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

Abstract

Full waveform inversion (FWI) reconstructs the underground velocity structures by minimizing the data residual between calculated wavefields and observed wavefileds. The conventional FWI usually uses some local optimization algorithms which lead to a strong dependency on initial velocity model. The objective function corresponding to low-frequency data components has less local minima. Reconstructing low-frequency information from recorded seismic data and using it in FWI can reduce cycle-skipping and thus weaken the dependency of inversion process on initial model. In this paper, based on the conventional frequency down-shifting method, we propose a sparse blind deconvolution-convolution low-frequency data reconstruction method, which can simultaneously update the wavelet and reconstruct the low-frequency components. First, we extract the subsurface reflection impulse responses (SRIR) by solving a L1 norm sparse constraint problem using the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). Then we test the accuracy of our algorithm, and discuss the effect of wavelet error and noises on the reconstruction result.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.