Introduction

Near-surface reverberations contaminate our CMP velocity analysis and stack image. Furthermore, the present AVO analysis incurs an even higher demand on these reverberations removal. Thus removing reverberations from reflection seismograms has been a longstanding problem of exploration geophysics. Standard predictive multiple attenuation techniques in marine reflection seismology are based on the periodicity of multiples. Since periodicity of multiples is only satisfied in a one-dimensional impulse response earth model, such techniques find trouble when applied to an offset section, for multiples are not periodic in time for a given nonzero offset. Researchers invent new domains to help. Taner (1981) applied predictive deconvolution along radial traces. Alam and Austin (1981) and Treitel et al. (1982) applied predictive deconvolution in the slant-stack domain. Their methods suffer the disadvantage that the period of waterbottom multiples varies from trace to trace in the new domains, and fail to attenuate water layer peglegs originating from subsurface reflections.

This paper discusses Abelian group theory (Muir, 1987) and applies the theory to perform velocity transformation on common shot gathers into Abelian group attributes domain for the separation of primary and multiple reflections (including peglegs). The method applies to layered earth models with finite sets of events. An attribute that is addable independent of ordering (zero-offset travel-time T, for example) forms an Abelian group. The results are that sets of multiples and peglegs lie equally spaced along parallel straight lines in this domain. We apply a simple rotation to turn them straight down the T axis, resulting in a new Abelian group attributes domain. Predictive multiple attenuation techniques work well in this domain. Conjugate inverse transforming all the way back to the space-time domain gives the reverberations attenuated section. Because this new Abelian group domain can handle the waterbottom multiples and peglegs efficiently at the same time, it is a prospectively good domain to work in. One main application would be AVO analysis in structure-free but variable lithology areas. Constructing a velocity transform that has a good inverse is the key to the success of this method.