Seismic signal recovery based on Earth Q model

We consider the problem of recovering the underlying reflectivity signal from its seismic trace, taking into account the attenuation and dispersion propagation effects of the reflected waves, in noisy environments. We present an efficient method to perform seismic time-variant inversion based on the earth Q-model. We derive theoretical bounds on the recovery error, and on the localization error. It is shown that the solution consists of recovered spikes which are relatively close to spikes in the true reflectivity signal. In addition, we prove that any redundant spike in the solution, which is far from the correct support, will have small energy. The robustness of our technique is demonstrated using synthetic and real data examples.