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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.

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Stanford Exploration Project

12/18/1997