Setting up Traveltime Equations and Solving for Slowness

OBJECTIVE: Construct overdetermined system of equations L s = t for data shown in picture below.

PROCEDURE:

1. Set up system of traveltime equations associated with data shown in above figure. Ls=t, where s is slowness vector and t is traveltime vector.

2. Solve by least squares method for optimal s. Plot out misfit function over a range of values, and grapphically determine optimal solution. Does it agree with your solution to normal equations? Are equations ill-conditioned? Explain.

3. Find [L^TL]^-1 and determine which is cell with smallest slowness variance (type inv(L'*L) to get inverse). Why is this cell the one with least slowness error?