Download PLATE MOTIONS: BASIC CONCEPTS

PLATE MOTIONS: BASIC CONCEPTS
North
American
plate
20 mm/yr
Eurasian
plate
Pacific
plate
35 mm/yr
North
American
plate
Iceland Spreading
Center, Thingvellir
San Andreas Transform Fault
Carrizo Plain
BASIC CONCEPTS: RIGID PLATES
Earth's outer shell made up of ~15 major rigid plates ~ 100 km thick
Plates move relative to each other at speeds of a few cm/ yr (about
the speed at which fingernails grow)
Plates are rigid in the sense that little (ideally no) deformation occurs
within them,
Most (ideally all) deformation occurs at their boundaries, giving rise to
earthquakes, mountain building, volcanism, and other spectacular
phenomena.
Style of boundary and intraplate deformation depends on direction &
rate of motion, together with thermo-mechanical structure
In most places
we know general
plate boundary
geometry from
geology,
topography, and
earthquakes
PLATE BOUNDARIES: GENERALLY BUT
NOT FULLY KNOWN
Ideal plate
boundaries very
narrow
Many real plate
boundaries especially
continental - are
deformation
zones up to 1000
km wide, with
motion spread
beyond nominal
boundary
Gordon & Stein, 1992
In some places: Indian Ocean. Mediterranean, NW
Asia, etc. we’re still trying to figure out plate geometry
NW ASIA
Not clear where
North America
boundary is
May be Okhotsk
plate distinct
from North
America
May be Amuria
plate east of
Baikal rift
distinct from
Eurasia
May be North
China plate
Wei and Seno, 1988
?
?
?
?
?
?
EULER VECTOR
Relative motion between two rigid plates on the spherical earth can be
described as a rotation about an Euler pole
At a point r along the boundary
between two plates, with latitude
λ and longitude µ, the linear
velocity of plate j with respect to
plate i , v ji , is given by the
vector cross product
Linear velocity
v ji = ωj i x r
r is the position vector to the
point on the boundary
r
ωj i is the angular velocity vector
or Euler vector described by its
magnitude (rotation rate) |ωj i |
and pole (surface position) (θ, φ)
Stein & Wysession, 2003
Direction of relative motion is a small circle
about the Euler pole
First plate ( j) moves counterclockwise ( right
handed sense) about pole with respect to
second plate (i).
ω21
2 wrt 1
Boundary segments with relative motion
parallel to the boundary are transforms, small
circles about the pole
Segments with relative motion away from the
boundary are spreading centers
Segments with relative motion toward
boundary are subduction zones
ω12
1 wrt 2
Magnitude (rate) of relative motion increases
with distance from pole because
|v ji | = |ωj i | | r | sin γ , where γ is the angle
between pole and site
All points on a boundary have the same
angular velocity, but the magnitude of linear
velocity varies from zero at the pole to a
maximum 90º away.
Stein & Wysession, 2003
GPS DATA RIGID
NORTH AMERICAN
PLATE ROTATING
ABOUT EULER
POLE
Direction follow
small circles
Rates increase
as sine of
angular distance
from pole
Velocities differ
from these in
nonrigid
boundary zone
Stein & Sella, 2002
CARTESIAN COMPONENTS OF ANGULAR VELOCITY ω
AND LINEAR VELOCITY v
At a point r on the
plate boundary, with
latitude λ and
longitude µ, linear
relative velocity v , is
given by the vector
cross product
v =ω x r
r is the position
vector to the point on
the boundary
ω is the angular
velocity or Euler
vector described by
its magnitude
(rotation rate) |ω |
and pole (surface
position) (θ, φ)
LINEAR VELOCITY TYPICALLY DONE AS EITHER
NS, EW COMPONENTS OR RATE & AZIMUTH
Scalar (dot)
product with
unit vectors
in NS & EW
directions
Gives
NS & EW
components
of linear
velocity
And hence
rate and
azimuth
BOUNDARY TYPE
CHANGES WITH
ORIENTATION
CONVERGENCE ALEUTIAN TRENCH
54 mm/yr
PACIFIC NORTH AMERICA
STRIKE SLIP SAN ANDREAS
PACIFIC wrt
NORTH
AMERICA
pole
EXTENSION GULF OF CALIFORNIA
Stein & Wysession, 2003
BOUNDARY TYPE CHANGES WITH ORIENTATION
