Download Earth`s energy budget

April 14, 2018 | Author: Anonymous | Category: , Science, Earth Science, Plate Tectonics
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Earth’s Energy Equation, simplified

Qsurface ≈ Hradioactive + Hmantle secular cooling + Qcore Qsurface ≈ 44 TW (surface heat flow measurements) Hradioactive ≈ 20 TW (chondrite-based composition models) Hsecular cooling ≈ 9-18 TW (50-100 K/Ga, based on petrologic studies and rates of continental uplift) Qcore ≈ 2-15 TW (geodynamo requirements, age of inner core, conductive heat flow across core/mantle boundary layer, heat transport by plumes)

How much heat are we loosing?

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Modified from Pollack et al. (1993)

•Generally accepted global value is ~44±1 TW (c.f., Pollack et al., 1993) •Hofmeister and Criss (2005) argue for much lower surface heat flow (~31 TW). •Difference reflects debate over the importance of hydrothermal circulation in transporting heat near mid-ocean ridges

Was mantle heat flow higher or lower in the past?

Standard view: Higher mantle temperatures in the early Earth result in lower mantle viscosity, more rapid convection, and higher surface heat flow.

Alternate view: Higher mantle temperatures in the early Earth result in deeper initiation of mantle melting and extraction of water and other volatile species. This increases viscosity of the melt-depleted region, resulting in thicker, stiffer tectosphere, more sluggish plate tectonics, and lower surface heat flow.

How much radiogenic heat production? Major element trends in chondrite meteorites and mantle xenoliths 0.16

0.12

melt depletion

Al/Si

Nebular processes 0.08

0.04

0.00 0.60

0.80

1.0

1.2

Mg/Si

1.4

1.6

Al2O3 and U concentration variations in chondrites 18

16

[U] (ppb.)

Approx. U content of Earth (~20-21 ppb in PM) 14

12

10

Approx. Al 2 O 3 content of Earth (~4.2 wt.% in PM)

8 1.5

2.0

2.5

Al2O3 (wt.%)

3.0

3.5

How much potassium? Bulk Silicate Earth Concentration (normalized to CI)

10

1

K

Volatile loss

Cu 0.1

Core formation

0.5%

Pb

1% 2% 4%

0.01

Sulfide segregation 0.001

0.0001 1800

1600

1400

1200

1000

800

50% Condensation temperature

(McDonough & Sun, 1995; Allegre et al., 2001)

600

400

K/U in MORB (Jochum et al., 1983) 20000

K/U

15000

Average = 12,700

10000

5000 0

500

1000

K (ppm)

1500

2000

Is the chondritic model valid?

146Sm

=> 142Nd T1/2 = 103 Ma Possible explanations for the difference in 142Nd/144Nd in terrestrial and chondritic samples include:

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1) Earth has non-chondritic relative abundances of Sm and Nd, possibly due to early impact erosion of proto-crust. 2) There is an enriched “hidden” reservoir with low 142Nd/144Nd somewhere in the mantle.

Could a giant impact such as the moonforming impact have ejected an early protocrust rich in incompatible heatproducing elements? QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture.

This scenario could account for the 142Nd depletion in terrestrial samples relative to chondrites but would suggest significantly less than 20 TW present-day radiogenic heat production in the Earth.

Hmantle secular cooling ≈ Mmantle*Cp*dT/dt How can we estimate rates of mantle cooling? Rates of continental uplift (constant freeboard argument) (c.f., Galer & Metzger,1996) FeO-MgO or REE fractionation trends in Archaean basalts or komatiites (adiabatic melting models) (c.f., Mayborn & Lesher, 2004) “Lock-in” ages of lithospheric mantle xenoliths (coupling between lithospheric and asthenospheric cooling) (c.f., Bedini et al., 2004) All of these methods suggest mantle secular cooling of ~50120 K/Ga, and most suggest 50-60 K/Ga since the archaean, but all are highly model-dependant.

How do we measure mantle cooling rates? Mantle cooling causes uplift of continental crust as the underlying mantle becomes denser. Average metamorphic pressures of exposed Archean terranes suggest mantle cooling rates of ~50-60 Ga since 3 Ga.

