Fast online orthonormal dictionary learning for efficient full waveform inversion

Full waveform inversion (FWI) delivers high-resolution images of a subsurface medium property by minimizing itera-tively the misfit between observed and simulated seismic data, and is commonly used by the oil and gas industry for geophysical exploration. FWI is a challenging problem because seismic surveys cover ever larger 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, so sparse regularization techniques can be used to accelerate and improve imaging results. In this paper, we propose a compressive sensing method for the FWI problem by exploiting the sparsity of geological model perturbations over learned dictionaries. Based on stochastic approximations, the dictionaries are updated itera-tively to adapt changing models during FWI iterations. Meanwhile, the dictionaries are kept orthonormal in order to maintain the corresponding transform in a fast and compact manner so that these transforms do not introduce extra computational overhead to FWI. Establishing such a sparsity regu-larization on the model enables us to significantly reduce the workload by only collecting 0.625% of the field data without introducing subsampling artifacts. Hence, the computational burden of large-scale FWI problems can be greatly reduced.