- 1.
- The velocity (slowness) range is not wide enough.
- 2.
- The sampling in the velocity domain is too coarse.

Inverse problems are often used to handle the non-unitarity of operators.
A prior advisable step in the design of an inverse problem
is to attribute some properties to the model in terms of moments
of corresponding distributions. A reasonable
property of the model space would be **sparseness**, meaning that we want to cluster
the components of the solution into a few large peaks Thorson and Claerbout (1985). The sparseness
would help to distinguish primaries and multiples in the velocity space.
Finally, we would like to design a solver that bears robustness to bad (inconsistent) data points.
These bad data points leave large values in the residual and attract most
of the solver's efforts Fomel and Claerbout (1995).
Unfortunately, seismic data are generally very noisy,
and the need for robust estimators is very pressing.

4/27/2000