Download ESS 211 Physical Processes of the Earth

ESS 211 Physical Processes of the Earth
Plate Tectonics - lab / homework exercises on plate kinematics
The theory of Plate Tectonics is primarily concerned with plate kinematics, describing the
past and present-day motions of plates. As we saw in the previous lab, the relative directions of
motion at plate boundaries help explain all kinds of important geological processes – volcanism,
the type, depth and magnitude of earthquakes, the location of mountain belts, and so on. Today’s
lab will teach you how to describe and calculate plate velocities.
First, a word about frames of reference. We generally define plate velocities relative to one
another, considering one of the plates fixed. For example, if you live in San Francisco, it would
make sense to think of the North American plate as fixed and view the Pacific Plate as sliding
past you in a northwesterly direction at 4.8 cm/yr. So when calculating a plate velocity, be sure
to state your frame of reference. (Note: You may recall that the tracks left by sliding over deepseated hotspots, such as the Hawaiian-Emperor seamount chain, map out the motion of plates
relative to the deep mantle. In theory this allows us to define a reference frame fixed to the
mantle beneath the plates. However, not all plates have detectable hotspot tracks, they can be
difficult to define in continental regions, they are not as continuous or extend as far back in time
as the magnetic “striping” of the seafloor, and we’re not sure whether hotspots actually remain
fixed within the mantle. For these reasons, plate motions are defined relative to one another).
Defining plate motion
The movement of spherical plates across the surface of a globe is a bit more difficult to describe
than the translation or rotation of flat plates on a plane. To cut a long story short …
The relative motion of any two
spherical plates is completely
described by rotation about a
pole. The "pole of rotation", or
“Euler pole” is an imaginary axis
passing through the center of the
Earth around which the plates
rotate. The angular velocity ω of
plate motion is measured in
radians per year. ω can
describe either separation
(spreading) or convergence. The
velocity of plate motion that an
observer measures on the Earth' s
surface (e.g. with GPS
instruments on the two plates)
depends on ω and the observer’s
distance from the pole of
rotation.
In the diagram above, the arrows showing spreading motion on the plate boundary should get
smaller and smaller the closer you get to the pole of rotation (you can write to Encyclopedia
Britannica and point out the error).
This diagram shows it a bit
more schematically, and
gives you the formula for
how to calculate the
spreading velocity:
v = ω R sin δ
where R is the radius of the
Earth (6370 km) and δ is the
angular distance from the
pole of rotation.
The maximum velocity is ω R at a point on the surface 90° around from the pole of rotation.
This may be hard to visualize in the abstract, so take a look at the pictures below showing the
Mid-Atlantic Ridge. The ridge is a divergent boundary which separates the Eurasian and African
plates from the North and South American plates. You may prefer to locate it in Google Earth
First, consider the North American and
Eurasian plates, which are moving away
from each other with an angular velocity:
ω = 3.73 x 10-9 radians/year
The pole of rotation between these plates
is located at latitude 62.4 N, longitude
135.8 E.
Suppose we want to calculate the spreading velocity and direction of motion between the plates
on the Mid-Atlantic Ridge, at latitude 52.8 N, longitude 35.2 W?
Let’s do this first problem step by step …
(i) Go to Google Earth and confirm that our observation point lies on the Mid-Atlantic Ridge.
To determine the plate velocity, we need the angle δ between the pole of rotation and our
observation point, where we want to measure the spreading rate. This is given by a nasty piece
of spherical trigonometry. But before we get to that, we need to define our co-ordinates:
You are familiar with everyday {latitude, longitude} co-ordinates, but these are cumbersome to
use in plate tectonic calculations. Instead we use the pair {co-latitude, east longitude}.
Co-latitude, which we will denote θ, is the polar angle of a point on a sphere. Co-latitude is
measured from the north polar axis rather than from the equator, and varies from zero to 180°.
Clearly, the co-latitude of a point with latitude Λ is given by:
θ = 90 – Λ
where south latitudes are given negative values.
Instead of using positive and negative values for east and west longitudes, we define east
longitude, φ, in degrees east of the Prime Meridian. φ ranges from zero to 360°.
Now back to the spherical trigonometry ….
If the {co-latitude, east longitude} co-ordinates of the rotation pole are {θP, φP}, and those of the
observation point are {θX, φX}, the angle δ between them is given by :
cos δ = cos θX cos θP + sin θX sin θP cos (φP – φX)
The diagram at right
may help to keep this
all straight.
(ii) Now fill in the tables and equations below:
Latitude
Longitude
Co-latitude
East longitude
Pole of rotation (P)
62.4 N
135.8 E
θP =
φP =
Point of observation (X)
52.8 N
35.2 W
θX =
φX =
cos δ =
cos θX
cos θP
=
+
sin θX
sin θP
cos (φP – φX)
+
=
So …angle δ =
And the spreading rate
=
ω R sin δ
= 3.73 x 10-9 x 6370 km x sin δ
=
km/yr
=
cm/yr
(iii) What about the direction of motion? To determine this we use another equation from
spherical trigonometry. Referring to the diagram above, we can calculate the angle p …
sin(# P $ # X )
sin p
=
sin " P
sin %
So p =
degrees.
!
This is the direction from the point of observation to the rotation pole. The spreading direction is
perpendicular to this, and Eurasia is moving east relative to North America, so
Spreading direction = 90° + p =
degrees.
(iv) Now go back our observation point in Google Earth. How does your calculated spreading
direction align with features on the floor of the North Atlantic Ocean? You can use the ruler tool
in Google Earth to measure bearings.
(v) How well does your calculated spreading rate predict the age of the seafloor either side of
the North Atlantic Ridge?
Download the map of seafloor ages that we used in Lab 1 from the class website
(http://faculty.washington.edu/kate1/ESS_211/Lab_files/Seafloor_age.kmz). You’ll also need a
key to identify the ages: (http://hess.ess.washington.edu/www/earth/Seafloor_age_legend.kml).
Double-click to open both these files in Google Earth. You can display or hide the colored bands
representing specific seafloor ages by checking or unchecking the boxes in the key.
Use the ruler tool in Google Earth to measure the separation between North America and Eurasia
over the last 5 Myr. How does this compare to the predicted separation based on your calculated
velocity. Be sure to measure in the direction of plate motion, and make your measurements a
little to the north of the transform fault, where the pattern is simple.
Use the same procedure to fill in the table:
Spreading since …
5 Myr
10 Myr
20 Myr
40 Myr
60 Myr
Predicted separation (km)
Measured separation (km)
(vi) Check your work … Doing this by hand is a lot of work. Fortunately there are now quite a
few plate motion calculators on the Web. For example, go to:
http://ofgs.ori.u-tokyo.ac.jp/~okino/platecalc_new.html
Set Eurasia as the moving plate and North America as the fixed plate. Select the NUVEL-1A
plate velocity model (more recent and a little more accurate than the NUVEL-1 model). Note
that this calculator takes standard latitude, longitude co-ordinates.
How does the result compare to your calculation?
(vii) While we’re here …. one last exercise.
Use the calculator to determine the speed and direction of the Pacific plate relative to fixed North
America on the San Andreas fault north of San Francisco. Use co-ordinates 38.1° N, 122.85° W
for the point of observation.
Go to this location (east of Point Reyes) in Google Earth. Can you find evidence of the fault in
the landscape? How does the direction of plate motion compare to the features you’ve
identified?