Seismic Data Reconstruction And Denoising Based On Compressive Sensing And Sparse Representation

Along with the further exploration of oil and gas, the potential fields and conditions for exploration are becoming more complex, which often increasingly distorts the acquired seismic data sets to be incomplete and irregular. It will affect the following data processing and interpretation, and then the identification of oil and gas. However, due to the limit of Nyquist sampling theory, most traditional reconstruction techniques require high-rate samples, and the way of survey and sampling cannot be adjusted to the practical conditions properly, which will increase the exploration costs. Based on a newly developed theory named compressive sensing and sparse representations for seismic records, this thesis presents a compressed reconstruction technique with more effective sampling schemes and denoising strategies for seismic data processing, by combining the two steps of seismic exploration with data recording and recovery. Both sampling rate and cost can be reduced by this technique, as well as the data quality being improved.According to the well-developed compressive sensing theory from signal processing field, it is even possible to recover extraordinarily incomplete data under its corresponding Nyquist rate. Based on this frame, firstly, this thesis studies two of the principal issues for compressed seismic data reconstruction, i.e., sparse representations and sampling schemes. As to the first issue, starting with Fourier basis, we use Poisson Disc sampling to control gaps between samples, which compensates drawbacks of the currently used random sampling. Further more, we employ curvelet transform, which is regarded to be the optimally sparse representation for seismic data, developing a curvelet-based recovery strategy by sparsity-promoting inversion, which requires much less samples as well as achieving higher-quality reconstruction. As to the second issue, this thesis introduces sampling schemes with blue noise spectrum into this field, including Jitter sampling, Poisson Disc sampling and Farthest Point sampling. We analyze their advantages and show the effectiveness through numerical experiments. These researches have great significances for seismic data acquisition and reconstruction.During the process of data regularization mentioned above, some artificial noise is probably involved. In addition, the practical seismic profiles acquired are also often interfered by real noise. Both would affect seismic processing and interpretation, including data reconstruction. The traditional transform-based methods, e.g., thresholding in transformed domain, usually cause non-smooth distortions in the vicinity of discontinuities like wavefronts, which would confuse the expected seismic features. In this thesis, total variation minimization strategy is employed, combining with curvelet threshoding method, in order to suppress this phenomenon, and the involved noise is eliminated as well. Further more, in order to improve the current sparse representations which cannot be adjusted to the targeted seismic data adaptively, this thesis introduces the idea of learning overcomplete redundant dictionary to deal with seismic noise, which is shrunk during the training and constructing process of the dictionary.