Lateral variations

Above we built interval velocity models as a function of depth only. Now we seek to build them as a function of depth and lateral location. A conventional method builds a velocity-depth model independently at each lateral location. To combine the estimation of a depth function at one location with neighboring locations, we enlarge the fitting goals. Instead of merely minimizing the vertical gradient of velocity $\bold u$,we minimize its vector gradient. We change the regularization to something like $\bold 0\approx\bold\Lambda\nabla\bold u$.Luckily we have preconditioning and the helix to speed the solution. Bob Clapp has gotten some good quality preliminary results.