From Galer & Metzger, 1996

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Constraints on heat flow across the core/mantle boundary Power requirements of the geodynamo: ??? Conduction along outer core adiabat: ~7 TW (c.f., Anderson, 2002)

Conduction across CMB: ~7-14 TW (c.f., Buffett, 2003) Heat transport by mantle plumes: ~2-13 TW (c.f., Davies, 1988; Zhong, 2006)

Qcond = A(dT/dZ)

Qcond, CMB = ~8-14 TW T = ~1000-1800 K  = 9.5 Wm-1K-1

h = 200 km

(dT/dZ)oc = ~0.94 K/km



46 Wm-1K-1

Qcond, oc = ~7 TW

c.f., Anderson, 2002; Buffett, 2003

Thermal consequences of inner core crystallization Egrav = 4.1x1028 J

Elatent = 7x1028 J Ecooling = 18.2x1028 J

Etotal = 29.3x1028 J (+/- 18x1028J) (Labrosse et al., 2003) For CMB heat flow of 6-15 TW, age of onset of inner core crystallization is less than ~1.5 Ga.

Largest sources of uncertainty are core Cp, slope of melting curve.

Segregation of crust, either early in Earth history or continuously through plate subduction, could store large amounts of U, Th, and K at base of mantle

CMB

Core-mantle heat flow decreases with increasing CMB radiogenic heat production 200 H

= 0 TW

H

= 10 TW

H

= 25 TW

CMB

Height above CMB (km)

CMB CMB

150

Q

100

core

Q

core

Q

core

-3.3 TW

3.4 TW

=

7.8 TW

50

0 -1000

=

=

-800

-600

-400

-200 o

 T ( C)

0

200

4500 D" heat production = 10 TW (primordial layer) D" heat production = 10 TW constant accumulation

O

Outer core temperature ( C)

D" heat production = 0 TW

4000

3500 4000

3000

2000

Time b.p. (Ma)

1000

0

Heat production within the core? Experimental and theoretical studies suggest potassium could partition into the core under the right circumstances. •Potassium can enter sulfide liquids at low pressure •At high pressure (>25 GPa) potassium acts like a transition metal, can enter metal phases directly •Low-pressure segregation of sulfides or high-pressure core/mantle equilibration could result in significant quantities of potassium in the Earth’s core. Were the conditions necessary for potassium to enter the Earth’s core present during core formation?

Effect of sulfide fractionation during core formation on Cu concentrations in the mantle Primitive Mantle (normalized to CI)

10

Volatile loss

1

Cu 0.1

Core formation

Pb

2% S

0.01

10% S 0.001

0.0001 1800

1600

1400

1200

1000

800

50% Condensation temperature (K)

(McDonough & Sun, 1995; Allegre et al., 2001)

600

400

CI-normalized Primitive Mantle Concentration

Alkali metal depletion trend-volatile loss or core segregation?

1

Li (s-p at ~1 TPa)

Volatile depletion trend

Na (~100 GPa)

(~25 GPa) K

Ga

Rb (~10 GPa)

0.1 1100

K

(1)

(2)

(~5 GPa) Cs 1060

1020

980

50% Condensation temperature s-d transition pressures from Young (1991) and other literature sources Condensation temperatures from Allegre et al. (2001) after Wasson (1985)

940

Silicate Earth K/Rb fractionation from high-P core formation 500

D

Rb

= 20x D (Hillgren et al., 2005) K

Silicate Earth K/Rb

450

Estimated BSE value

400

350

300

250

Chondritic value 200 0

20

40

[K]

60

core

(ppm)

80

100

Questions an anti-neutrino observatory could help answer: 1) What is the total radiogenic heat budget of the Earth? What is the composition of the Earth? 2) Are heat-producing elements concentrated in the lower mantle or at the core/mantle boundary? 3) Does the core contain heat-producing elements? What is really needed:

1) Detection of neutrinos or anti-neutrinos produced from decay of 40K 2) Directional detectors

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