EURASIA - NUBIA (west Africa)
NORTH
AMERICA
EXTENSION
TERCEIRA
RIFT
EURASIA
STRIKE-SLIP
GLORIA
TRANSFORM
OBLIQUE CONVERGENCE
NORTH AFRICA
NUBIA
SMALL CIRCLE ABOUT POLE
NUVEL-1
Argus et al., 1989
+ EURASIA wrt NUBIA POLE
FINDING EULER VECTORS
Until recently, done by combining different types of
data from different boundaries
Spreading rates from sea-floor magnetic anomalies
Directions of motion from orientations of transform faults and slip
vectors of earthquakes on transforms and subduction zones
Problems with resulting geologic plate motion models:
No way to measure rates at subduction boundaries
Data average over different time scales:
-magnetic anomalies typically 3 Myr
-transform azimuths millions of years
-slip vectors seconds
Data only at plate boundaries
Inversion assumes rigid plates
SPREADING RATES
FROM MAGNETIC
ANOMALIES
ANOMALY:
2’
2
Match observed
profiles to synthetics
for different spreading
rates
Time resolution limited
by magnetic reversal
history
NUVEL-1 uses anomaly
2’ (3 ma) and so
averages over that time
Can’t go finer than
central anomaly
corresponding to last
reversal (780 ka)
DeMets et al., 1987
GULF OF CALIFORNIA
PACIFIC - NORTH AMERICA
CENTRAL
TRANSFORM FAULT AZIMUTH FROM BATHYMETRY AND
STRIKE-SLIP EARTHQUAKE FOCAL MECHANISMS
Measure
azimuth from
bathymetry
PACIFIC
Highresolution
(Seabeam,
Gloria) is best
Averages over
millions of
years
Earthquake
mechanisms
also used, less
precise
ANTARCTIC
Stein & Wysession, 2003
NORTH AMERICA
CONVERGENCE ALEUTIAN TRENCH
54 mm/yr
SUBDUCTION
AZIMUTH FROM
TRENCH THRUST
FAULT
MECHANISM SLIP
VECTORS
PACIFIC
Common problem: for oblique (not trench
normal) convergence
Fault plane
Forearc sliver moves distinctly from both
plates
Slip vectors record motion of sliver relative
to oceanic plate, not major plate motion
Stein & Wysession, 2003
FINDING EULER POLE FROM RELATIVE MOTION DATA
Geometric
conditions:
Slip vectors and
transform faults
lie on small circles
about the pole, so
pole lies on a great
circle at right angles
to them
Rate of plate motion
increases with sine
of distance from
pole
Cox & Hart, 1986
INVERSE PROBLEM - FIND EULER VECTORS FROM DATA
POSE INVERSE
PROBLEM FIND EULER
VECTORS
FROM DATA
Set up model
vector m (Euler
vectors)
and data vector d
(observed rates
and azimuths)
Form partial
derivative matrix G
LEAST SQUARES
SOLUTION TO
INVERSE
PROBLEM
Find change in
model vector ∆m
from starting model
(Euler vectors)
using partial
derivative matrix G
to minimize
misfit ∆d to data
vector (observed
rates and azimuths)
Pre-NUVEL models assumed
single Indo-Australian plate
Deformation in Central Indian
Ocean shown by large
earthquakes & folding
New model: distinct Indian and
Australian plates separated by a
diffuse boundary zone perhaps
formed by Himalayan uplift
New model better fits focal
mechanisms & magnetics
Improved fit statistically significant,
so two plates resolved
Subsequent studies refined model
and show that India and Australia
have been distinct for at least 3
Myr and likely longer.
Wiens et al., 1985
IMPROVED PLATE
GEOMETRY: DISTRICT INDIA
& AUSTRALIA
SUCCESSIVE MODELS FIT USE MORE DATA & FIT BETTER
DeMets et al., 1990
More data
Smaller misfit
NUVEL-1A GLOBAL RELATIVE PLATE MOTION MODEL
Plate motions averaged over past 3 Ma
Demets, Gordon, Argus & Stein, 1994
EULER VECTOR OPERATIONS
To reverse sense of motion, use negative (same rate and with antipole:
negative latitude, longitude +180°)
ωjk = -ω kj
We assume that plates are rigid, so all motion occurs at their
boundaries. We can then add Euler vectors
ω jk = ω ji + ω ik
because the motion of plate j with respect to plate k equals the sum
of the motion of plate j with respect to plate I and the motion of plate i
with respect to plate k
Thus from a set of vectors with respect to one plate, e.g. i
ωjk = ω ji - ω ki
we form any Euler vector needed.
