Sparse-promoting full-waveform inversion based on online orthonormal dictionary learning

Abstract

Full-waveform inversion (FWI) delivers high-resolution images of the subsurface by minimizing iteratively the misfit between recorded and calculated seismic data. We have attacked this misfit successfully with the Gauss-Newton method and sparsity-promoting regularization based on fixed multiscale transforms that permit significant subsampling of the seismic data when the model perturbation at each FWI data-fitting iteration can be represented with sparse coefficients. Rather than using analytical transforms with predefined dictionaries to achieve sparse representation, we developed an adaptive transform called the sparse orthonormal transform (SOT), whose dictionary is learned from many small training patches taken from the model perturbations in previous iterations. The patch-based dictionary is constrained to be orthonormal and trained with an online approach to provide the best sparse representation of the complex features and variations in the entire model perturbation. The complexity of the training method is proportional to the cube of the number of samples in one small patch. By incorporating compressive subsampling and the adaptive SOT-based representation into the Gauss-Newton least-squares problem for each FWI iteration, the model perturbation can be recovered after an [Formula: see text]-norm sparsity constraint is applied on the SOT coefficients. Numerical experiments on synthetic models determined that the SOT-based sparsity-promoting regularization can provide robust FWI results with reduced computation.