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In Cunha (1990) I used a set of *sine*-like and *cosine*-like square
functions to describe the velocity model in a
traveltime inversion scheme for elliptically anisotropic media.
This specific decomposition of the model allowed the implementation
of a fast nonlinear algorithm that retrieves a different
frequency-component of the model at each step. A drawback of this
decomposition is that the basic set is neither orthogonal nor
complete. Although the non-orthogonality can be somewhat useful
(in this nonlinear scheme) for correcting errors in the
components estimated by previous steps, the lack of completeness
strongly reduces the resolution of the algorithm.
It is possible to use instead another set of square functions
- the Walsh functions -
that form an orthogonal and complete set inside the interval
where the model is defined. However, as illustrated in a synthetic
example, the results obtained with the Walsh functions are inferior
to the results obtained with the use of the *sin*- and
*cosine*-like square functions.
In addition, both results are inferior to those attained by
a linearized inversion that uses
the individual layers as the basis parameters for describing the model.

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Stanford Exploration Project

12/18/1997