# Geodynamics Lecture 2 Kinematics of plate tectonics

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1 Geodynamics Lecture 2 Kinematics of plate tectonics Lecturer: David Whipp david.whipp@helsinki.fi! Geodynamics 1

2 Goals of this lecture Present the three types of plate boundaries and their geodynamic importance! Establish a kinematic framework for describing plate motions! Discuss plate margin triple junctions! Learn the basic concepts of plate motions on a sphere 2

3 Plate boundaries Three different principal types of plate boundaries Divergent (accreting) Convergent (subduction) Transform 3

4 Plate boundaries - Divergent (accreting) Fig. 1.4, Turcotte and Schubert, 2014 Plate boundary where new plates form and with divergent motion Thermal buoyancy produces topographic highs near spreading ridges, which decrease away from the ridge Typical spreading rates: 4 cm per year 4

5 Plate boundaries - Divergent (accreting) Plate accretion occurs via decompression melting, where the nearly isothermal asthenosphere ascends beneath a spreading center and crosses the solidus for the basaltic component Fig. 1.5, Turcotte and Schubert, 2014 Assume a simple linear solidus T (K) = p (in MPa) where T(K) is the temperature in Kelvins and p is pressure in MPa If we assume the density of the rising asthenosphere is ρ = 3300 kg m -3, g = 10 m s -2 and constant temperature, at what depth y does the asthenosphere begin to melt? Note: Pressure p = ρgy. 5

6 Plate boundaries - Divergent (accreting) Plate accretion occurs via decompression melting, where the nearly isothermal asthenosphere ascends beneath a spreading center and crosses the solidus for the basaltic component Fig. 1.5, Turcotte and Schubert, 2014 Assume a simple linear solidus T (K) = p where T(K) is the temperature in Kelvins and p is pressure in MPa If we assume the density of the rising asthenosphere is ρ = 3300 kg m -3, g = 10 m s -2 and constant temperature, at what depth y does the asthenosphere begin to melt? Note: Pressure p = ρgy. 6

7 Plate boundaries - Divergent (accreting) Plate accretion occurs via decompression melting, where the nearly isothermal asthenosphere ascends beneath a spreading center and crosses the solidus for the basaltic component Fig. 1.5, Turcotte and Schubert, 2014 Assume a simple linear solidus T (K) = p where T(K) is the temperature in Kelvins and p is pressure in MPa If we assume the density of the rising asthenosphere is ρ = 3300 kg m -3, g = 10 m s -2 and constant temperature of 1600 K, at what depth y does the asthenosphere begin to melt? Note: Pressure p = ρgy. 7

8 Plate boundaries - Divergent (accreting) F RP F RP Fig. 1.4, Turcotte and Schubert, 2014 Divergent plate movement here is a form of gravitational sliding driven in part by the ridge push force FRP owing to the high elevations of the ridge relative to the majority of the oceanic plate 8

9 Age of the oceanic crust 9

10 Plate boundaries - Convergent (subduction) Fig. 1.7, Turcotte and Schubert, 2014 Plate boundary where the sense of motion is convergent Subduction destroys oceanic lithosphere, recycling it within the Earth Geometry varies, but most have a trench, accretionary sedimentary prism, volcanic line (or arc) 10

11 Plate boundaries - Convergent (subduction) Fig. 1.7, Turcotte and Schubert, 2014 Why does the plate subduct? 11

12 Plate boundaries - Convergent (subduction) Fig. 1.7, Turcotte and Schubert, 2014 Why does the plate subduct? As the lithosphere cools and contracts, its density increases, eventually exceeding that of the underlying asthenosphere F SP This results in a gravitational instability where the oceanic plate wants to sink into the underlying asthenosphere As it sinks, plate motion is driven in part by the dense sinking end of the plate pulling it along via the slab pull force FSP 12

13 Plate boundaries - Convergent (subduction) The geometry of subducting plates is quite variable, but typical subduction angles are ~45! If gravity drives subduction, why don t slabs subduct with 90 dips? Fig. 1.9, Turcotte and Schubert,

14 Plate boundaries - Convergent (subduction) The geometry of subducting plates is quite variable, but typical subduction angles are ~45! If gravity drives subduction, why don t slabs subduct with 90 dips? Fig. 1.9, Turcotte and Schubert,

15 Induced mantle flow and back-arc spreading Mantle corner flow Slab roll-back Fig. 1.11, Turcotte and Schubert, 2014 Subduction induces flows in the mantle that may control the slab dip angle These flows may also produce enigmatic back-arc spreading. Why is there extension at a convergent plate margin? 15

16 Plate boundaries - Transform Map view Cross sectional view Fig. 1.12, Turcotte and Schubert, 2014 This is the most common form of transform fault, between two spreading ridge segments 16

17 Plate boundaries - Transform Map view Cross sectional view Fig. 1.12, Turcotte and Schubert, 2014 This is the most common form of transform fault, between two spreading ridge segments - What is the slip rate on the transform fault above? 17

18 Plate boundaries - Transform Wilson, 1965 Six types of dextral transform fault predicted by Wilson 18

19 The Wilson cycle In 1966, Wilson proposed the opening and closing of ocean basins is cyclic! A simple case is outlined here, with initial rifting of a continent and formation of a spreading center Fig. 1.42, Turcotte and Schubert,

20 The Wilson cycle Continued extension leads to formation of an ocean basin Fig. 1.42, Turcotte and Schubert,

21 The Wilson cycle As the seafloor ages and density increases and eventually the margin founders, initiating subduction Fig. 1.42, Turcotte and Schubert,

22 The Wilson cycle The ridge may eventually be subducted, drawing the two continental margins together into eventual collision Fig. 1.42, Turcotte and Schubert,

