SEISMIC-REFLECTION ESTIMATION WITH COLORED NOISE

The convolutional model of a seismic trace consists of a seismic pulse convolved with the reflectivity series plus noise. Assuming coloured noise with known or estimated auto-correlation functions, two approach es to inverse filtering are compared. A maximum-likelihood estimate of the reflectivity series is obtained by filtering the data with a whit ening filter and using a least-squares inversion technique. Alternativ ely, a pulse-shaping Alter is applied to the data. The design of the f ilter is based on the known pulse and the known auto-correlation funct ion of the noise. The different approaches are compared on synthetic a nd real seismic data. Maximum-likelihood estimation and pulse-shaping filter give almost identical results, and both methods give clearly su perior results compared to assuming white noise. Optimal pulse-shaping filter is the best technique, since it is computationally fast and nu merically more stable. (Maximum-likelihood estimation requires a matri x inversion for each trace).