Deconvolution of seismic records with optimization of weighted normalized quadratic functionals.
2. Frequency band
© Yu.K. Tyapkin, E.A. Silinskaya
In the previous paper , a restriction on the relative noise level at the output from a filter was introduced in order to regularize the solution of the problem for deconvolution optimizing weighted normalized quadratic functionals of a filtered signal as a measure of seismic data resolution. Without such a restriction, this approach yields trivial non-correct ideal inverse filtering. Another way to overcome such a shortcoming of the limiting case of the solution is to perform this type of deconvolution in a limited frequency band where signal predominates over noise. This paper is devoted to the solution of the problem. Some shortcomings of ideal corrective filtering, which flattens the spectrum in a specified frequency band, and some advantages of the new approach when using one family of weighting functions have been considered. Some properties of the solution obtained are demonstrated with simple synthetic seismograms using one of a frequency band.