = surface heat loss - heating from the core ≈ 33 - 44 TW Bulk Silicate Earth (BSE) radiogenic heat production ≈ 21 - 41 TW dT dt
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Bulk Silicate Earth (BSE) radiogenic heat production ≈ 21 - 41 TW Mean Uranium concentration (assuming chondritic Th/U and K/U) ≈ 0.022 - 0.044 ppm
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CRUST Enriched in U, Th and K Lithospheric mantle (rigid root) Radiogenic heat production in continental lithosphere Q s = Q c + Q LM + Q b QcQc Q LM Basal heat flux Q b
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BSE radiogenic heat production ≈ 21 - 41 TW Heat production in continental crust (+ lithos. mantle) ≈ 6 - 8 TW Internal heat generation for mantle convection ≈ 13 - 35 TW
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