EAS-450 – Physics and Chemistry of the Earth

Lab exercise – Current plate motions

Objective: Manipulate relative plate motions.

The horizontal velocity of any site on a plate is perpendicular to the small circle centered on the pole of rotation that describe the motion of that plate. The rate depends on the location of the sites with respect to the pole: it increases with distance from the pole.

Let’s assume a rotation pole P located at latitude p, longitude p and an angular velocity  around that pole. We are looking for the velocity v (rate) and its azimuth  with respect to north at a site X located at latitude x, longitude x:

The magnitude of the velocity at X is given by:

With R = 6371000m (Earth radius) and a = 90 -x.

The azimuth of the velocity at X is:

We need to find a and C. To do so, let’s look at the [NXP] spherical triangle. The angular lengths of its sides are a, b, c. The angular lengths b and c are known, they are the colatitude of X and P:

For the same reason, angle A is known:

Angles B anc C, as well as angular distance a are unknown.

The cosine and sine rules of triangles apply to spherical triangles, giving:

and

By subsitution:

and

WARNING: the inverse sine funtion above is doubled value: always check that you have the correct value for C.

Example:

Nazca-South America pole at 56.0N / 94.0W, angular velocity 7.6x10-7 degrees/year.

For a site located at 28S / 71W on the Peru-Chile trench, the equations above give:

a = 86.26 degrees

C = -12.65 degrees

v = 8.43 cm/yr

 = 77.35 degrees.

Assignment:

  1. Program the above equations in Excel, verify that your program works by using the example above.
  2. Identify the plates on the map below (plate boundaries are drawn as thick grey lines). Write their name on the map.
  3. Add symbols or colors to the plate boundaries to indicate whether they are ridges, trenches, or transforms.
  4. Given the following rotation parameters:

Plates / Latitude
(deg.) / Longitude
(deg.) / Ang. Velocity
(10-7 deg/yr)
Eurasia – North America / 62.4N / 135.8W / 2.2
Eurasia – Pacific / 61.1N / 85.8W / 9.0
Pacific – Australia / 60.1S / 178.3W / 11.2
North America – Pacific / 48.7N / 78.2W / 7.8
  1. Calculate the velocity at Honolulu with respect to (1) Eurasia, (2) North America, (3) Australia.
  2. Plot the 3 vectors at Honolulu on the map below.
  3. Calculate the velocity at 25 sites along the subduction zones on the figure below (you chose them).
  4. Draw a symbol on the map at each of the sites you choose, chose an identifier for each site, and write it by the symbol. Plot the velocity as a vector at each of the sites that you have chosen. Turn in the map below and a table with the velocity magnitude and azimuth for each site.
  5. Based on your results and additional information you may know or find, write a short comment for each of the subduction plate boundaries.