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
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