Absorption in subsurface media has a considerable impact on amplitude and wave shape of recorded seismic data. Inverse Q filtering is a commonly used technique to remove these absorption effects. In recent years, some inversion-based absorption compensation methods have been proposed. Among them sparse deconvolution method is one of the most effective methods. However, these are all trace-by-trace deconvolution methods. In the presence of noise, all these methods can be unstable. The events appear to be discontinuous in lateral direction. To overcome the effects of noise, we proposed a novel absorption compensation method based on sparse deconvolution. There are two kinds of prior information in the proposed method. One is within and the other is across the seismic traces. For the former, we use the modified Cauchy norm to suppress noise, and for the latter we use a prediction error filter (PEF) which is calculated through a t-x domain random noise reduction procedure to preserve the signal and enhance the coherence of seismic events across midpoints. We testify the proposed method on a synthetic seismic data and the results obtained from sparse deconvolution method and the proposed method are compared. Besides, we also compare the results obtained from sparse deconvolution after noise attenuation and the proposed method. Synthetic data example demonstrates the effectiveness of the proposed method.
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