Sparse Seismic Time-Variant Deconvolution Using Q Attenuation 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 introduce an efficient method to perform seismic time-variant deconvolution based on the earth Q-model. We present 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, any redundant spike in the solution, which is far from the correct support, has a small energy. The proposed method is demonstrated using synthetic and real data examples.