Review of Heat and Mass Transfer in the Mantle and the Evolution of the Earth

1. Review

3. The nature of heat and mass transfer in the mantle amd the evolution of the Earth

4. Ingredients for a unified mantle model • Seismology:1D and 3D structure of the Earth • Geochemistry: bulk composition of the Earth; heat production; geochemical tracers of “mantle reservoirs” • Mineral physics: thermoelastic properties of materials at high T and P (equations of state); phase transformations; rheology of mantle materials • Geodynamics: flow models, geoid constraints, mantle convection, effects of phase transformations and viscosity variations on convection, thermochemical convection, thermal history.

5. Early history of the Earth – consequences of a moon-forming impact – isotopic constraints on timing of early Earth history • Arguments for “chondritic” composition • Mantle samples, pressure release melting. and “pyrolite”

7. Principles of Isotope Geology: Conventional radiogenic isotope systematics used in geology: 147Sm - 143Nd t 1/2 = 10.6 x 1010 yrs 87Rb - 87Sr t 1/2 = 48.8 x 109 yrs 238U - 206Pb t 1/2 = 4.47 x 109 yrs 235U - 207Pb t 1/2 = 0.704 x 109 yrs 232Th- 208Pb t 1/2 = 14.01 x 109 yrs 187Re - 187Os t 1/2 = 42.3 x 109 yrs 176Lu - 176Hf t 1/2 = 35.7 x 109 yrs

8. Hf is enriched in the silicate mantle after core formation

9. 1D structure of the Earth – use of free oscillation frequencies to constrain structure • Concept of resolution and trade-off between resolution and error. How well do we know the 1D Earth? • 5% in density and 1% in Vs and Vp when averaged over about 200km in the mantle. Use these when fitting mineralogical models to lower mantle

11. Thermodynamic review: the concept of fundamental thermodynamic relations • Equilibrium: maximizing entropy • Intensive/extensive parameters and the use of the Legendre transform to generate new fundamental relations: F, H, G • Maxwell relations

13. Conservation of mass and linear momentum • Equilibrium state: hydrostatic pressure from seismic models • Thermal state of a vigorously convecting region. Conductive and convective time scales. Peclet number • Adams-Williamson equation

15. Concept of “high” temperature. Debye theory and Debye temperature • Behavior of thermodynamic properties at high P and T • Mie-Gruneisen EOS – uses Debye model for thermal energy and finite strain to model “cold’ part. Parameterization of the behavior of Gruneisen’s ratio. EOS defined by a few parameters

16. Specific heat

18. Once have F(V.T) -- can get everything

19. Properties of composites • Fitting the lower mantle • Is the lower mantle compositionally distinct from the upper mantle? • Tradeoffs between temperature and composition

20. Bulk Sound Speed Correlation of shear and compressional velocity can tell us about the physical cause of an anomaly S velocity: P velocity: Bulk Sound Speed:

21. Parameters used to specify the compositional model • Xpv=Pv/(Pv + Mw + CaPv) • Xca=CaPv/(Pv + Mw + CaPv) • Xfe= Fe / (Mg + Fe) • Kd= partition coefficient for iron • Also need T, assumed adiabatic specified by T660.

23. Red=density Blue=Vc Green=Vs Xpv=0.65: “pyrolite”

24. Phase transformations: Clapeyron slope for single component • Behavior and importance of chemical potentials. Phase equilibria in the mantle • Solid state solutions and mixtures. Phase loops • Explanations for 410/520/660 and the sharpness of discontinuities • Simple “laws” of melting and mantle solidus

28. Phase diagram for iron (core) – shock waves not so important now but now DAC experiments indicate high melting temperature • Possible light allowing elements in the core • Temperature profiles for the Earth

29. Extrapolation done using Simon Law, Ticb=6200+-500

31. Seismological constraints on 3D structure • Resolution and error in tomographic models • Importance of secondary issues such as earthquake location • Thermal versus compositional explanations for seismic anomalies. Anticorrelation of shear and bulk sound speed • LLSVPs, ULVZs, PPV

33. Shear velocity -- +-1% isovelocity surfaces Includes S and SS cluster analysis data

35. Geochemical contraints on structure of mantle – overall energy budget • Helium/heat problem and Ar budget • OIB story – evidence for recycling of different components into the mantle • Standard geochemical model doesn’t work but evidence for some layering

37. Deformation mechanisms of mantle materials • Dislocation and diffusion creep. Stress and grain size dependence • Effective viscosity is strongly pressure and temperature dependent • Dislocation creep can lead to recrystallization and anisotropic fabric

39. Momentum equation in mantle flow – dimensional analysis and dynamic similarity – Reynolds number and Stokes flow • Simple flows: asthenospheric flow, corner flow, stokes flow, stream function and 2D flow • Post glacial rebound – constraints on upper mantle viscosity – the Haskell value • Geoid modelling and 1D models of mantle viscosity

43. Mantle convection – Boussinesq approximation (incompressible flow) – adding in energy equation • Importance of Rayleigh number and the critical Rayleigh number • Effects of various things on mantle flow • Boundary layer theory and the importance of the Nusselt number • Thermal history of mantle

45. Transition zone layering Yanagisawa et al., PEPI, 2010

46. From mobile-lid to “plate tectonics” • Regime of Mobile-lid convection exhibits an entire spectrum of how deformation is concentrated on the surface • (A,B) Mush-tectonics: only small patches of surface are rigid • (C,D) “plate-like” mobile lid • (E,F) stagnant lid • use measures of surface mobility and “plateness” to indicate the extent of recycling and how diffuse/narrow the zones of deformation are Tackley, Science, 2000

47. Compressible convection – anelastic liquid approximation – the dissipation number. • Energetics of core convection and “efficiency” • The effects on convection of compressibility • Thermochemical convection and the buoyancy number • The behavior of plumes and how they are connected to the base of the mantle (or not)

48. Hotspots and Mantle Plumes Richards et al Science, 1989

49. Starting Plumes Campbell and Griffiths, EPSL, 1990

50. Plumes and Mantle Convection • Plate scale flow can move dense piles and their attached plumes circular embayment Hassan et al., Nature, 2016 buoyant upwelling buoyant upwelling