Wavelet estimation and deconvolution

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Abstract
Three methods have been presented for constructing a smooth wavelet from either a (possibly poor) estimate of the reflectivity sequence or an approximate inverse filter for the source wavelet. An approximate reflectivity sequence might be derived from a velocity log at, or near, the site where the normal incidence seismogram was recorded, or it might be equated to the averages obtained from minimum entropy deconvolution (MED). The approximate inverse filter for the source wavelet is provided by MED. All methods performed well when tested on data generated from wavelets of different character, and this provides optimism that these methods will work satisfactorily in a variety of geophysical problems where the data are the convolution of a smooth wavelet and a “spikey” model. The deconvolution problem discussed here is nonunique, and satisfactory wavelet constructions require that some subjectivity be introduced by the investigator. Even so, we present one example where the computed wavelet and reflectivity sequence, both of which appear geophysically reasonable, differed significantly from the “true” functions. This example illustrates the nonuniqueness inherent in this problem and shows the importance of additional constraints on the deconvolution results.

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