23 The Wilson cycle Fig. 1.42, Turcotte and Schubert,

24 Goals of this lecture Present the three types of plate boundaries and their geodynamic importance! Establish a kinematic framework for describing plate motions! Discuss plate margin triple junctions! Learn the basic concepts of plate motions on a sphere 24

25 Relative plate motions on a flat Earth vab 8 For a pair of plates (A and B), the relative velocity will be the vector that indicates the relative rate of movement Plate A Plate B vba The velocity of plate A with respect to an observer on plate B is vab, and the opposite is true for an observer on plate A. Thus, vab = -vba or vab + vba = 0 Note that for spreading ridges, velocities are typically given relative to the spreading center After Fowler,

26 Relative plate motions on a flat Earth vab For a pair of plates (A and B), the relative velocity will be the vector that indicates the relative rate of movement 8 Plate A Plate B 6 6 vab vba 6 6 vba The velocity of plate A with respect to an observer on plate B is vab, and the opposite is true for an observer on plate A. Thus, vab = -vba or vab + vba = 0 Plate A Plate B Note that for spreading ridges, velocities are typically given relative to the spreading center After Fowler,

27 Triple junctions A ridge-ridge-ridge (RRR) triple junction Fig. 1.36, Turcotte and Schubert, 2014 Plate boundaries can only end in a triple junction, where they intersect another boundary Triple junctions are typically listed in shorthand based on the types of plate boundaries involved in the triple junction: R = ridge, T = trench (subduction), F = transform fault RRR = ridge-ridge-ridge triple junction 27

28 Triple junctions For spreading ridges, we can assume spreading is perpendicular to the ridge axis For plates A and B, this means spreading at an azimuth of 90 Up to 10 types of triple junctions are possible, but some of those cannot exist (e.g., FFF) Fig. 1.36, Turcotte and Schubert, 2014 For a triple junction to exist, the vectors of relative motion must form a closed triangle In other words, vba + vcb + vac = 0 28

29 Triple junctions Let s consider an example based on the RRR triple junction Assume we know vba = 100 mm yr -1 and vcb = 80 mm yr-1! Using the geometry and spreading rates of two of the ridges, we can find the orientation and spreading rate of the third since vba + vcb + vac = 0 Fig. 1.36, Turcotte and Schubert,

30 Triple junctions Let s consider an example based on the RRR triple junction Assume we know vba = 100 mm yr -1 and vcb = 80 mm yr-1! Using the geometry and spreading rates of two of the ridges, we can find the orientation and spreading rate of the third since vba + vcb + vac = 0 Fig. 1.36, Turcotte and Schubert,

31 Triple junctions We can find vac using the law of cosines: c 2 = a 2 + b 2-2abcosα Thus, vac = (vba 2 + vcb 2-2 vba vcb cos 70 ) 1/2 vac = ~105 mm yr -1 We can find the orientation of vac using the law of sines: sin = sin = sin a b c or more simply, a b = sin sin Thus, α =??? v CB v AC = sin ( 180 ) sin 70 Fig. 1.36, Turcotte and Schubert,

32 Triple junctions We can find vac using the law of cosines: c 2 = a 2 + b 2-2abcosα Thus, vac = (vba 2 + vcb 2-2 vba vcb cos 70 ) 1/2 vac = ~105 mm yr -1 We can find the orientation of vac using the law of sines: sin = sin = sin a b c a or more simply, b = sin sin Thus, α = ~230 v CB v AC = sin ( 180 ) sin 70 Fig. 1.36, Turcotte and Schubert,

33 But the Earth is not flat The Earth is not a perfect sphere, but it is close! Thus, distances between points on the surface and the displacement of plates on the surface are best described as distances or displacements on a sphere using spherical coordinates! Fig. 1.33, Turcotte and Schubert, 2014 For any relative plate motion, the displacement can be described using Euler s theorem and selecting a suitable pole of rotation P with an angular velocity ω 33

34 But the Earth is not flat The relative plate motion of any two plates is completely described by the latitude and longitude of P and the angular velocity ω Transform faults can be used to find the location of P and ω can be determined from seafloor magnetic lineaments Fig. 1.33, Turcotte and Schubert, 2014 The relative velocity v between two plates is given by v = ωa sin Δ where a is the radius of the Earth and Δ is the angle between the pole of rotation P and the position along the plate boundary A taken at the center of the Earth 34

35 But the Earth is not flat The relative plate motion of any two plates is completely described by the latitude and longitude of P and the angular velocity ω Transform faults can be used to find the location of P and ω can be determined from seafloor magnetic lineaments Fig. 1.34, Turcotte and Schubert, 2014 The relative velocity v between two plates is given by v = ωa sin Δ where a is the radius of the Earth and Δ is the angle between the pole of rotation P and the position along the plate boundary A taken at the center of the Earth 35

36 But the Earth is not flat Fig. 1.35, Turcotte and Schubert, 2014 The angle Δ can be found using the to the colatitude θ and east longitude ψ of the pole of rotation P and the colatitude θ and east longitude ψ of the point along the plate margin A cos = cos cos 0 +sin sin 0 cos ( Note that the colatitude is 90 minus the latitude of the point of interest Also, the surface distance s between points A and P is simply s = aδ 36 0 )

37 Recap Three types of plate boundaries define the margins of the tectonic plates and how they interact Plate motions on a flat Earth can easily be described using vector addition with an accompanying vector diagram Triple junctions are where three plates meet and plate relative motions and displacement directions can be found using vector diagrams Relative motion of plates of a sphere is more complicated, but it can be described using rotation poles and spherical geometry 37

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