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Convection in the Earth's Mantle the Mantle Geotherm

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Convection in the Earth's Mantle the Mantle Geotherm Convection in the Earth’s mantle Reading: Fowler p331-337, 353-367 EPS 122: Lecture 20 – Convection The mantle geotherm convection rather than conduction more rapid heat transfer Adiabatic temperature gradient Raise a parcel of rock… If constant entropy: lower P expands larger volume reduced T This is an adiabatic gradient Convecting system close to adiabatic EPS 122: Lecture 20 – Convection 1 The adiabatic temperature gradient Need the change of temperature with pressure at constant entropy, S using reciprocal theory Some thermodynamics… Maxwell’s thermodynamic S V relation = P T T P coefficient of thermal expansion specific heat Substitute… …adiabatic gradient as a function of pressure EPS 122: Lecture 20 – Convection The adiabatic temperature gradient …adiabatic gradient as a function of pressure …but we want it as a function of depth For the Earth Substitute… …adiabatic gradient as a function of radius Temperature gradient for the uppermost mantle 0.4 °C km-1 using T = 1700 K = 3 x 10-5 °C-1 at greater depth 0.3 °C km-1 g = 9.8 m s-2 cp = 1.25 x 103 J kg °C-1 due to reduced EPS 122: Lecture 20 – Convection 2 Adiabatic temperature gradients Models agree that gradient is close to adiabatic, particularly in upper mantle …why would it not be adiabatic? greater uncertainty for the lowest 500-1000 km of the mantle big range of estimated T for CMB 2500K to ~4000K This is the work of Jeanloz and Bukowinski in our dept EPS 122: Lecture 20 – Convection Melting in the mantle 100 km Different 200 km adiabatic gradient for fluids: ~ 1 °C km-1 Potential temperature: T of rock at surface if rises along the adiabat EPS 122: Lecture 20 – Convection 3 1D velocity model for the Earth Uppermost mantle low-velocity zone Transition zone: 410-660 km VS VP Lower mantle Using the arrival times of seismic phases at stations Core-mantle around the globe we boundary can calculate a 1D average velocity Outer core: must be model for the Earth fluid as VS = 0 Inner core solid EPS 122: Lecture 20 – Convection Density and elastic moduli for whole Earth P-velocity S-velocity two equations, three unknowns K, μ and bulk modulus, shear modulus and density Adams-Williamson equation – the 3rd equation tells us the density gradient as a function of depth using our understanding of gravitational attraction and the radial mass distribution of the Earth EPS 122: Lecture 20 – Convection 4 Adams-Williamson equation Mr is the mass within radius r …which we don’t know Start at Earth’s surface and work inwards applying the equation successively to shells of uniform composition self compression model 1. Choose a density for the top of the mantle and work downward to the CMB Additional constraints: 2. Choose a density for the top of the core 1. Moment of inertia – 3. Once at the center of the Earth, the total mass distribution of mass must equal the known value. If not, pick a within the Earth new starting density and re-calculate. 2. Need to account for changes in phase as final model satisfies seismic data well as composition and mass of the Earth EPS 122: Lecture 20 – Convection Density and elastic moduli Density from the Adams-Williamson equation then EPS 122: Lecture 20 – Convection 5 Mantle convection? What is mantle convection? Why do we believe there is convection in the mantle? EPS 122: Lecture 20 – Convection Convection In a fluid: • Occurs when density distribution deviates from equilibrium • Fluid may then flow to achieve equilibrium again In a viscous solid heated from below: • Initially heat is transported by conduction into the fluid at the base • Increased temperature reduces the density making the material at the base less dense than fluid above • Once the buoyancy force due to the density contrast overcomes the inertia of the fluid convection begins EPS 122: Lecture 20 – Convection 6 Rayleigh-Benard convection Newtonian viscous fluid: stress = dynamic viscosity x strain rate As fluid at the base As heating proceeds, a Continued heating heats up, initial second set of rolls forms – hexagonal pattern convection is in 2D perpendicular to the first rolls – bimodal Then a spoke pattern, and finally an irregular pattern forms as vigorous convection takes place (not shown) EPS 122: Lecture 20 – Convection Rayleigh number Non-dimensional number which describes the nature of heat transfer g - gravity - density - thermal expansion coefficient T - temperature variation a - length scale: thickness of fluid layer c – conductive time constant - thermal diffusivity – advective time constant a - viscosity The critical Rayleigh number: • the point at which convection initiates • approximately 103 (dependent on geometry) • By knowing the material properties and physical geometry we can determine if there will be convection and the nature of that convection EPS 122: Lecture 20 – Convection 7 Rayleigh number and convective mode Convection plan view Rayleigh number of the mantle: 106 Upper mantle (thickness 700 km): 106 105 Lower mantle (thickness 2000 km): 3x107 104 Whole mantle Rayleigh number (thickness 2700 km): 108 103 EPS 122: Lecture 20 – Convection Simple convection models the effect of heating • Heat from below • T fixed on upper boundary aspect ration of 1 …not what we see on Earth • Heat from below • Constant heat flow across upper boundary large aspect ratio • Internal heating only no upwelling sheets EPS 122: Lecture 20 – Convection 8 Simple convection models the effect of heating • Isotopic ratios of oceanic basalts are very uniform but different from bulk earth values the mantle is well mixed any body smaller than 1000 km is reduced to less than 1 cm thick in 825 Ma! EPS 122: Lecture 20 – Convection The many views of the mantle increasing lower mantle viscosity Constant viscosity incompressible mantle Factor of 30 internally heated difference short wavelength, flow dominated by sheets that extend through numerous the mantle …more Earth like downwellings Compressible Heating from fluid the core short hot wavelength upwellings again dominate Bunge models EPS 122: Lecture 20 – Convection 9 The many views of the mantle Phase changes at 400 and 660 avalanches km of material into lower increasing mantle Rayleigh number mantle becomes stratified Yuen EPS 122: Lecture 20 – Convection What about the plates? One layer or two? Subduction ? Downwelling Ridges ? Upwelling EPS 122: Lecture 20 – Convection 10 Downwelling = subduction Low temperature high density slabs observed extending through the entire mantle EPS 122: Lecture 20 – Convection Subduction and mantle convection Farallon slab • Originates from a time when there was subduction all along the western US. • We find evidence of this slab extending all the way to the core-mantle boundary EPS 122: Lecture 20 – Convection 11 Subduction Western pacific Some evidence for slab penetration into the lower mantle Kuril slab Japan trench Izu slab EPS 122: Lecture 20 – Convection Lau Basin Subduction Lau Basin Observations: • High velocity slab, low velocity wedge • Earthquakes in slab and rift • Large number of compressional 3D viewing available at earthquakes above 660 km http://ldorman.home.mindspring.com/VRC/VRmjl.html EPS 122: Lecture 20 – Convection 12 Lower mantle subduction Two slabs do extend into the lower mantle • Farallon and Tethys EPS 122: Lecture 20 – Convection Modes of mantle convection Subduction ? Downwelling …Yes • Slabs clearly represent the downwelling mode in the upper mantle • Some slabs pass through the transition zone into the lower mantle …and upwelling? EPS 122: Lecture 20 – Convection 13 .
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