Operations easily done using Cartesian components
DIFFERENT TYPES OF EULER VECTORS
GLOBAL EULER VECTOR - derived using all data from all plate
boundaries, assumes all plates are rigid.
BEST FITTING VECTOR - for a plate pair using only data from that
pair of plates' boundary
CLOSURE FITTING VECTOR - using only data from the other plates’
boundaries
Ideally, if the plates were rigid and data perfect:
- all three vectors would be the same.
-for three plates meeting at a triple junction, the best fitting vectors for
each of the three plate pairs would sum to zero.
These provide tests for plate rigidity
SPACE GEODESY & GEOLOGIC
PLATE MOTION MODELS
GENERALLY AGREE
Plate motions over a few years
observed by space geodesy very
similar to predictions of NUVEL-1
or similar geologic models
describing average motions over
past 3 Ma
Hence plate motions are
generally steady, presumably
because viscous asthenosphere
damps episodic motions at plate
boundaries
However, in places NUVEL-1
and space geodesy disagree.
Why?
Robbins et al., 1993
GLOBAL PLATE CIRCUIT CLOSURE
Because we only have certain types of data for some boundaries, others
are inferred by vector summation assuming rigid plates. In particular,
convergence rates at subduction zones are estimated by global closure,
combining data from all plate boundaries.
Predicted rate at
which the Cocos
plate subducts
beneath North
America depends on
measured rates of
Pacific-North
America spreading in
the Gulf of California
and Cocos-Pacific
spreading on the
East Pacific Rise.
DeMets et al., 1990
SOME BOUNDARIES - NO DIRECT DATA
In some cases, such as relative motion between North and South America,
no direct data were used because the boundary location and geometry are
unclear, so the relative motion is inferred entirely from closure
Motion is poorly
known
EU
NA
NB
SA
Wysession et al., 1995
Motions of plate pairs based on both rate
and azimuth data are best known
AT TRIPLE JUNCTIONS,
WHERE THREE PLATES
MEET, ADD LINEAR
VELOCITY VECTORS
Direction & rate of Juan de Fuca plate
subduction beneath North America found
by combining:
Direction & rate of Juan de Fuca-Pacific
spreading at Juan de Fuca ridge
Direction & rate of North America-Pacific
motion from Gulf of California and San
Andreas (transform) fault
Plate motion showed subduction, despite
no trench or thrust fault earthquakes
CASCADE VOLCANOES
INDICATE JUAN DE FUCA
SUBDUCTION BENEATH
NORTH AMERICA
Mt Saint Helens
1980 eruption
USGS
EURASIA - NUBIA (West Africa) motion
Primarily derived from small differences in spreading
rate & direction between North America - Eurasia and
North America - Nubia motion at Mid-Atlantic Ridge
NORTH
AMERICA
EURASIA
Eurasia - Nubia
spreading at
Azores Triple
junction
NUBIA
Argus et al., 1989
Relative motions between plates are most important
In some applications important to consider absolute
plate motions, those with respect to the deep mantle
In general both plates and plate boundaries move
with respect to the deep mantle
For example, assume Africa were not moving with
respect to the deep mantle. If so, as lithosphere is
added by spreading at the Mid-Atlantic ridge, both
the ridge and South America move westward
relative to the mantle.
Conversely, as the African plate lost area by
subduction beneath Eurasia in the Mediterranean,
the trench "rolls backwards”, moving south relative
to the mantle.
