In seismic prospecting, fi eld conditions and other factors hamper the recording of the complete seismic wavefi eld; thus, data interpolation is critical in seismic data processing. Especially, in complex conditions, ...In seismic prospecting, fi eld conditions and other factors hamper the recording of the complete seismic wavefi eld; thus, data interpolation is critical in seismic data processing. Especially, in complex conditions, prestack missing data affect the subsequent highprecision data processing workfl ow. Compressive sensing is an effective strategy for seismic data interpolation by optimally representing the complex seismic wavefi eld and using fast and accurate iterative algorithms. The seislet transform is a sparse multiscale transform well suited for representing the seismic wavefield, as it can effectively compress seismic events. Furthermore, the Bregman iterative algorithm is an efficient algorithm for sparse representation in compressive sensing. Seismic data interpolation methods can be developed by combining seismic dynamic prediction, image transform, and compressive sensing. In this study, we link seismic data interpolation and constrained optimization. We selected the OC-seislet sparse transform to represent complex wavefields and used the Bregman iteration method to solve the hybrid norm inverse problem under the compressed sensing framework. In addition, we used an H-curve method to choose the threshold parameter in the Bregman iteration method. Thus, we achieved fast and accurate reconstruction of the seismic wavefi eld. Model and fi eld data tests demonstrate that the Bregman iteration method based on the H-curve norm in the sparse transform domain can effectively reconstruct missing complex wavefi eld data.展开更多
Assuming seismic data in a suitable domain is low rank while missing traces or noises increase the rank of the data matrix,the rank⁃reduced methods have been applied successfully for seismic interpolation and denoisin...Assuming seismic data in a suitable domain is low rank while missing traces or noises increase the rank of the data matrix,the rank⁃reduced methods have been applied successfully for seismic interpolation and denoising.These rank⁃reduced methods mainly include Cadzow reconstruction that uses eigen decomposition of the Hankel matrix in the f⁃x(frequency⁃spatial)domain,and nuclear⁃norm minimization(NNM)based on rigorous optimization theory on matrix completion(MC).In this paper,a low patch⁃rank MC is proposed with a random⁃overlapped texture⁃patch mapping for interpolation of regularly missing traces in a three⁃dimensional(3D)seismic volume.The random overlap plays a simple but important role to make the low⁃rank method effective for aliased data.It shifts the regular column missing of data matrix to random point missing in the mapped matrix,where the missing data increase the rank thus the classic low⁃rank MC theory works.Unlike the Hankel matrix based rank⁃reduced method,the proposed method does not assume a superposition of linear events,but assumes the data have repeated texture patterns.Such data lead to a low⁃rank matrix after the proposed texture⁃patch mapping.Thus the methods can interpolate the waveforms with varying dips in space.A fast low⁃rank factorization method and an orthogonal rank⁃one matrix pursuit method are applied to solve the presented interpolation model.The former avoids the singular value decomposition(SVD)computation and the latter only needs to compute the large singular values during iterations.The two fast algorithms are suitable for large⁃scale data.Simple averaging realizations of several results from different random⁃overlapped texture⁃patch mappings can further increase the reconstructed signal⁃to⁃noise ratio(SNR).Examples on synthetic data and field data are provided to show successful performance of the presented method.展开更多
基金supported by the National Natural Science Foundation of China(Nos.41274119,41174080,and 41004041)the 863 Program of China(No.2012AA09A20103)
文摘In seismic prospecting, fi eld conditions and other factors hamper the recording of the complete seismic wavefi eld; thus, data interpolation is critical in seismic data processing. Especially, in complex conditions, prestack missing data affect the subsequent highprecision data processing workfl ow. Compressive sensing is an effective strategy for seismic data interpolation by optimally representing the complex seismic wavefi eld and using fast and accurate iterative algorithms. The seislet transform is a sparse multiscale transform well suited for representing the seismic wavefield, as it can effectively compress seismic events. Furthermore, the Bregman iterative algorithm is an efficient algorithm for sparse representation in compressive sensing. Seismic data interpolation methods can be developed by combining seismic dynamic prediction, image transform, and compressive sensing. In this study, we link seismic data interpolation and constrained optimization. We selected the OC-seislet sparse transform to represent complex wavefields and used the Bregman iteration method to solve the hybrid norm inverse problem under the compressed sensing framework. In addition, we used an H-curve method to choose the threshold parameter in the Bregman iteration method. Thus, we achieved fast and accurate reconstruction of the seismic wavefi eld. Model and fi eld data tests demonstrate that the Bregman iteration method based on the H-curve norm in the sparse transform domain can effectively reconstruct missing complex wavefi eld data.
文摘Assuming seismic data in a suitable domain is low rank while missing traces or noises increase the rank of the data matrix,the rank⁃reduced methods have been applied successfully for seismic interpolation and denoising.These rank⁃reduced methods mainly include Cadzow reconstruction that uses eigen decomposition of the Hankel matrix in the f⁃x(frequency⁃spatial)domain,and nuclear⁃norm minimization(NNM)based on rigorous optimization theory on matrix completion(MC).In this paper,a low patch⁃rank MC is proposed with a random⁃overlapped texture⁃patch mapping for interpolation of regularly missing traces in a three⁃dimensional(3D)seismic volume.The random overlap plays a simple but important role to make the low⁃rank method effective for aliased data.It shifts the regular column missing of data matrix to random point missing in the mapped matrix,where the missing data increase the rank thus the classic low⁃rank MC theory works.Unlike the Hankel matrix based rank⁃reduced method,the proposed method does not assume a superposition of linear events,but assumes the data have repeated texture patterns.Such data lead to a low⁃rank matrix after the proposed texture⁃patch mapping.Thus the methods can interpolate the waveforms with varying dips in space.A fast low⁃rank factorization method and an orthogonal rank⁃one matrix pursuit method are applied to solve the presented interpolation model.The former avoids the singular value decomposition(SVD)computation and the latter only needs to compute the large singular values during iterations.The two fast algorithms are suitable for large⁃scale data.Simple averaging realizations of several results from different random⁃overlapped texture⁃patch mappings can further increase the reconstructed signal⁃to⁃noise ratio(SNR).Examples on synthetic data and field data are provided to show successful performance of the presented method.
