Plates II: Dynamics
(Finite Plate Rotations)
ƒ Before considering plate dynamics, consider
finite plate rotations … needed when you
actually want to reconstruct where plates were,
or will be, in the future.
ƒ Unlike instantaneous plate motions (triple
junctions, etc.) finite rotations are not vectors,
but act like tensors.
ƒ See Finite Rotation handout at class website:
http://www.geo.arizona.edu/geo5xx/geo519.071/lectures/
Outline:
ƒ Plates have negligible momentum.
ƒ Some consequences of negligible
momentum.
ƒ Candidates for driving mechanism.
ƒ Evidence for driving mechanism models.
Plate Momentum
ƒ As shown in “Plate Momentum” handout, plates
have negligible momentum.
ƒ Consequences:
ƒ Observation: plates move with constant speed for
long periods of time, but are capable of sudden
changes.
ƒ … Forces must be very well balanced!
ƒ It is very likely that some force(s) are velocity
dependent.
ƒ Driving Mechanism must include driving AND
resisting forces.
Plate Motion Constancy/Change
ƒ Pacific plate has moved to NW over
hotspot for last 40-45 Myr, but went N
before that.
Driving Mechanism Candidates
ƒ Outside Forces (Coriolis, tides, etc.)
ƒ Convection cells driving from below
ƒ Slab Pull
ƒ Ridge Push
ƒ Trench ‘Suction’
ƒ In addition to ‘driving’ forces, must specify
resisting forces (otherwise plates
accelerate quickly!)
A Digression on Convection I …
ƒ We need to be clear what we mean by
convection as a driving mechanism.
ƒ There is zero doubt that the mantle
convects (material ‘added’ at subduction
zone has to get to a ridge somewhere).
ƒ Are the plates part of the convection???
ƒ For our purposes, ‘convection,’ as far as
moving plates, refers to drag exerted on
the base of the plates due to mantle flow
beneath the plates moving faster than the
plate.
Outside Forces …
ƒ Coriolis and tidal forces are small
compared to all other candidates.
ƒ They are large enough to potentially be
important from momentum arguments, but
too small to account for the work done by
plate tectonics (energy released by
earthquakes, volcanoes).
ƒ Hence, they are considered too small.
Slab Pull Force FS
ƒ Slab is ~500oC
FS
φ = ~45o
Δρ = ~ 50 kg/m3
F = l g L Δρ
= 100km * 10m/s2
* 1000km * 50 kg/m3
= 5 x 1013 kg/s2
= 5 x 1013 N/m of slab
FH = F * sin (φ) = FS … or
FS = 3 x 1013 N/m
Δρ
L
l
cooler, hence more
dense, than
surrounding mantle
ƒ Total force, F, acts
downward
ƒ FS is the horizontal
force, per unit length
of slab, capable of
pulling plate toward
trench
See T&S, Eqn 6-392, p281, for an alternative approach, leading to 4.9 x 1013 N/m
See also http://www.sciencemag.org/cgi/content/full/298/5591/207 for more.
Ridge Push Force FR
Ridge
L = ~ 1000km
Δρ
Old sea
floor
h
l
φ
F = l g L Δρ
= 100km * 10m/s2
* 1000km * 1000 kg/m3
= ~1015 kg/s2
= ~1015 N/m of ridge
FH = F * sin (φ) = FR … or
FR = 3 x 1012 N/m
FR
ƒ Ridge sits about
h = 3km above
old sea floor
ƒ Δρ ~ 1000kg/m3
ƒ Ridge push is
an order of
magnitude
smaller than
slab pull
See T&S, Eqn 5-171, p224 for an alternative approach, leading to 3.4 x 1012 N/m
Driving Drag Force FD
ƒ If the mantle is
Lithosphere
Velocity V
Viscosity μ
h
Shear stress τ ~ μV
h
If V ~10 cm/yr, μ ~ 1019 Pa-s,
and h ~ 300 km, then
τ ~ 105 Pa = 0.1 MPa
convecting faster than
the plates, you may
apply a shear stress τ on
the base of the plate.
ƒ If plates have an average
dimension of 5000 km,
then τ is equivalent to
FD = 5 x 103 km * 105 Pa
= 5 x 1011 N/m
Trench Suction FSU
ƒ Origin of force
FSU
acting on the
overriding plate,
toward trench,
is poorly known,
but may be due
to ‘wedge’ flow
or roll back of
trench as slab
falls into mantle.
See http://virtualexplorer.com.au/journal/2001/03/mantovani/paper2.html
for more discussion
Resisting Forces????
ƒ For Slab, there
may be resistance
on the sides, and
especially the
bottom, of the slab.
ƒ Also, interface with
overriding plate.
ƒ Slab resistance
may depend on
velocity.
Resisting Forces, Con’t
ƒ If plate is moving
Lithosphere
Velocity V
Viscosity μ
h
Shear stress τ ~ μV
h
If V ~10 cm/yr, μ ~ 1019 Pa-s,
and h ~ 300 km, then
τ ~ 105 Pa = 0.1 MPa
faster than mantle,
drag force will resist
plate motion
ƒ Drag could be
concentrated
beneath continents
(increased viscosity
or a continental
‘keel’).
Resisting Forces, Con’t
Ridge
ƒ There could be
resistance to plate
motion at transform
faults due to friction
across the plate
boundary.
