Fast Implementation Technique of Adaptive Kalman Filtering Deconvolution Via Dyadic Wavelet Transform

Abstract

Abstract A new approach of adaptive Kalman filtering deconvolution (AKFD) via dyadic wavelet transform is proposed. Due to the computing complexity of the approach, a fast implementation technique is proposed. The AKFD via dyadic wavelet transform discards the assumption of stationarity for signals in predictive deconvolution, and solves the problem of improving resolution at the price of decreasing signal‐to‐noise rate (SNR) and therefore has a better ability of resistance noise. Suppressing false reflections and improving resolution in dyadic wavelet transform domain is better than that in time domain. The new approach also overcomes the drawback of increasing the low‐frequency component of AKFD in time domain. The fast implementation technique makes use of the assumption of local stationary for 2D seismic data. The technique reduces the calculated amount of calculating the adaptive predictive operators by calculating an adaptive predictive operator in each segment, and then applying the algorithm of spline interpolation to interpolate in transverse and in portrait. The aim of fast implementation is thus achieved. A large number of experiments indicates that computing speed can be increased several hundred times. However, it retains the original calculation effect.