Increasingly, it seems that such motions may have
significant tectonic consequences
No direct way to measure absolute motions, need to
infer indirectly
ABSOLUTE
PLATE MOTIONS
NNR - NO NET
ROTATION
ABSOLUTE
MOTIONS
NNR reference frame obtained assuming no net rotation of the lithosphere
as a whole, so sum of the absolute motion of all plates weighted by their
area is zero
NNR reference frame similar to hotspot frame
Despite unresolved questions about the nature and existence of hot spots
and plumes, NNR reference frames often used to infer absolute motions
ABSOLUTE MOTION CALCULATION
To compute absolute motions, recognize that motions in an absolute
reference frame correspond to adding a rotation to all plates
Use Euler vector formulation and treat absolute reference frame as
mathematically equivalent to another plate
For example, given NNR Euler vector relative to North America ωNNRNA its negative ω NA-NNR is the absolute Euler vector ΩNA for North
America in NUVEL-NNR reference frame
Hence absolute and relative motions related by
ωij = ΩI - Ωj
and linear velocity in absolute reference frame at point r on
plate i is
Vi = Ωi x r
RIDGES TYPICALLY MIGRATE WITH RESPECT TO THE
MANTLE
May have effects on topography, spreading process,
magma chemistry
Stein et al, 1977
Hot spot hypothesis assumes certain
linear volcanic trends result from plate
motion over a hot spot, fixed source of
volcanism, causing melting in the
overriding plate.
If the overriding plate is oceanic, get
progression from active volcanism that
builds islands, to older islands, to
underwater seamounts as sea floor
moves away from hot spot, cools, and
subsides. Get topographic swell around
hotspot and volcanic age progression
away from it.
Direction and age of volcanic chain give
motion of plate with respect to hot spot.
Hot spot tracks beneath different plates
and assuming hot spots fixed with
respect to deep mantle (or move relative
to each other more slowly than plates),
yields hot spot reference frame.
ABSOLUTE MOTION
FROM HOT SPOTS
Often assumed hot
spots result from
plumes of hot material
rising from great
depth, perhaps coremantle boundary
Plumes would be
secondary convection
mode, ~ 5% of heat
transfer, bringing up
deep mantle material.
Would be important in
Earth’s thermal &
chemical evolution.
Would have tectonic
significance - heads
of new plume might
cause continental
breakup and flood
basalts
HOTSPOT / PLUME HYPOTHESIS
HOTSPOT / PLUME CONTROVERSY
Concepts of hot spots and plumes are attractive and widely used, but the
relation between the persistent volcanism and possible deep mantle plumes is
under active investigation because of many deviations from what would be
expected:
Some hot spots move significantly
Some chains show no clear age progression
Oceanic heat flow data show little or no thermal anomalies at the swells
Seismological studies find low-velocity anomalies, but assessing their depth
extent and relation to possible plumes is difficult and controversial
Convection models of plumes rising from core-mantle boundary may not
correctly include pressure effects
HOTSPOT TYPES:
MIDPLATE CONTINENTAL (Yellowstone,…)
MIDPLATE OCEANIC (Hawaii, Bermuda,…)
ON OR NEAR RIDGE (Iceland, Azores, Easter…)
YELLOWSTONE NATIONAL PARK, WYOMING USA
Type example of continental hot spot?
AGE PROGRESSIVE VOLCANISM
Trend consistent with absolute motion of North America
Stein & Wysession, 2003
COMPLEXITY: additional
volcanic progression to
west - Newberry
volcanics
Proposed alternative:
forced mantle flow and
decompression melting
resulting from local plate
motions. Near subduction
zone upper mantle forced to
flow northwest because of
corner flow driven by
subducting plate. Yellowstone
and Newberry magmatism
follow these trends as fertile
mantle flows past residuum
and ascends (red-to-white
arrows).
Humphreys et al., 2000
MIDPLATE OCEANIC
HOTSPOT: HAWAIIAN
EMPEROR CHAIN
Bend in the Hawaiian-Emperor
chain interpreted as indicating
Pacific plate changed direction
about 43 Ma, leaving bend as
plate moved over fixed hotspot
now under Hawaii
Mauna Loa
PROBLEM 1:
THE 43 Ma
“NONEVENT”
No evidence for
change in
relative plate
motions at 43
Ma, since
fracture zone
orientations
unaffected
PROBLEM 2:
HAWAIIAN
HOTSPOT
HAS NOT
BEEN FIXED
Fixed hotspot
would cause all
seamounts to
have same
paleolatitude
Hawaiian hotspot
actually drifted
southward
between 47 and
81 Ma
Tarduno and Cottrell
(1997)
SUMMARY
Absolute motions can be defined relative to either No Net
Rotation or Hotspot reference frames
GPS data given in ITRF, designed to be like NUVEL-NNR
Absolute motions may have roles in tectonics but details
unclear
Hotspot/plume model has major problems and may need to
be discarded, but it’s not clear what the alternatives are