Semi-Blind Time-Variant Sparse Deconvolution Using a Weighted L1 Norm

According to the acoustic wave theory, the amplitude and phase variations of seismic wave are usually dominated by the coupling of the structures-associated reflectivity and the fluids-associated intrinsic attenuation. However, either the intrinsic attenuation or reflectivity interference is ignored when improving seismic resolution by using the conventional methods. To solve the issue, we introduce a weighted L1 norm to evaluate the relationship between the sparsity of the inverted reflectivity and the tested Q. Through measuring the sparsity of the inverted reflectivity with different tested Q, we proposed semi-blind time-variant sparse deconvolution using a weighted L1 norm to separate Q and reflectivity, and to further obtain the high-resolution result. Furthermore, the weighted L1 norm can enhance the contributions of weak signals and meanwhile suppress the contributions of strong signals by using different weights inversely proportional to amplitude, which can reduce the dependence of our method on the reflectivity model. Finally, the proposed method is tested on statistically synthetic, physical modeling and field data.