Download Surface heat flow

Teil 1 Surface heat flow (am Beispiel der Venus) VO Meth. Grundlagen der Planetologie SS 2010

Mean Global Surface Heat Flow on Earth: well determined in-situ in thousands of different locations: Location

Amount [mW m-2]1,2

oceanic crust

101 ± 2.2

continental crust

65 ± 1.6

mid-ocean-ridges

up to 400

oceanic basins

~ 60

subduction zones ~ 35 AEarth = 5.1 x 108 km2 Ac = 2 x 108 km2 Ao = 3.1 x 108 km2

Global mean surface heat flow: ~ 4.43 × 1013 W or 87 ± 2 mW/m2 1Turcotte

D.L. and Schubert G., 2002 2 Fowler, C.M.R., 2005

 geothermal gradient: ~ 20 - 30 K km-1

Measurement of the Surface Heat Flow on Earth: Measurement Procedure: Determination of (1) the thermal gradient in deep drill holes, because climatic variations in the Earth’s surface temperature influence the temperature in the near-surface rocks for example: daily variations (~ 30 cm) yearly variations (~ 5 m) ice-ages (~ 1000 m)

and (2) the thermal conductivity of the rocks.

For continental crust at least 100 m are necessary to avoid convective groundwater heat transfer.

Mean Global Surface Heat Flow on Venus:

no measurements up to now

Estimations derived from: (1) Global scalings according to Earth (2) Catastrophic/episodic resurfacing model (3) Parameterized convection models (4) Capacities of the heat transport mechanisms model

(1) Global Scalings According to Earth:

(a) Solomon S. C. and Head J. W., 1982:

results in: 78 mW m-2

qVenus  0.815qEarth mass ratio between Venus and Earth

(1) Global Scalings According to Earth: (b) Leitner J. J. and Firneis M. G., 2005: Assumption: 2 different kinds of crust Venus surface: low- and uplands (± 1.5 km of planetary datum, 92 %) ~ oceanic crust highlands (~8 %) ~ continental crust

Scaling: mean heat flow of continental crust on Venus: ~ 53 mW m-2 mean heat flow of oceanic crust on Venus: ~ 82 mW m-2

mean global heat flow results in: ~ 80 mW m-2

(1) Global Scalings According to Earth: Model assumption:

-) identical heat loss per unit mass on Earth and Venus (due to cosmochemical models, which show comparable bulk abundances by mass for heat-generating elements in the terrestrial planets) but 40Ar enrichment in the Venusian atmosphere is some less than the expected value under the assumption of an equal content per unit mass of radioactive elements lowered efficiency of outgassing on Venus??? some less 40K per unit mass in the interior of Venus??? K/U ratio in Venusian crustal rocks ~ 7 x 103, in contrast to terrestrial crustal rocks with ~ 1.2 x 104 (Kaula W. M., 1999) maximum reduction of the surface heat flow only 6 % -) comparable efficiency of heat transport in the upper mantle on Earth and Venus no, due to the apparent lack of plate-tectonics

(2) Catastrophic/Episodic Resurfacing Model: Turcotte D. L., 1992, 1993 and 1999

‘standard’ model for Venusian resurfacing Main statements:  strong time-dependent (episodic?) heat loss  an active period characterized by extensive plate-tectonics (especially subduction) or extensive hot-spot-volcanism and a high surface heat loss with a duration of ~ 150 million years  resulted in a too cold lithosphere, which could not support active plate-tectonics anymore (since ~ 500 million years)  since the last resurfacing period only thermal conduction active  continuous heat production in the planet’s interior, which reheats the upper mantle  increasing temperature results in an unstable lithosphere and initiates a new (global) resurfacing event

(2) Catastrophic/Episodic Resurfacing Model:

1

k (Tm  Ts ) qVenus  (t )1/ 2

1Turcotte

D. L., 1993

results in ~ 11 mW m-2

Tm Ts k κ t

mean mantle temperature surface temperature thermal conductivity thermal diffusivity time, since the lithosphere has stabilized (mean surface age)

(2) Catastrophic/Episodic Resurfacing Model: Error calculation for the catastrophic resurfacing model:

12.6 ± 3.0 mW m-2

would imply that Venus is a geological dead planet  not consistent with our surface data!

