Could the processed seismic wavelet be simpler than we think

J. P. Lindsey, (1988) in a clearly written short piece, opens an old question which concerns the analytic properties of seismic wavelets. This well conceived study concludes that most of the roots of a seismic wavelet as expressed by its z transform representation lie on or are very near the unit circle. The present discussion does not seek to characterize the form of all seismic wavelets, but only many if not most of those which have been processed with deconvolutions or “inversion” type operators to have reduced length, broadened bandwidth, and some desirable phase property. For such wavelets, despite the diversity by which they are obtained, remarkably simple operations having very few parameters can be extremely effective. As a case in point, constant‐phase rotations appear to carry such wavelets to zero‐phase symmetric form to a very good approximation. I start with empirical attributes which appear to characterize most processed seismic wavelets. Such wavelets tend to be of 40–100 ms duration with a...