Likelihood-Ratio-Based Recovery for Seismic Reflectivity Series

This article proposes a likelihood-ratio-based method for recovering sparse reflectivity series from noisy seismic signals. Unlike the existing methods, the proposed method is specifically developed to be adaptive to the variance of the observational noise. This enhances the robustness of the reflectivity series recovering, as shown experimentally. 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 nonzero 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. Experimental results verified the reliability of the reflectivity series recovery from noisy seismic traces.