Upper Mantle Viscous Drag on the Lithosphere David Terrell Warner Pacific College March 2006.
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Transcript of Upper Mantle Viscous Drag on the Lithosphere David Terrell Warner Pacific College March 2006.
Upper Mantle Viscous Drag on Upper Mantle Viscous Drag on the Lithosphere the Lithosphere
David Terrell
Warner Pacific College
March 2006
Historical BackgroundHistorical Background
Continental Drift.Ocean Floor SpreadingPlate Tectonics.
1957/8 international Geophysical year.
1961-8 papers on world seismology and paleo-magnetism
Vine 1966 Science “Spreading of the Ocean Floor”
Isaks, Oliver, and Sykes 1968 J. G. R. “Seismology and the New Global Tectonics.”
Seismic Analysis/GeomorphologySeismic Analysis/Geomorphology
Isostacy – (explains mountain gravity anomalies)
Global earthquake distribution – Follows definite patterns
Earthquake Depth – Relative to some continental margins
SubductionSubduction
Locality/Depth of Earthquakes.
VolcanismVolcanism
Friction/Phase change
Ocean Floor SpreadingOcean Floor Spreading
Ocean Floor Magnetic Anomalies
Earth’s configurationEarth’s configuration
Lithosphere (0 – 100 km)– Crust
Asthenosphere (Soft) Mantle (100 – 2890 km)– Upper– Lower
Nucleus/Core (2890 – 5378 km)– Outer– Inner
...
**
Layer boundariesLayer boundaries
Mohorovicic discontinuity– Physical – chemical changes– About 5 km under mid-oceanic ridges– About 75 km under continents
Gutenberg discontinuity– Between silicate mantle/iron nickel core
Lehman discontinuity– Between “liquid” outer and “solid” inner core
Mantle ConvectionMantle Convection
Mantle ConvectionMantle Convection
Internally Generated Heat Asymmetric Equations of Fluid-Dynamics– Mass conservation– Continuity
Normal ConvectionNormal Convection
Thermal ConvectionThermal Convection
Symmetric
Asymmetric
FOR MORE INFO...
Butler and Peltier 2002 J.G.R. Thermal Evolution of The Earth: Models with time-dependent layering of mantle convection which satisfy the Urey ratio constraint.
www.gps.caltech.edu/~gurnis/Movies/movies-more.html
Internally Heated ConvectionInternally Heated Convection
Upper mantle convectionUpper mantle convection
Heat generated during accretionHeat generated by Radioactivity– 40K– U– Th– Others now in smaller amounts• (Rb, Sm, etc.)
Stress-Strain Stress-Strain
Mantle deformation– Fluid dynamics– Elastic modulus
FOR MORE INFO...
Non-linear rheology:
http://www.geo.ucalgary.ca/~wu/Goph681/Rheology.pdf
Equations of MotionEquations of Motion
Fluid Dynamics Equations that govern motionEquation of mass conservation 0 u
dvt
dsii
is density; i is normal unitary vector defining integration surface; and vi is 1st order tensor defining velocity
Equation of continuity
Mass conservation
http://www.navier-stokes.net/nsfield.htm
Heat EquationHeat Equation
HTkTut
Tcp
2)(
)](1[ 00 TT Cp is the heat capacity and
is the expansion coefficient
Rayleigh’s numberRayleigh’s number
3Tg
R
Convection occurs if R > 1100 - 1700
StressStress
A first approximation:
z
vi
Density ρ is about 3.4x103 kg/m3 and viscosity ν is about 1024 poises (1 poise = 10-1 Pa·s)
Accumulated stressAccumulated stress
Using estimated values for heat generated and the current estimates for the movement of some plates– Say speeds of ~2-3 cm/y
Values for accumulated stress in about 200 Ma of about 300-400 bars can be calculated
These values are well below values calculated for isostacy in some places but big enough to break a thin (<10 km) crust.
Current StatusCurrent Status
Even though this is an old problem new computing (modeling) technologies as well as experimental data have opened this area to new research.
Thanks so much for listening!Thanks so much for listening!
Some useful web sites:www.warnerpacific.edu/personal/dterrell http://anquetil.colorado.edu/VE/convecti
on2.shtmlhttp://www.gps.caltech.edu/~gurnis/Movi
es/movies-more.html
http://www.mantleplumes.org/Convection.html