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THE HEAT LOSS OF THE EARTH Claude Jaupart Jean-Claude Mareschal Stéphane Labrosse Institut de Physique du Globe de P PowerPoint Presentation
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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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slide1

THE HEAT LOSS

OF

THE EARTH

Claude Jaupart

Jean-Claude Mareschal

Stéphane Labrosse

Institut de Physique du Globe

de Paris

slide2

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

slide3

Core has no

U, Th, K?

Mantle

Core

slide4

AIMS

Evaluate heat loss and uncertainty

Constraints on secular cooling

Breakdown between core and mantle

slide5

Heat flux ~ (age)-1/2

(Cooling by conduction in upper boundary layer)

slide7

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

slide12

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

slide14

OCEANIC HEAT LOSS = 32 ± 2 TW

(includes contributions from “hot spots” (mantle plumes)

Main uncertainty :

time-variations of age distribution

slide17

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

slide18

Continental Heat Flow

m(Q) s(Q) N

WORLD

All values 79.7 162 14123

slide19

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

slide20

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

slide21

Earth’s secular cooling rate

From the composition of mid-ocean ridge basalts

and similar magmas

From Abbott et al. (1994)

slide22

50 K Gy-1

≈ 50 ± 25

K Gy-1

slide23

Sub-solidus convection.

Constraints from phase-diagram

slide25

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)

slide26

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

slide27

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

slide28

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

slide29

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