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THE HEAT LOSS OF THE EARTH Claude Jaupart Jean-Claude Mareschal Stéphane Labrosse Institut de Physique du Globe de P

THE HEAT LOSS OF THE EARTH Claude Jaupart Jean-Claude Mareschal Stéphane Labrosse Institut de Physique du Globe de Paris. SECULAR COOLING EQUATION M C p = - ∫ q r dA + ∫ H dV + ∫ y dV = - heat loss + internal heat production

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THE HEAT LOSS OF THE EARTH Claude Jaupart Jean-Claude Mareschal Stéphane Labrosse Institut de Physique du Globe de P

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  1. THE HEAT LOSS OF THE EARTH Claude Jaupart Jean-Claude Mareschal Stéphane Labrosse Institut de Physique du Globe de Paris

  2. SECULAR COOLING EQUATION M Cp = - ∫ qr dA + ∫ H dV + ∫ y 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

  3. Core has no U, Th, K? Mantle Core

  4. AIMS Evaluate heat loss and uncertainty Constraints on secular cooling Breakdown between core and mantle

  5. Heat flux ~ (age)-1/2 (Cooling by conduction in upper boundary layer)

  6. OCEANIC HEAT FLUX

  7. Cooling model (based on boundary layer theory, consistent with laboratory experiments and numerical simulations) k Tm Q = √pk t Tm = mid-ocean ridge temperature k, k = thermal conductivity, diffusivity t = age

  8. t-1/2 model

  9. Juan de Fuca ridge

  10. Well-sedimented areas worldwide

  11. Check no.1 = depth variations of the ocean floor (contraction due to cooling) Check no.2 = temperature at mid-ocean ridges Tm = 1350 ± 50 °C consistent with basalt composition k Tm Q = √pk t

  12. Heat flux through old sea floor

  13. OCEANIC HEAT LOSS = 32 ± 2 TW (includes contributions from “hot spots” (mantle plumes) Main uncertainty : time-variations of age distribution

  14. CONTINENTAL HEAT FLUX

  15. Radiogenic heat production in continental lithosphere Qs = DQc + DQLM + Qb CRUST Enriched in U, Th and K DQc Lithospheric mantle (rigid root) DQLM Basal heat flux Qb

  16. Continental Heat Flow m(Q) s(Q) N WORLD All values 79.7 162 14123

  17. Continental Heat Flow Averaging over different scales (windows) Scale m(Q) s(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

  18. Continental Heat Flow Averaging over different scales (windows) Scale m(Q) s(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

  19. Earth’s secular cooling rate From the composition of mid-ocean ridge basalts and similar magmas From Abbott et al. (1994)

  20. 50 K Gy-1 ≈ 50 ± 25 K Gy-1

  21. Sub-solidus convection. Constraints from phase-diagram

  22. Solid fraction ≈ 60% @ 1800 ± 100K

  23. CORE HEAT LOSS 2 methods 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 (Upper bound preferred because of constraints on boundary layer at the core-mantle boundary)

  24. M Cp = - ∫ qr 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

  25. 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

  26. Radiogenic heat production in continental lithosphere Qs = DQc + DQLM + Qb CRUST Enriched in U, Th and K DQc Lithospheric mantle (rigid root) DQLM Basal heat flux Qb

  27. 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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