Sparse inversion for water bubble removal and spectral enhancement

The simple waveform coming from a bubble-free airgun source can significantly simplify the determination and control of the processed wavelet phase function, and thus it will improve stratigraphic reliability of the seismic data. In this paper, we propose a novel approach for simultaneous water bubble removal and spectral enhancement by frequency-wavenumber domain sparse inversion. We use the concept of target source, comparable to the well-known airgun source. The target source is a single-lobe bubble-free airgun source. We formulate an estimation problem in order to invert the seismic data that is acquired as if using the target source. As the basic idea of the approach is by convolution and deconvolution, there will exist random noise in the time-space domain because of the stability factor. We propose to iteratively remove the random noise while doing deconvolution by constraining using frequency-wavenumber (f-k) domain thresholding. Compared with the traditional wiener filtering, the proposed approach can obtain a nearly perfect result, without the extra added noise and artifacts. We use one linear-event synthetic data and the more realistic Marmousi model to demonstrate the performance of the proposed approach. The results show that our approach can successfully remove water bubbles and fill in the spectrum notches.