Geophysical Journal | 2007 volume 29 5

Deconvolution of seismic records with optimization of weighted normalized quadratic functionals. 1. Temporal area

© Tyapkin Yu.K.

This paper is devoted to the general theory of seismic deconvolution that optimizes weighted normalized quadratic functionals as a measure of data resolution. The problem is solved in the time domain. For correctness, a restriction on the relative noise level is introduced in the solution. In this resolution measure, a family of power weighting functions (in module) is suggested for utilization due to its advantages over the others. The choice of such a measure is substantiated by certain shortcomings of the conventional Wiener criterion, which is the basis for filters of the same name. In the first place, these are non-co-ordination with the human visual system mechanism and integral dependence on both the degree of resolution and the signal-to-noise ratio. The two limiting cases of the solution are analyzed, which lead either to non-correct ideal inverse filtering or to energy filtering having a rather low resolving power.

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