The present paper treats the application of the Kalman-Bucy filter (KBF), organized as a deconvolution (KBDF), for the extraction of the reflectivity function from seismic data. This means that the process is described as non-stationary, and corresponds to a generalization of the Wiener-Kolmogorov theory. The mathematical description of the KBF preserves its relationship to the Wiener-Hopf filter (WHF) that deals with the counterpart stationary stochastic process. The strategy to solve the problem is structured in parts: (a) The optimization criterion; (b) The a priori knowledge; (c) The algorithm; and (d) The quality. The a priori knowledge includes the convolutional model, and establishes statistics to its components (effective source wavelet, reflectivity function, and geological and local noises). To demonstrate the versatility, applicability and limitations of the method, we performed systematic deconvolution experiments under several situations of additive noise levels and effective source wavelet. First, we demonstrate the necessity of equalizer filters, and second that the spectral coherence factor is a good measure of the quality of the process. We also justify the present study for its application in real data, as exemplified.
Kalman filter; Deconvolution in time domain; Non-stationary processes
