Hybrid Tikhonov + total-variation regularization for imaging large-contrast media by full-waveform inversion
Résumé
Full waveform inversion (FWI) is a waveform matching procedure which can potentially provide subsurface models with a wavelength-scale resolution. However, sophisticated regularization techniques are required to decrease the sensitivity of FWI to the initial model and noise and reduce the ill-posedness of the problem resulting from uneven illumination. The subsurface may be considered as a combination of a blocky part and a smoothly-varying part. Due to the difference in statistical properties of each part, different techniques are needed to regularize them. To tackle this issue, we propose a new hybrid regularization method, which combines Tikhonov and total-variation (TV) regularizers. The Tikhonov regularization is used to stabilize the reconstruction of the smoothly-varying background part of the subsurface, while the TV regularization is used for recovering the large contrasts associated with salt bodies for example. The new Tikhonov-TV (TT) regularization is implemented in frequency-domain FWI based on wavefield reconstruction, an efficient penalty method to extend the parameter-search space, using an iterative refinement strategy and the split Bregman technique. The relevance of the TT-regularized FWI is illustrated with two synthetic examples, a toy example and a target of the large-contrast 2004 BP salt model. The results show that the TT method outperforms the TV method in recovering both the smooth and blocky parts of the subsurface.