Chris Goldfinger

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Chris Goldfinger Burt 282 7-5214 gold_at_coas.ore
gonstate.edu
OCE 661 Plate Tectonics
Suggested supplemental reading Cox and Hart p.
60-84 Paper copy in Burt 284
Course notes at activetectonics.coas.oregonstate.
edu
Course notes modified in part after notes
developed by D. Muller, University of Sydney
School of Geosciences, Division of Geology and
Geophysics, Sydney Australia
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Plate Tectonic Concepts 1) The active mobile
belts on the surface of the earth are
not isolated but continuous 2) These belts are
marked by active earthquakes and separate
the earth into a set of rigid plates 3) The
seismic belts consist of ridges where plate is
created trenches where plate is destroyed
transform faults, which connect the other two
belts to each other There are three types of
plate boundaries Divergent boundaries -- where
new crust is generated as the plates pull away
from each other. Convergent boundaries -- where
crust is destroyed as one plate dives under
another. Transform boundaries -- where crust is
neither produced nor destroyed as the plates
slide horizontally past each other.
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Plate Properties (1) Continuity of plate
boundaries Plate boundaries are outlined by
active Earthquake epicenters. Morgan (1968)
separated the world into 10 plates. Today, we
know that the actual number of plates is much
larger. All major plates are surrounded by
spreading centers, subduction zones, and
transform faults. (2) Rigidity The concept of
internal rigidity of tectonic plates together
with Euler's Theorem allows us to model the
relative motion of plates quantitatively. (3)Rela
tive motion All plates can be viewed as rigid
caps on the surface of a sphere.
Spreading rates are a key bit of information
critical to understanding plate motions and
creating reconstructions. They are usually
symmetric, but not always
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Relative Plate motions

• some examples of actual values of relative plate
  motion

• some inconsistencies caused by plate-margin
  deformation
• some edges are accommodating the movement
  (India-Asia), SW USA, Philippine Sea
• changes in relative motion over time imply shift
  in Euler Poles.