(3) Parameterized Convection Models: 2 different ways for the exploration of the thermal history: -) 2D/3D solutions of the Navier-Stokes equations require high numerical effort many models are limited to low Ra-numbers (Ra-number of the Venusian mantle is distinctly higher than Earth one)

-) Parameterized convection models not directly based on the governing fluid dynamic equations, but on relationships between the Rayleigh, Nusselt and Prandtl numbers

At present (in lack of any seismic measurements on Venus) parameterized convection models allow the “as best as possible” exploration of the thermal history.

(3) Parameterized Convection Models: Summary of existing parameterized convection models: Model

Global heat flow [mW m-2]

Turcotte, Cooke and Willeman, 1979 (uniformly heated from within, whole mantle convection, no core heat component, identical heat generation per unit mass as on Earth, no phase transitions)

Fixed surface: 66.9 Free surface: 65.2

Phillips and Malin, 1983 (upward concentration of heat-generating elements, whole mantle convection, no core heat component, fixed surface, no phase transitions)

50

Solomatov and Moresi, 1996 (2D conv. cell in a square cell with fixed temp. difference between convection cell boundaries, no phase transitions, no core heat component , uniform distribution)

non-stagnant lid regime: ~50 15.4 ± 1.2 Stagnant lid regime: ~15

Near-surface geothermal gradients [K km-1]

20.6 ± 1.6 20.1 ± 1.5

15.4 ± 1.2

4.6 ~ 0.4

(3) Parameterized Convection Models: Main results of Solomatov and Moresi, 1996: In contrast to the other models, which are based on a constant viscosity regime, this work includes the viscosity dependence on the temperature.

Constant viscosity regime (non-stagnant-lid) ceased about 500 Myr ago and is switched to a stagnant-lid regime. After the switch the heat flux and the lithospheric thickening are purely controlled by a diffusion cooling lithosphere melting and related magmatism decreases, because a thicker lithosphere implies that the convective flow cannot reach close to the surface (as earlier) and can only reach a depth of ~ 300 km, where the melting temperature is about 500 K higher resurfacing ends continued heat generation reheats the upper mantle region

(3) Parameterized Convection Models:

Lithospheric thickness: 200 – 400 km on average up to 550 km (!!!) beneath Beta Regio

Surface heat flow: Non-stagnant lid: ~ 50 mW m-2 Stagnant lid: ~ 15 mW m-2

this model is not able to explain recent surface activities and the origin of Coronae

(3) Parameterized Convection Models: A 3-D Convection Model (Arkani-Hamed et al., 1984): 3D Convection model with a time-dependent temperature and pressure for a Newtonian fluid Some assumptions: -) no phase-transitions -) energy release during core formation was assumed to happen in the first Gyr of the planet’s history -) surface temperature was assumed to be as high as nowadays during the planet’s history!!! Further: Assumption: 20 % iron are present in the upper mantle surface heat flow results in 42 mW m-2 and tbl in ~ 150 km Assumption: 90 % of heat producing elements are concentrated in the outer 150 km of the planet and the missing 10 % are distributed uniformly surface heat flow results in 80 mW m-2 and tbl in ~ 30 km

(4) Capacities of the Heat Transport Mechanisms:

Which mechanisms contribute how much to the present surface heat loss?

on Earth1!

1Leitner

and Firneis, 2005

on Venus1?

