Modul BWP12 16.06.2010 Zustandsgleichungen (III): dynamische Eigenschaften.

Präsentation zum Thema: "Modul BWP12 16.06.2010 Zustandsgleichungen (III): dynamische Eigenschaften."—  Präsentation transkript:

1 Modul BWP12 16.06.2010 Zustandsgleichungen (III): dynamische Eigenschaften

2 Modul BWP12 16.06.2010 Antriebskraft: thermische Konvektion Rayleigh Zahl Ra Ra = 0 Tgd 3 Thermischer Auftrieb (Energiequelle) Schicht- dicke Viskosität (behindernd) Thermische Dissipation (behindernd) - thermischer Ausdehnungskoeffizient g - Schwerebeschleunigung 0 - Dichte

3 Modul BWP12 16.06.2010 Übergang zu einer kontinuumsmechanischenBeschreibung

4 Modul BWP12 16.06.2010 zu lösendes Gl.-System ! - thermischer Ausdehnungskoeffizient 0 - Dichte - thermische Leitfähigkeit - dynamische Viskosität c p - spezifische Wärmekapazität g - Schwerebeschleunigung Erhaltungssatz für die Masse * Erhaltungssatz für die Energie * Erhaltungssatz für den Impuls * (Kräftebilanz) * D/Dt / t + v i / x i (substanzielle Ableitung)

5 Modul BWP12 16.06.2010 Zur Bestimmung der dynamischen Eigenschaften im Erdinnern benötigt man die Kenntnis der Materialparameter, c p, c p als Funktion der Tiefe ! (d.h. insbesondere in Abhängigkeit von Druck und Temperatur etc.)

6 Modul BWP12 16.06.2010 Numerische Lösung des denkbar einfachsten Falls: alle Materialparameter konstant

7 Modul BWP12 16.06.2010 numerische Lösung für Ra = 10 4 (finite element solver citcom) Raum-zeitliche Entwicklung der Temperatur T

8 Modul BWP12 16.06.2010 numerische Lösung für Ra = 10 5 (finite element solver citcom) Raum-zeitliche Entwicklung der Temperatur T

9 Modul BWP12 16.06.2010 numerische Lösung für Ra = 10 6 (finite element solver citcom) Raum-zeitliche Entwicklung der Temperatur T

10 Modul BWP12 16.06.2010 Stabilitätsanalyse für den Wärmetransport in diesem Fall

11 Modul BWP12 16.06.2010 kritische Rayleigh-Zahl Ra cr = 658

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14 Modul BWP12 16.06.2010 Thermal modeling gives a driving force for subduction due to the integrated negative buoyancy (sinking) of cold dense slab from density contrast between it and the warmer and less dense material at same depth outside. Negative buoyancy is associated with the cold downgoing limb of mantle convection pattern. Since the driving force depends on thermal density contrast, it increases for (i) Higher v, faster subducting & hence colder plate (ii) Higher L, thicker and older & hence colder plate Expression is similar to that for ridge push since both forces are thermal buoyancy forces SLAB PULL plate driving force

15 Modul BWP12 16.06.2010 Abschätzung von tektonischen Kräften ridge-push vs. slab-pull ~ 10 12 Nm -1 ~ 10 13 Nm -1

16 Modul BWP12 16.06.2010 Coldest portion reaches only ~ half mantle temperature in about 10 Myr, about the time required for the slab to reach 660 km. Thus restriction of seismicity to depths < 660 km does not indicate that the slab is no longer a discrete thermal and mechanical entity. From thermal standpoint, there is no reason for slabs not to penetrate into lower mantle. When a slab descends through lower mantle at the same rate (it probably slows due to the more viscous lower mantle), it retains a significant thermal anomaly at the core-mantle boundary, consistent with models of that region Slabs are not thermally equilibrated with mantle Stein & Stein, 1996

17 Modul BWP12 16.06.2010 Was passiert, wenn die Viskosität in der Erde nicht konstant ist, d.h. mit der Tiefe abnimmt ?

18 Modul BWP12 16.06.2010 Lithosphäre stagnant lid

19 Modul BWP12 16.06.2010 Plattentektonik 3 Typen von Plattengrenzen OzeaneKontinente

20 Modul BWP12 16.06.2010 simple scaling view L W D FRFR FBFB v plate T density after expansion t) 1/2 cooling thickness time t - bouyancy force F R - resistance force