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h
Flat Earth Plate Geometry Simple vector addition
can be used to approximate motion of plates on a
sphere for a local area. Spherical trig
solutions are needed for global solutions.
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The east African Rift is part of a RRR triple
junction
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The motion of a plate can be described by a
rotation about a virtual axis which passes
through the center of the sphere (Euler's
Theorem). In terms of the Earth this implies
that motions of plates on a sphere can be
described by an angular velocity vector
originating at the center of the globe. The most
widespread parameterization of such a vector is
using latitude, longitude, describing the
location where the rotation axis cuts the surface
of the Earth, and a rotation rate that
corresponds to the magnitude of the angular
velocity (degrees per m.y. or microradians per
year). The latitude and longitude of the angular
velocity vector are called the Euler
pole. Because angular velocities behave as
vectors, the motion of a plate can be expressed
as a rotation w w k, where w is the angular
velocity, k is a unit vector along the rotation
axis, w the rotation rate. The motion of
individual plates can be described by an absolute
motion angular velocity. The motion between two
plates, which have different absolute motion
poles, can be expressed by an angular velocity of
relative motion. Plate tectonic theory
was developed by determining relative motion
between plates, which - in general - is easier to
measure than their absolute motions.
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w angular velocity, also called Euler vector w
rotation rate at point on sphere, measured in
radians/year (rad/yr) r vector pointing to a
position on sphere. The magnitude of this vector
corresponds to the radius of the sphere, measured
in meters (m). v linear velocity vector at r v
speed at r, measured in millimeters/year
(mm/yr). The rotation of a plate can be
represented as angular velocity w about a fixed
axis originating at the center of the sphere. The
Euler pole is the intersection of the Euler
vector w and the surface of the sphere.
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The following figure illustrates how the rotation
speed increases from the pole of rotation, and
that transform faults offsetting both ridges and
trenches are small circles about the rotation
pole. The first figure shows a counterclockwise
rotation of plate B relative to plate A,
separated by a ridge, whereas the figure on the
right shows a counterclockwise rotation,
separated by a subduction zone. Notice the
difference in the sense of the rotation.
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Approximating a pole of rotation using ridge and
transform orientation
The relative motion of two plates sharing a
mid-ocean ridge is assumed to be parallel to the
transform faults, because the arcs of the faults
are expected to be small circles. (What if this
is not the case, is this possible?) This would
imply that the rotation pole must lie somewhere
on the great circle perpendicular to the small
circles defined by the transform faults. Hence,
if two or more transform faults between a plate
pair are used, the intersection of the great
circles approximates the position of the rotation
pole.
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Stage rotations Finite rotation poles, but
based on the assumption that an instantaneous
rotation can be extrapolated to a finite
time. They approximate the plate motion during
a geological stage, and are computed by adding
two (total) finite rotations to each other, one
with its sign reversed.
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Stage poles represent extensions of the concept
of instantaneous rotation poles to the
geological past. Since we cannot measure real
instantaneous plate rotations for the past, we
make the assumption that a particular
instantaneous pole of motion has been constant
for a geological stage. Instantaneous
rotations Describe rotations for an infinitely
small period of time, i.e. present day plate
motions (angular velocity vectors). Finite
rotations Describe rotations for a finite time
interval in the geological past (total)
finite rotations reconstruct a plate from its
present day position to a past position.
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Equivalent rotation No matter what set of
rotations are applied to a rigid body one single
equivalent rotation can restore the body to its
original position. gt True both on a plane and on
a sphere. After applying a complex set of
rotations to a pair of plates, a single rotation
can be found that will restore the original
position of the plates.
Finite rotations not stationary with time
Consider three plates, and three rotation poles
that describe their relative motion to each
other, i.e. AWB, BWC, and CWA. If AWB and BWC
are fixed in space and time, then CWA will change
continuously through time. gt As there is no
reason to assume that any set of finite rotation
poles are stationary, then all must be moving.
However, it is found in the real world that
some rotation poles seem to vary very little in
position even over long periods of time.
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FINITE ROTATIONS THEORY OF FINITE
ROTATIONS Non-commutativity of finite plate
rotations Finite rotations are
non-commutative. Rotations are mathematically
described by matrix transformations and are
sensitive to the order in which the
transformations are carried out. Unlike in the
case of vectors, if A, B are matrices, then AB ¹
BA. This can be shown easily by rotating a book
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Summary (1) All transform faults are small
circles about the pole of rotation representing
the motion between the two plates. (2) The
velocity of separation of two plates increases
as the sine of the colatitude away from the
rotation pole. (3) At a triple junction the
velocity vectors sum to zero. (4) Taking any
path over the surface of the earth beginning and
ending on the same plate, the angular velocity
vectors sum to zero. 5) The above leads directly
to Global plate circuits such as Minster and
Jordan, 1978, and the NUVEL-1 model.
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Marine gravity anomalies from satellite
altimetry Satellite radar altimetry has
revolutionized our knowledge of the topography of
oceanic basement, and helped greatly to construct
better plate tectonic models through geologic
time. Radar altimetry works by measuring the
distance between the satellite and the sea
surface by radar (below). These data are used to
provide a geoid map. The geoid is an
equipotential field.
From these geoid anomalies we can derive
anomalies in the gravity field. Gravity anomalies
are deviations of the gravity field of that
caused by the best ellipsoid approximation of the
Earth (i.e. the Earths shape can roughly be
described by an ellipsoid, but not quite there
are many deviations. Short wavelength marine
gravity anomalies are mostly caused by oceanic
basement topography, such as fracture zones,
seamounts, ridges and trenches (see figure below).
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EXPLORING THE OCEAN BASINS WITH SATELLITE
ALTIMETER DATA David T. Sandwell - Scripps
Institution of Oceanography - sandwell_at_geosat.ucsd
.eduandWalter H. F. Smith - Geosciences
Laboratory, NOAA - walter_at_amos.grdl.noaa.gov
According to the laws of physics, the surface of
the ocean is an "equipotential surface" of the
earth's gravity field. (Lets ignore waves, winds,
tides and currents for the moment.) Basically
this means that if one could place balls
everywhere on the surface of the ocean, none of
the balls would roll down hill because they are
all on the same "level". To a first
approximation, this equipotential surface of the
earth is a sphere. However because the earth is
rotating, the equipotential ocean surface is more
nearly matched by an ellipsoid of revolution
where the polar diameter is 43 km less than the
equatorial diameter. While this ellipsoidal shape
fits the earth remarkably well, the actual ocean
surface deviates by up to 100 meters from this
ideal ellipsoid. These bumps and dips in the
ocean surface are caused by minute variations in
the earth's gravitational field. For example the
extra gravitational attraction due to a massive
mountain on the ocean floor attracts water toward
it causing a local bump in the ocean surface a
typical undersea volcano is 2000 m tall and has a
radius of about 20 km. This bump cannot be seen
with the naked eye because the slope of the ocean
surface is very low.
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These tiny bumps and dips in the geoid height can
be measured using a very accurate radar mounted
on a satellite (Figure). For example, the Geosat
satellite was launched by the US Navy in 1985 to
map the geoid height at a horizontal resolution
of 10-15 km (6 - 10 mi) and a vertical resolution
of 0.03 m (1 in). Geosat was placed in a nearly
polar orbit to obtain high latitude coverage (-
72 deg latitude). The Geosat altimeter orbits the
earth 14.3 times per day resulting in an ocean
track speed of about 7 km per second (4 mi/sec).
The earth rotates beneath the fixed plane of the
satellite orbit, so over a period of 1.5 years,
the satellite maps the topography of the surface
of the earth with an ground track spacing of
about 6 km (4 mi).
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The point of all this is to reconstruct past
plate motions, and to predict current and future
motions
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The point of all this is to reconstruct past
plate motions, and to predict current and future
motions