CONCLUSIONS

Solving the nonlinear traveltime problem in successive steps of increasing resolution, through a frequency decomposition of the model space, has diverse limitations that depend on the specific choice of velocity basis functions. Walsh functions form an orthonormal complete set for representing discrete functions on a finite interval but, because of their orthogonality, the estimation of components associated with later steps of the algorithm cannot correct the errors in the previously estimated components. Using sine- and cosine-like square functions allow for these corrections, but the resulting set is not complete and the resolution is therefore (severely) limited. For the specific synthetic model tested in this study, the direct linearized solution proves to be much more stable, and to have a better resolution than the iterative nonlinear solutions based on the two types of square functions decomposition.