Preconditioning

Lateral variations

The analysis above appears one dimensional in depth. Conventional interval velocity estimation builds a velocity-depth model independently at each lateral location. Here we have a logical path for combining measurements from various lateral locations. We can change the regularization to something like $\bold 0\approx \nabla\bold u$ . Instead of merely minimizing the vertical gradient of velocity we minimize its spatial gradient. Luckily we have preconditioning and the helix to speed the solution.