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.

Likewise the construction of the data quality screen $\bold G$would naturally involve the full three-dimensional setting.