This article deals with the ubiquitous problem of wavelet estimation. In essence, the problem consists of estimating, at best, two unknowns from one equation. In the seismic case, as it is well known, the model of the recorded seismic trace, xt, is generally formulated as a convolution, xt=wt*rt, where wt is the seismic source signature, or wavelet, and rt is the reflectivity series which is comprised of all primary and multiple reflections. Since, in general, we can assume that rt is white (or nearly so), the amplitude signature of wt may be estimated with some degree of confidence. It is, of course, the phase of wt that presents the difficulty. It turns out, perhaps somewhat counterintuitively, that, except for rather special circumstances, the phase of a signal uniquely determines the signal to within a scale factor. The amplitude spectrum plays no part whatsoever (we explore this further below). No wonder, then, that the phase is the all-important factor.
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Ulrych et al. (1995) studied this question.