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Geodynamics Plate-driving forces Lecture 10.4 - Plate driving forces; Slab pull I Lecturer: David Whipp [email protected] Geodynamics www.helsinki.fi/yliopisto 1 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 2 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 3 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 4 Slab (or trench) pull FSP Forsyth and Uyeda, 1975 • Slab pull results from the gravitational body force acting on the dense, sinking oceanic lithosphere. • 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 5 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 6 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 7 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 8 Let’s see what you’ve learned… • If you’re watching this lecture in Moodle, you will now be automatically directed to the quiz! • 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 9