Design of quadratic filters based on the D norm for seismic deconvolution

In this paper, quadratic filters are designed for seismic deconvolution. These nonlinear filters can be easily obtained from optimizing the D norm for the Minimum Entropy Deconvolution (MED) algorithm. Due to the symmetric structure of the quadratic filter, the actual number of filter coefficients is reduced. In finding the filter coefficients, a system of linear equations is obtained. Recently, efficient methods to realise these quadratic filters have been reported. Simulation results show that low order quadratic filters are usually sufficient and that the filtered output indicates the seismic events even when the seismic wavelet is nonminimum phase. When the data are contaminated with noise, quadratic filters can still perform reasonably well. In the case of a complex reflectivity series, nonlinear filtering is superior to linear filtering. Examples of processing synthetic seismic data by linear and nonlinear filtering are presented.