1. velocity on a sphere 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) Rp  V

2. 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

3. 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

4. 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: A v pb =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

5. Know lat (λ) and long (Φ) of point Want to get x, y, z coordinates Mauritania X-> 0° longitude y-> 90° East longitude z-> north pole

6. Now we have the coordinates of p Can get velocity Mauritania Which gives us velocity in x,y,z space But, want local geographic coord.

7. Mauritania But, want local geographic coord. (N-S, E-W, up-down)

8. Mauritania Now have velocity in terms of North, East, and up-down Ex: A v pb =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

9. 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

10. Today’s lab plate_vel.m will be a function The first line of your code will declare that you plate_vel is a function Function vl=plate_vel(lat, lon, latp, lonp, omega) So, once you have written and saved the function, you can go to the command line and and get the velocity of a point on the Pacific plate (at lat=37° and long=-123°) relative to North America

11. 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 is the N-S E-W And up-down Components of the velocity