Abstract
The idea of designing a deconvolution operator for the vertical seismic profile (VSP) based on its downgoing waves is well known (Anstey, 1976; Gaiser et al., 1984; Hubbard, 1979; Lee and Balch, 1983; Kennett et al., 1980). Many variations of the scheme exist. Anstey (1976) recommends the average of the downgoing wave from all levels as the basis for designing an inverse operator. Lee and Balch (1983) use the downgoing wave from a single level to deconvolve all the VSP traces. Gaiser et al. (1984) and Hubbard (1979) recommend doing the deconvolution independently at each depth level. As observed by Hubbard, there are similar disparities in the literature about whether all or only part of the downgoing wave train should be used in the design of an inverse operator. Although all of the above approaches are identical if multiples are generated in a limited zone near the sea bottom, they differ for more complex media. We recommend, and in this note we explore the theoretical properties of, the level‐by‐level deconvolution based on the entire downgoing wave train. The expressions we develop apply to the general case of the vertical VSP response to any number of horizontal layers with any degree of complexity in the process that generates multiples.
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