Abstract
Deconvolution is one of the most important aspects of seismic signal processing e.g. for oil exploration, etc. The objective of the deconvolution procedure is to remove the obscuring effect of the wavelet's replicas making up the seismic trace and consequently obtain an estimate of the reflection coefficient sequence. In this paper generic formulas for obtaining optimal estimates of the reflection coefficient sequence are derived. These formulas can utilize any estimation/smoothing scheme and yield optimal fixed-point, fixed-lag and fixed-interval estimates of the reflection coefficient sequence. New deconvolution algorithms are derived by use of the new formulas and Lainiotis' partitioning filter and smoother. The new algorithms are compared to previous ones with respect to computational complexity, memory requirements, performance and parallelism efficiency. Additional results concerning the algorithms' asymptotic behavior are given and validated through extensive computer simulation.
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