Regularization Algorithms For Seismic Imaging

Seismic data imaging is the core step of geological Survey, the imaging accuracy directly relates to the accuracy of interpretation and exploration. From the mathematical point of view, Seismic data imaging is a typical inverse problem, and the problem is ill-posed, there exists some serious difficulties in both theoretical analysis and numerical calculation. Conventional imaging methods are migration, such as Kirchhoff integral migrated method, frequency wave number domain migration, not only computation is intensive, but also the migration of the image is a rough approximation of the structure formation. With the geological exploration to deeper geological structure formation and the development of more complex, these methods are increasingly difficult to meet the needs of high-precision oil and gas exploration.In response to these problems, this thesis starting from the ill-posedness of the problems, research the regularization theory for seismic data imaging of numerical algorithms. This article firstly applies BB (Barzilai-Borwein) algorithm, CG (Conjugate Gradient) method in seismic imaging, and based on these,we amend the step size to improve the CG method. Numerical results show that, compared with CG method and BB algorithm,the improved CG method requires fewer iteration steps,and the computation is time shorter, SNR is higher. The academic innovation consists of two parts:Firstly, based on Tikhonov regularization, the regularized iterative algorithm for seismic data imaging, which is different from traditional migrated methods, is new ideas, solving ill-posed inverse problem, and a new way;Secondly, based on the BB algorithm, CG method and other traditional optimization methods, in order to reduce search criteria of the iterative method from the start, we design an improved CG method for seismic imaging, and the numerical experiment is validated. Not only can this method reduce the amount of computation required iterations, but also significantly improve the signal to noise ratio.