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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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Presentation on theme: "THE HEAT LOSS OF THE EARTH Claude Jaupart Jean-Claude Mareschal Stéphane Labrosse Institut de Physique du Globe de Paris."— Presentation transcript:

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 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

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

4 AIMS (1)Evaluate heat loss and uncertainty (2)Constraints on secular cooling (3)Breakdown between core and mantle

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

6 OCEANIC HEAT FLUX

7 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

8 t -1/2 model

9 Juan de Fuca ridge

10

11 Well-sedimented areas worldwide

12 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

13 Heat flux through old sea floor

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

15 CONTINENTAL HEAT FLUX

16

17 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 QcQc  Q LM Basal heat flux Q b

18  (Q)  (Q) N WORLD All values Continental Heat Flow

19 Scale  (Q)  (Q) N CANADIAN SHIELD All values km km km Continental Heat Flow Averaging over different scales (windows)

20 Scale  (Q)  (Q) N CANADIAN SHIELD All values km km km WORLD All values °x 1° (≈100 km) °x 2° °x 5° Continental Heat Flow Averaging over different scales (windows)

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

22 50 K Gy - 1 ≈ 50 ± 25 K Gy -1

23 Sub-solidus convection. Constraints from phase-diagram

24 Solid fraction ≈ 1800 ± 100 K

25 (1)Assume same secular cooling rate than the mantle. Accounting for latent heat release and potential energy change due to crystallization: TW (2) Use magnetic field intensity and dynamo efficiency TW CORE HEAT LOSS 2 methods (Upper bound preferred because of constraints on boundary layer at the core-mantle boundary)

26 M C p = - ∫ q r dA + ∫ H dV Secular cooling rate ≈ K Gy -1 ≈ TW (for mantle + crust) Present-day crust + mantle heat loss = surface heat loss - heating from the core ≈ TW Bulk Silicate Earth (BSE) radiogenic heat production ≈ TW dT dt

27 Bulk Silicate Earth (BSE) radiogenic heat production ≈ TW Mean Uranium concentration (assuming chondritic Th/U and K/U) ≈ ppm

28 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 QcQc  Q LM Basal heat flux Q b

29 BSE radiogenic heat production ≈ TW Heat production in continental crust (+ lithos. mantle) ≈ TW Internal heat generation for mantle convection ≈ TW

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