Seismic Trace Reflectivity Series Recovery for Interpretation Enhancement using Kalman Filter

This paper proposes to use a Kalman Filter to re-cover seismic trace reflectivity series for enhancing interpretation. The proposed method is briefly summarized as follows: First, the convolutional model of seismic signals is reformulated as a discrete-time linear system. In this linear system, the non-zero reflectivity impulses are treated as abrupt state changes with unknown magnitudes occurring at unknown times. Second, a Kalman filter is applied to the linear system without considering the changes. Third, the likelihood ratio as a function of both the magnitudes and occurring times is evaluated by using the Kalman filtering innovations. Fourth, the magnitudes and occurring times of the changes are estimated by alternately fixing one parameter and maximizing the ratio with the other parameter. Finally, the reflectivity series are reconstructed from the estimated magnitudes and occurring times of the changes. The reliability of the proposed method is demonstrated experimentally on real and synthetic seismic datasets.