21 Modul BWP12 16.06.2010 densitysize gravity massacceleration * bouyancy force stress area resistance force because of Plate tectonics: scaling view (I) F B = DW ) g F R = v/L DW ) and = = v L

22 Modul BWP12 16.06.2010 FBFB FRFR ~ Ra 2/3 Plate tectonics: scaling view (II)

23 Modul BWP12 16.06.2010 T = 1400 K temperature difference = 3 ·10 -6 m 2 /sthermal expansion = 10 22 Pa sviscosity = 10 -6 m 2 /sthermal diffusivity = 3 ·10 3 kg/m 3 density g = 10 m/s 2 grav. acceleration L = 3 ·10 6 mlayer thickness plate velocity ~ 14 cm/yr !

24 Modul BWP12 16.06.2010 Stein & Wysession, Blackwell 2003 Different stresses result if weight of column of material supported in different ways similar to what seismic focal mechanisms show ! Forces within subducting plates

25 Modul BWP12 16.06.2010 Clapeyron slope describes how mineral phase changes occur at different depths in cold slabs use thermal model to find dT, phase relations to find and thus dP convert to depth change dz

26 Modul BWP12 16.06.2010 Opposite deflection of mineral phase boundaries Upward deflection of the 410 km and downward deflection of the 660 km discontinuities have been observed in travel time studies. In contrast, the ringwoodite ( spinel phase) to perovoskite plus magnesiowustite transition, thought to give rise to the 660 km discontinuity, is endothermic (absorbs heat) so H > 0. Because this is a transformation to denser phases ( V < 0), Clapeyron slope is negative, and the 660 km discontinuity should be deeper in slabs than outside Because spinel is denser than olivine, V < 0. This reaction is exothermic (gives off heat) so H < 0 is also negative, causing a positive Clapeyron slope. The slab is colder than the ambient mantle ( T<0 ), so this phase change occurs at a lower pressure ( P<0), corresponding to shallower depth

27 Modul BWP12 16.06.2010 Kirby et al., Rev. Geophys. 1996 Metastable delay of mineral phase transformations

28 Modul BWP12 16.06.2010 Predicted mineral phase boundaries and resulting buoyancy forces in slab with and without metastable olivine wedge For equilibrium mineralogy cold slab has negative thermal buoyancy, negative compositional buoyancy from elevated 410 km discontinuity, and positive compositional buoyancy from depressed 660 km discontinuity Metastable wedge gives positive compositional buoyancy and decreases force driving subduction Stein & Rubie, Science 1999 negative buoyancy favours subduction, whereas positive buoyancy opposes it. Metastable delay of mineral phase transformations

29 Modul BWP12 16.06.2010 Deep earthquakes from metastable olivine ? Kirby et al., Rev. Geophys. 1996

30 Modul BWP12 16.06.2010 Intermediate depth earthquakes (I) Under equilibrium conditions, eclogite should form by the time slab reaches ~70 km depth. However, travel time studies in some slabs find low-velocity waveguide interpreted as subducting crust extending to deeper depths. Hence eclogite- forming reaction may be slowed in cold downgoing slabs, allowing gabbro to persist metastably. Oceanic crust should undergo two important mineralogic transitions as it subducts. Hydrous (water-bearing) minerals formed at fractures and faults warm up and dehydrate. Gabbro transforms to eclogite, rock of same composition composed of denser minerals. Kirby et al., Rev. Geophys. 1996

31 Modul BWP12 16.06.2010 Intermediate depth earthquakes (II) Support for this model comes from the fact that the intermediate earthquakes occur below the island arc volcanoes, which are thought to result when water released from the subducting slab causes partial melting in the overlying asthenosphere. In this model intermediate earthquakes occur by slip on faults, but phase changes favor faulting. The extensional focal mechanisms may also reflect the phase change, which would produce extension in the subducting crust. Kirby et al., Rev. Geophys. 1996

32 Modul BWP12 16.06.2010 various kinetic processes during subduction P. van Keken, 2004

33 Modul BWP12 16.06.2010 Deep subduction process is a chemical reactor that brings cold shallow minerals into temperature and pressure conditions of mantle transition zone where these phases are no longer thermodynamically stable. Because there is no direct way of studying what is happening and what comes out, one seeks to understand the system by studying earthquakes that somehow reflect what is happening. Kirby et al., 1996 Complex thermal structure, mineralogy & geometry of subducted slabs in the mantle transition zone