Download Kinematics of Plate Tectonics

Geodynamics
Lecture 2
Kinematics of plate tectonics
Lecturer: David Whipp
[email protected]
!
4.9.2013
Geodynamics
www.helsinki.fi/yliopisto
1
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
Plate boundaries
•
Three different principal types of plate boundaries
•
•
•
Divergent (accreting)
Convergent (subduction)
Transform
3
Plate boundaries - Divergent (accreting)
Fig. 1.4, Turcotte and Schubert, 2014
•
•
Plate boundary where new plates form and with divergent motion
•
Typical spreading rates: 4 cm per year
Thermal buoyancy produces topographic highs near spreading ridges, which
decrease away from the ridge
4
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
•
Assume a simple linear solidus
T (K) = 1500 + 0.12p (in MPa)
Fig. 1.5, Turcotte and Schubert, 2014
•
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
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
•
Assume a simple linear solidus
T (K) = 1500 + 0.12p
Fig. 1.5, Turcotte and Schubert, 2014
•
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
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
•
Assume a simple linear solidus
T (K) = 1500 + 0.12p
Fig. 1.5, Turcotte and Schubert, 2014
•
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
Plate boundaries - Divergent (accreting)
FRP
FRP
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
Age of the oceanic crust
9
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
Plate boundaries - Convergent (subduction)
Fig. 1.7, Turcotte and Schubert, 2014
•
Why does the plate subduct?
11
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
FSP
•
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
12
pulling it along via the slab pull force 𝐹SP
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, 2014
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, 2014
14
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
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
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
Plate boundaries - Transform
Wilson, 1965
•
Six types of dextral transform fault predicted by Wilson
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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, 2014
19
The Wilson cycle
•
Continued extension leads to
formation of an ocean basin
Fig. 1.42, Turcotte and Schubert, 2014
20
The Wilson cycle
•
As the seafloor ages and density
increases and eventually the margin
founders, initiating subduction
Fig. 1.42, Turcotte and Schubert, 2014
21
The Wilson cycle
•
The ridge may eventually be
subducted, drawing the two
continental margins together into
eventual collision
Fig. 1.42, Turcotte and Schubert, 2014
22
The Wilson cycle
Fig. 1.42, Turcotte and Schubert, 2014
23
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
Relative plate motions on a flat Earth
8
4
4
•
For a pair of plates (A and B), the relative
velocity will be the vector that indicates the
relative rate of movement
•
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
8
Plate A
Plate B
𝑣BA
𝑣AB = -𝑣BA or
𝑣AB + 𝑣BA = 0
•
After Fowler, 2005
Note that for spreading ridges, velocities are
typically given relative to the spreading center
25
Relative plate motions on a flat Earth
8
4
4
•
For a pair of plates (A and B), the relative
velocity will be the vector that indicates the
relative rate of movement
•
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
8
Plate A
𝑣BA
Plate B
6
Plate A
6
Plate B
After Fowler, 2005
𝑣AB 6
𝑣AB = -𝑣BA or
𝑣AB + 𝑣BA = 0
6 𝑣BA
•
Note that for spreading ridges, velocities are
typically given relative to the spreading center
26
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
Triple junctions
•
For spreading ridges, we can assume spreading is
perpendicular to the ridge axis
•
Fig. 1.36, Turcotte and Schubert, 2014
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)
•
For a triple junction to exist, the vectors of
relative motion must form a closed triangle
•
In other words,
𝑣BA + 𝑣CB + 𝑣AC = 0
28
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
!
•
Fig. 1.36, Turcotte and Schubert, 2014
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
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
!
•
Fig. 1.36, Turcotte and Schubert, 2014
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
30
Triple junctions
•
We can find 𝑣AC using the law of cosines:
𝑐2 = 𝑎2 + 𝑏2 - 2𝑎𝑏cos𝛼
•
•
•
Thus, 𝑣AC = (𝑣BA2 + 𝑣CB2 - 2 𝑣BA 𝑣CB cos 70°)1/2
𝑣AC = ~105 mm yr-1
We can find the orientation of 𝑣AC using the law of
sin
sin
sines: sin ↵
=
=
a
b
c
•
•
Fig. 1.36, Turcotte and Schubert, 2014
or more simply, a = sin ↵
b
sin
vCB
sin (↵ 180 )
=
Thus, v
sin 70
AC
𝛼 = ???
31
Triple junctions
•
We can find 𝑣AC using the law of cosines:
𝑐2 = 𝑎2 + 𝑏2 - 2𝑎𝑏cos𝛼
•
•
•
•
•
Fig. 1.36, Turcotte and Schubert, 2014
Thus, 𝑣AC = (𝑣BA2 + 𝑣CB2 - 2 𝑣BA 𝑣CB cos 70°)1/2
𝑣AC = ~105 mm yr-1
We can find the orientation of 𝑣AC using the law of
sin
sin
sines: sin ↵
=
=
a
b
c
a
sin ↵
or more simply, =
b
sin
vCB
sin (↵ 180 )
=
Thus, v
sin 70
AC
𝛼 = ~230°
32
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
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
•
•
Fig. 1.33, Turcotte and Schubert, 2014
Transform faults can be used to find the
location of 𝑃 and 𝜔 can be determined
from seafloor magnetic lineaments
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
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
•
•
Fig. 1.34, Turcotte and Schubert, 2014
Transform faults can be used to find the
location of 𝑃 and 𝜔 can be determined
from seafloor magnetic lineaments
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
But the Earth is not flat
•
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 (
0
•
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
Fig. 1.35, Turcotte and Schubert, 2014
36
)
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