(4) Capacities of the Heat Transport Mechanisms: (a) Thermal Conduction: Leitner J. J. and Firneis M. G., 2005

Leitner J. J. and Firneis M. G., 2005

for 500 Myr old crust on Venus: qcond ~ 33.5 mW m-2 in a good agreement with Turcotte, 1995 (37.7 mW m-2)

(4) Capacities of the Heat Transport Mechanisms: (b) Hot-Spot/Corona Volcanism: Are Coronae the Venusian equivalents to terrestrial hot-spots? Are Novae/Arachnoids stages in the Coronae evolution? known numbers of Coronae, Arachnoids and Novae vary from catalogue to catalogue:  USGS catalogue: 328 Coronae  Stofan E. R. et al., 2001: 515 Coronae (type 1 and type 2)  Brown University database: 206 Coronae, 265 Arachnoids and 63 Novae

qcor

dV  nW  (cP T  H f ) dt nW as a weight-factor for all presumably active plume-induced structures at present

1Leitner

J. J. and Firneis M. G., 2006

1

results in 6.0  1.4 mW m-2 ρ and cP Hf dV/dt ΔT

density and the specific heat of the volc. mat. fusion heat of the magma volumetric flux of magma with time temp. difference between the eruption temp. of the magma and the surface temp.

(4) Capacities of the Heat Transport Mechanisms: (b) Hot-Spot/Corona Volcanism: assumption: each Venusian Corona/Arachnoid/Nova (= hot-spot) is caused by a separate mantle plume neglecting: multiple Coronae, potential Corona-chains and large volcanic constructs

(4) Capacities of the Heat Transport Mechanisms: (c) Plate-Tectonics:

MAGELLAN revealed that on Venus nowadays plate-recycling is not operative!!!

Model calculations:  van Thienen P. et al., 2004: considerations only based on buoyancy arguments resulted in no explanation for the present lack of plate-tectonics  Leitner J. J. and Firneis M. G. 2005: plate-recycling driving forces model

at present on Earth: 13:1 (trench pull to ridge push) at present on Venus: 0.7:1 no present contribution to the total heat loss

(4) Capacities of the Heat Transport Mechanisms: (c) Plate-Tectonics: plate-recycling driving forces model: 2D model for a convection cell in a fluid heated from below  2  T  T   FR  gmv T1  T0 1  m v 1 0 t  (  m   )   1/ 2

    FT 1  2bg0 v TC  T0   2u0  2TC  T0 os       0  2u0 

(2)

1/ 2

FT 2

(3)

FT1 FT2 ρm ρω ρ0 γ t κ T1 T0 Tc λ u0 Δρos b g αv

(1)

gravitational body force due to its temperature deficit relative to the adjacent mantle downward grav. body force due to the phase boundary elevation mantle density density of the Venusian atmosphere at the surface of the planet mean density slope of the Clapeytron curve age of the crust thermal diffusivity base temperature of the convection cell surface temperature temperature in the nearly isothermal core of the convection cell dimension parameter of the convection cell horizontal fluid velocity positive density difference between the Olivin/Spinel Phases depth of the convection cell equatorial surface acceleration volumetric coefficient of thermal expansion

(4) Capacities of the Heat Transport Mechanisms: Thermal conductivity: 33.5 mW m-2 Corona/hot-spot volcanism: 6 ± 1.4 mW m-2 Plate-recycling: no contribution at present

Mean surface heat flow on Venus at present: ~ 39.5 ± 1.4 mW m-2 on Earth

on Venus

Summary of the Models:

Model type

Present-day heat flow [mW m-2]

global scalings according to Earth

~ 78

catastrophic resurfacing model

12.6 ± 3.0

parameterized convection models (Solomatov and Moresi, 1996)

non-stagnant lid: ~ 50 stagnant lid: ~ 15

capacities of the heat transport mechanisms model

39.5 ± 1.4

In-Situ Determination on Venus: … the extreme surface conditions on Venus make it very improbable to drill an adequate borehole for determining the vertical thermal gradient …

An alternative: heat flow sensor in direct contact with the surface

Possible on Venus due to:  the lack of surface- and groundwater and  the stable surface temperature

Teil 2 Plattentektonik VO Meth. Grundlagen der Planetologie SS 2010

Arten von Plattengrenzen:

Divergente Plattengrenzen:

Konvergente Plattengrenzen:

Anden

Transforme Plattengrenzen: