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 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

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 are the N-S E-W up-down Components of the velocity

12. Note error in table: Nazca-Pacific… longitude of Euler pole is - 90.1 E