Transform
Fault
Ridge
Resisting Forces, Con’t
ƒ Continental Collisions can resist further
plate motion:
ƒ As continents converge and the crust is
thickened and uplifted, it gains gravitational
potential energy.
ƒ This excess gravitational potential energy
‘pushes back’ on lower regions.
(See, for example, Coblentz et al., J Geophys. Res.,
103, 919-931, 1998.)
Observations …
1. Plates with a lot of attached slab tend to
move faster.
2. Plates with a lot of continent tend to
move slower.
3. There is no correlation between plate
size and plate velocity.
4. No correlation between amount of
transform fault and plate speed.
Observations, Con’t
Ridge
ƒ Heat flow (measure
Transform
Fault
Ridge
of friction) is low
over San Andreas
fault … friction is
low.
ƒ … Transform friction
is probably small.
Observations, Con’t
5. Plate boundaries move with respect to
each other at plate speeds.
• This
kind of picture is
very common. But, slab
to W of South America
and Mid-Atlantic ridge
are separating at rate
South American plate is
being created.
• It is not possible to
keep convection limbs
underneath plate
boundaries for long!
A Digression on Convection II…
ƒ The form of convection in the mantle is
poorly known, although getting better with
seismic tomography.
ƒ Some argue for separate convection in the
upper (above ~670km) and lower mantle.
ƒ In lab/computer, convection tends to be
equidimensional (roughly ‘circular’).
ƒ Plates are of vary variable dimensions.
Observations, Con’t
ƒ Driving Drag should be proportional to
plate area. No correlation between plate
area and plate velocity.
ƒ Two fastest moving plates are Pacific
(largest) and Cocos (one of smallest).
Pacific Plate
Aspect ratio for Pacific is at least
5 times larger than for Cocos …
Cocos
Consequences of Forces?
ƒ Forces lead to stress in the plates.
ƒ Observed stresses in plate may help
distinguish between force models.
ƒ Predictions:
ƒ If Slab Pull dominates, and resistance is
distributed, expect surface plates in tension.
ƒ If Ridge Push dominates, and resistance is
distributed, expect surface plates in
compression.
Stress Predictions, Con’t
ƒ If Driving Drag dominates, expect stress to
grow more compressional in direction of
plate motion …
τ
If uniform τ = 0.1 MPa applied along 5000 km long,
100 km thick plate free on right hand side (RHS) and
fixed on left hand side (LHS), compressional stress in
plate grows from zero on RHS to 50 MPa on LHS.
World Stress Map
http://www-wsm.physik.unikarlsruhe.de/pub/introduction/introduction_frame.html
ƒ
ƒ
ƒ
ƒ
Arrows show direction of maximum horizontal compression
Blue = thrust; Green = strike slip, Red = normal, Black = unknown.
Red dominates near ridges, on continents (esp high topography).
Oceans complicated, but away from ridge, mostly strike slip and
compressional.
North American Stress Data
ƒ NE-SW
compression
for most of
NAM except
far west.
ƒ Except far
west, most
everything
either thrust
or strike slip.
South American Stress Data
ƒ Mostly
compression
except in high
topography
(above 3km).
ƒ Directions
complicated, but a
lot of EW.
India/Australia Stress Data
ƒ Compression
direction goes
from NS in India
to EW in
Australia.
ƒ Compression is
parallel to
subduction in
Indonesia
ƒ Very little
extension (some
behind Philippine
arc (See Pacanovsky
et al., J. Geophys. Res.,
104, 1095-1110, 1999.)
Summary of Stress Data
ƒ Away from ridges and high topography, stress
field is dominated by compression and strike
slip.
ƒ Stress orientations show a lot of scatter, but also
patterns on a plate-wide scale (e.g., North
America, South America, India/Australia).
ƒ No evidence for lots of tension toward
subduction zone or increase in stress in
direction of plate motion.
Seismic Tomography
ƒ As we will see later in the semester,
seismic tomography useful in locating fast
(cold) and slow (warm) regions.
ƒ Slow (warm) regions below ridges are
shallow (< 200km).
ƒ Slabs are long-lived, and sometimes
penetrate 670 km ‘boundary.’
Putting it All Together …
ƒ Largest density contrasts are in the plates
(e.g., in the slabs and mid-ocean ridges).
ƒ Mantle convection is complicated, but
feeding of ridges is shallow … no big cell
beneath the ridge.
ƒ Mantle convection hard to appeal to for
rapid changes in plate motions (e.g.,
Hawaii-Emperor bend).
Putting it All Together, con’t …
ƒ Slab ‘pull’ is big, but lack of extension in
oceans says that balancing force is local
(trench and below) and surface plates
don’t see the pull!
ƒ Plates well modeled with compression
from mid-ocean ridges.
ƒ Trench Suction may play a role locally
(e.g., Philippian Sea)
Putting it All Together, con’t …
ƒ Resistance may be best modeled as
velocity-dependent drag between moving
plate and underlying (passive) mantle.
ƒ This velocity dependence may explain why
plates move with constant speed for 10’s
of millions of years.
ƒ Plates able to change velocity suddenly
when boundaries change (ridge subducts,
continental collision).
Putting it All Together, con’t …
ƒ Bottom line, plates determine where plates
go.
ƒ Slabs, ridges both important because
slabs have both a large pull and a large
local resistance, the sum of which is small.
ƒ And if you don’t believe me, go talk to the
half of the world that doesn’t agree with
me!