Download Slab pull I

Geodynamics
Plate-driving forces
Lecture 10.4 - Plate driving forces; Slab pull I
Lecturer: David Whipp
[email protected]
Geodynamics
www.helsinki.fi/yliopisto
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Goals of this lecture
•
Introduce the main forces driving tectonic plate motions
•
Review the part of the slab pull force owing to the slab being
colder than the surrounding mantle
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What drives tectonic plate motions?
The driving forces of plate motion
Forsyth and Uyeda, 1975
Resisting forces
FDF = Drag force
FDF = Drag force
FSP = Slab pull
FTF = Transform resistance
FCD = Continental drag
FCR = Colliding resistance
165
Driving forces
Downloaded from http://gji.oxfordjournals.org/ at Dalhousie University on September 1, 2013
FRP = Ridge push
FSR = Slab resistance
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What drives tectonic plate motions?
The driving forces of plate motion
Forsyth and Uyeda, 1975
Resisting forces
FDF = Drag force
FDF = Drag force
FSP = Slab pull
FTF = Transform resistance
FCD = Continental drag
FCR = Colliding resistance
165
Driving forces
Downloaded from http://gji.oxfordjournals.org/ at Dalhousie University on September 1, 2013
FRP = Ridge push
FSR = Slab resistance
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Slab (or trench) pull
FSP
Forsyth and Uyeda, 1975
•
Slab pull results from the gravitational body force acting on the dense, sinking
oceanic lithosphere.
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It can be divided into two components:
Downloaded from http://gji.oxfordjournals.org/ at Dalhousie University on September 1, 2013
•
•
•
Fb1, the force resulting from the slab being colder than the surrounding mantle
Fb2, the force resulting from the elevation of the olivine→spinel phase change
Mathematically, we can say
FSP = Fb1 + Fb2
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Slab (or trench) pull
FSP
•
Forsyth and Uyeda, 1975
For one half of a sinking mantle plume, Turcotte and Schubert show
✓
◆1/2
u0

Fb = 2⇢0 g↵v b(Tc T0 )
v0 2⇡u0
Downloaded from http://gji.oxfordjournals.org/ at Dalhousie University on September 1, 2013
•
We can simplify this relationship slightly for a sinking slab to estimate the slab
pull force resulting from the relatively cold temperature of the slab
𝜌0 Reference mantle density
𝑇0 Temperature at LAB
𝑔 Gravitational acceleration
𝑢0 Horiz. velocity of upper layer
𝛼𝑣 Coeff. of thermal expansion
𝑣0 Average vertical velocity
𝑏
𝜅 Thermal diffusivity
Convecting layer thickness
𝑇𝑐 Temperature at conv. center
𝜆 Width of 2 convection cells
LAB = Lithosphere-asthenosphere boundary
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Slab (or trench) pull
FSP
Forsyth and Uyeda, 1975
6.21 A Steady-State Boundary-Layer Theory
509
Downloaded from http://gji.oxfordjournals.org/ at Dalhousie University on September 1, 2013
•
•
Here is the simplified
convection cell geometry
used for calculating the
force acting on a sinking
mantle plume
Note that areas in each
triangle are equal, so mass is
Fig. 6.41, Turcotte and Schubert, 2014
conserved, or
1 Linear velocity profiles used to model the core flow in a conv0
l. The areas under the triangles are equal to conserve fluid.
= u0 b
2
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Slab (or trench) pull
FSP
Forsyth and Uyeda, 1975
•
Because a sinking slab is rigid, we can assume that 𝑢0 = 𝑣0, so the force
resulting from the slab being colder than the surrounding mantle is
✓
◆1/2

Fb1 = 2⇢0 g↵v b(Tc T0 )
2⇡u0
•
If we use typical values for these variables, we see that 𝐹𝑏1 is ~3×1013 N m-1
Downloaded from http://gji.oxfordjournals.org/ at Dalhousie University on September 1, 2013
•
To be clear, this value is the force per meter of trench length
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Let’s see what you’ve learned…
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If you’re watching this lecture in Moodle, you will now be
automatically directed to the quiz!
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Reference(s):
Forsyth, D., & Uyeda, S. (1975). On the Relative Importance of the Driving Forces of Plate Motion*.
Geophysical Journal International, 43(1), 163–200. doi:10.1111/j.1365-246X.1975.tb00631.x
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