Sparse blind deconvolution based low-frequency seismic data reconstruction for multiscale full waveform inversion

When the wavelet is inaccurate, we update the amplitude of wavelet by alternately inverting L1 norm constraint and Tikhonov regularization problems, and correct the time-shift error by cross-correlating the direct waves. After that we can get the accurate wavelet and SRIR simultaneously. Then using the reconstructed data successively as observed data, combining it with dynamic random sources and layer-stripping methods, we propose a new strategy for the fast multiscale FWI. We test our method by numerical examples in several cases including blended acquisition cases. The results show that it has good anti-noise property and it can reconstruct valid low-frequency components when the observed data lacking low-frequency information. The example using inaccurate wavelet shows that the blind deconvolution-convolution algorithm is able to obtain accurate wavelet and low-frequency data simultaneously.