SEISMIC DATA RECONSTRUCTION VIA COMPLEX SHEARLET TRANSFORM AND BLOCK COORDINATE RELAXATION

摘要

Due to practical and economic limitations, real seismic data is not densely sampled in all coordinates, which will affect the subsequent seismic data processing steps, such as migration, surface-related multiple elimination and inversion. Therefore, it is necessary to reconstruct the incomplete seismic data. This paper explains the application of the complex shearlet transform to seismic data reconstruction. With a L-1 constraint and the Block Coordinate Relaxation (BCR) method, performance of the complex shearlet-based, real shearlet-based and well-accepted curvelet-based reconstruction are compared in terms of recovered f-k spectrum and signal to noise ratio (SNR). We also discuss the shift invariance of the complex shearlet transform and compare the performances of the BCR and the widely used Projection Onto Convex Sets (POCS) method. The numerical experiments on synthetic and real data with different under-sampling rates demonstrate the validity of the proposed method, especially for the case of large amounts of traces missing.