Figure 3

Figures *a* and *b* show that,
contrary to what we would expect, the results obtained with the Walsh
functions are inferior to the ones obtained with the *sine*- and
*cosine*-like square functions. Although Walsh functions form
a complete set, their orthogonality impedes
further steps from correcting errors in previously estimated
components of the model in this kind of iterative scheme. Moreover,
both nonlinear schemes are inferior to the linearized
algorithms shown in Figures *c* and *d*.
The result in c was obtained with an iterative scheme that uses
the least-squares solution of equation (8) by
successively increasing (by a power of 2) the number of layers at each step.
The difference between c and d is the introduction
into the objective function of an extra term that corresponds to
the difference between the traveltime-derivatives relative to
the receiver positions. As a result the solution
for *V*^{z} in d becomes more stable since with this term
the inversion will try to fit not only the traveltimes, but also
the form of the traveltime curves.

12/18/1997