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

...

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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