Introduction

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.