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

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Mean Global Surface Heat Flow on Earth: well determined in-situ in thousands of different locations: LocationAmount [mW m -2 ] 1,2 oceanic crust101 ± 2.2 continental crust65 ± 1.6 mid-ocean-ridgesup to 400 oceanic basins~ 60 subduction zones~ 35 Global mean surface heat flow: ~ 4.43 × 10 13 W or 87 ± 2 mW/m 2 1 Turcotte D.L. and Schubert G., 2002 2 Fowler, C.M.R., 2005 A Earth = 5.1 x 10 8 km 2 A c = 2 x 10 8 km 2 A o = 3.1 x 10 8 km 2 geothermal gradient: ~ 20 - 30 K km -1

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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 ground- water heat transfer.

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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

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(1) Global Scalings According to Earth: (a)Solomon S. C. and Head J. W., 1982: mass ratio between Venus and Earth results in: 78 mW m -2

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(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

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(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 40 Ar 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 40 K per unit mass in the interior of Venus??? K/U ratio in Venusian crustal rocks ~ 7 x 10 3, in contrast to terrestrial crustal rocks with ~ 1.2 x 10 4 (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

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(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

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(2) Catastrophic/Episodic Resurfacing Model: 1 Turcotte D. L., 1993 T m mean mantle temperature T s surface temperature kthermal conductivity κthermal diffusivity ttime, since the lithosphere has stabilized (mean surface age) 1

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(2) Catastrophic/Episodic Resurfacing Model: Error calculation for the catastrophic resurfacing model: would imply that Venus is a geological dead planet not consistent with our surface data! 12.6 ± 3.0 mW m -2

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(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.

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(3) Parameterized Convection Models: Summary of existing parameterized convection models: ModelGlobal heat flow [mW m -2 ] Near-surface geothermal gradients [K km -1 ] 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 20.6 ± 1.6 20.1 ± 1.5 Phillips and Malin, 1983 (upward concentration of heat-generating elements, whole mantle convection, no core heat component, fixed surface, no phase transitions) 5015.4 ± 1.2 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 Stagnant lid regime: ~15 15.4 ± 1.2 4.6 ~ 0.4

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(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

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(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

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(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

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(4) Capacities of the Heat Transport Mechanisms: Which mechanisms contribute how much to the present surface heat loss? on Earth 1 !on Venus 1 ? 1 Leitner and Firneis, 2005

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(4) Capacities of the Heat Transport Mechanisms: for 500 Myr old crust on Venus: q cond ~ 33.5 mW m -2 in a good agreement with Turcotte, 1995 (37.7 mW m -2 ) (a) Thermal Conduction: Leitner J. J. and Firneis M. G., 2005

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(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 1 Leitner J. J. and Firneis M. G., 2006 ρ and c P density and the specific heat of the volc. mat. H f fusion heat of the magma dV/dtvolumetric flux of magma with time ΔTtemp. difference between the eruption temp. of the magma and the surface temp. n W as a weight-factor for all presumably active plume-induced structures at present 1

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(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

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(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

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(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 F T1 gravitational body force due to its temperature deficit relative to the adjacent mantle F T2 downward grav. body force due to the phase boundary elevation ρ m mantle density ρ ω density of the Venusian atmosphere at the surface of the planet ρ 0 mean density γ slope of the Clapeytron curve t age of the crust κ thermal diffusivity T 1 base temperature of the convection cell T 0 surface temperature T c temperature in the nearly isothermal core of the convection cell λ dimension parameter of the convection cell u 0 horizontal fluid velocity Δρ os positive density difference between the Olivin/Spinel Phases b depth of the convection cell g equatorial surface acceleration α v volumetric coefficient of thermal expansion

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(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 Earthon Venus

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Summary of the Models: Model typePresent-day heat flow [mW m -2 ] global scalings according to Earth~ 78 catastrophic resurfacing model12.6 ± 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

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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

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Teil 2 Plattentektonik VO Meth. Grundlagen der Planetologie SS 2010

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Arten von Plattengrenzen:

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Divergente Plattengrenzen:

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Konvergente Plattengrenzen:

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Anden

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Transforme Plattengrenzen:

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