velocity on a sphere
V
Rp

Velocity depends on
-how fast it is spinning, 
-distance from rotation axis Rp
(where R is the radius of the Earth, and p is the location of the point)
The North American plate is rotating about the blue triangle
Velocity at a point depends on
-how fast it is spinning, 
-distance from the point to the rotation axis R
We’ll be finding relative velocities of a point
on one plate with respect to another plate
Ex: What is the velocity of Mauritania relative
to the NA plate?
Mauritania
What is the velocity of Mauritania relative to the
NA plate? Table 1 gives us the plate rotation vectors (the
angular velocity and the lat long of the Euler pole)
We want velocities in terms of N-S, E-W,
up-down: Ex: Avpb=0.5 cm/yr north + 2.0 cm/yr east
need to do some conversions:
Know lat (λ) and long (Φ) of point Want to get x, y, z
coord.
Mauritania
Know lat (λ) and long (Φ) of point
Want to get x, y, z coordinates
z-> north pole
y-> 90° East longitude
X-> 0° longitude
Mauritania
Now we have the coordinates of p
Can get velocity
Which gives us velocity in x,y,z space
But, want local geographic coord.
Mauritania
But, want local geographic coord.
(N-S, E-W, up-down)
Mauritania
Now have velocity in terms of North,
East, and up-down
Ex:Avpb=0.5 cm/yr north + 2.0 cm/yr east
Can also determine magnitude and
direction of relative velocity Ex. 45 mm/yr
102° SE
Mauritania
Today’s lab
• Functions vs scripts
• Today you’ll be making functions- a
function is slightly fancier than a script.
• A function can be run from the command
line, with input and output variables
• Today you will be writing a function to
compute the relative velocity of a point on
one plate with respect to another plate
Today’s lab
• plate_vel.m will be a function
• The first line of your code will declare that
plate_vel is a function
•
Function vl=plate_vel(lat, lon, latp, lonp, omega)
– v1 will be the output (the velocity of the point)
– (lat, lon, latp, lonp, omega) will be the input (the location of the
point, location of the euler pole, and the rotational velocity
• So, once you have written and saved the
function, you can go to the command line
and and get the velocity of a point relative
to another plate
Today’s lab
• To find the velocity of a point on the Pacific
plate (at lat=37° and long=-123°) relative to
North America by look up the rotation vector
in table 1 (48.7, -78.2, 0.78) and type
•
Vl=plate_vel(37, -123, 48.7, -78.2, 0.78)
– Matlab will return
Which are the
N-S
E-W
up-down
Components of the
velocity
Note error in table:
• Nazca-Pacific… longitude of Euler pole is 90.1 E