Sparse seismic signal processing using adaptive dictionaries
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Seismic surveys have become the primary measurement tool of exploration geophysics, both onshore and offshore, with significant signal processing needed to estimate the properties of earth subsurface via seismic wave propagation. The typical workflow for seismic includes three phases: acquisition, imaging, and interpretation. A high-quality imaging result for interpretation necessitates accurate data acquisition and efficient imaging algorithms. However, seismic data gathers may suffer from noisy and missing traces during acquisition which could possibly limit their use in the following imaging phase. As a convincing quantitative imaging technique, full waveform inversion (FWI) searches for the correct velocity model that can match the acquired seismic dataset. However, due to the high dimensionality of the model space, FWI is inherently a challenging problem, so that regularization techniques are typically applied to yield better posed models. Moreover, FWI also suffers from its prohibitive computational costs that mainly arise from forward modeling of the seismic wavefield for multiple sources at each iteration of a nonlinear minimization process. 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 thesis presents a new reconstruction method to mitigate noise and interpolate missing traces in the acquired seismic dataset, as well as a new FWI framework to estimate subsurface models more accurately and efficiently. Both contributions involve sparse approximation of various types of data with respect to adaptive dictionaries that are learned by different strategies. The new seismic data reconstruction method involves a sparse representation over a parametric dictionary, which bridges a gap between model-based and data-driven sparse approximations. The new FWI framework adapts velocity model perturbations to orthonormal dictionaries that are trained in an online manner, and then exploits compressive sensing to significantly reduce the computational cost by requiring many fewer calculations of the forward model. Numerical experiments on synthetic seismic data and velocity models indicate that the new methods can achieve better performance compared to other state-of-the-art methods.