velocity on a sphere

Velocity depends on -how fast it is spinning, ω-distance from rotation axis Rp(where R is the radius of the Earth, and p is the location of the point)

Rp ω

V

The North American plate is rotating about the blue triangleVelocity at a point depends on

-how fast it is spinning, ω-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 plateEx: 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 eastneed 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 pointWant to get x, y, z coordinates

Mauritania

X-> 0° longitude

y-> 90° East longitude

z-> north pole

Now we have the coordinates of pCan get velocity

Mauritania

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

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-SE-Wup-down

Components of the velocity

Note error in table:

• Nazca-Pacific… longitude of Euler pole is -90.1 E