Sparse-promoting Full Waveform Inversion based on Online Orthonormal Dictionary Learning

Full waveform inversion (FWI) delivers high-resolution images of a subsurface medium model by minimizing iteratively the least-squares misfit between the observed and simulated seismic data. Due to the limited accuracy of the starting model and the inconsistency of the seismic waveform data, the FWI problem is inherently ill-posed, so that regularization techniques are typically applied to obtain better models. FWI is also a computationally expensive problem because modern seismic surveys cover very large areas of interest and collect massive volumes of data. The dimensionality of the problem and the heterogeneity of the medium both stress the need for faster algorithms and sparse regularization techniques to accelerate and improve imaging results. This paper reaches these goals by developing a compressive sensing approach for the FWI problem, where the sparsity of model perturbations is exploited within learned dictionaries. Based on stochastic approximations, the dictionaries are updated iteratively to adapt to dynamic model perturbations. Meanwhile, the dictionaries are kept orthonormal in order to maintain the corresponding transform in a fast and compact manner without introducing extra computational overhead to FWI. Such a sparsity regularization on model perturbations enables us to take randomly subsampled data for computation and thus significantly reduce the cost. Compared with other approaches that employ sparsity constraints in the fixed curvelet transform domain, our approach can achieve more robust inversion results with better model fit and visual quality.