THE HEAT LOSSOF

THE EARTH

Claude JaupartJean-Claude Mareschal

Stéphane Labrosse

Institut de Physique du Globede Paris

SECULAR COOLING EQUATION

M Cp = - ∫ qr 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

dTdt

Core

Man

tle Core has noU, Th, K?

AIMS

(1) Evaluate heat loss and uncertainty(2) Constraints on secular cooling

(3) Breakdown between core and mantle

Heat flux ~ (age)-1/2

(Cooling by conduction in upper boundary layer)

OCEANIC HEAT FLUX

k TmQ = √ t

Cooling model(based on boundary layer theory,

consistent with laboratory experiments and numerical simulations)

Tm = mid-ocean ridge temperaturek, = thermal conductivity, diffusivity t = age

t-1/2 model

Juan de Fuca ridge

Well-sedimented areas worldwide

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 TmQ = √ t

Heat flux through old sea floor

OCEANIC HEAT LOSS = 32 ± 2 TW(includes contributions from “hot spots” (mantle

plumes)Main uncertainty :time-variations of age distribution

CONTINENTAL HEAT FLUX

CRUSTEnriched in U, Th and K

Lithospheric mantle(rigid root)

Radiogenic heat productionin continental lithosphere

Qs = Qc + QLM + Qb

Qc

QLM

Basal heat flux Qb

(Q) (Q) N

WORLDAll values 79.7 162 14123

Continental Heat Flow

Scale (Q) (Q) N

CANADIAN SHIELDAll values 40.6 8.9 31650 km 39.8 8.8250 km 39.5 7.3500 km 39.9 4.3

Continental Heat FlowAveraging over different scales (windows)

Scale (Q) (Q) N

CANADIAN SHIELDAll values 40.6 8.9 31650 km 39.8 8.8250 km 39.5 7.3500 km 39.9 4.3

WORLDAll values 79.7 162 141231°x 1° (≈100 km) 65.3 822°x 2° 64.0 575°x 5° 63.3 35

Continental Heat FlowAveraging over different scales (windows)

From Abbott et al. (1994)

Earth’s secular cooling rate

From the composition of mid-ocean ridge basaltsand similar magmas

50 K Gy-1

≈ 50 ± 25 K Gy-1

Sub-solidus convection.Constraints from phase-diagram

Solid fraction ≈ 60% @ 1800 ± 100 K

(1) Assume same secular cooling rate than the mantle.Accounting for latent heat release and potential energychange due to crystallization:

2 - 6 TW

(2) Use magnetic field intensity and dynamo efficiency.

5 - 10 TW

CORE HEAT LOSS2 methods

(Upper bound preferred becauseof constraints on boundary layerat the core-mantle boundary)

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

dTdt

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

CRUSTEnriched in U, Th and K

Lithospheric mantle(rigid root)

Radiogenic heat productionin continental lithosphere

Qs = Qc + QLM + Qb

Qc

QLM

Basal heat flux Qb

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