Research On Regularized Processing Method Of Multidimensional Seismic Signals

With the development of unconventional energy,such as coal bed methane and shale gas,a higher requirement is put forward for the regularity and integrity of seismic data.However,obstacles,mining areas,collection costs and other factors result in incomplete and irregular seismic data,conventional processing methods are often too rough to meet actual production needs.According to the inherent characteristics of seismic data,such as sparseness and low rank,it is a hot topic to adopt a more efficient algorithm to reconstruct seismic data.Multi-dimensional seismic signal recovery is based on the characteristics of seismic data with the regularization constraints,achieving the reconstruction of seismic data.At present,the constraints of the kernel norm and the regular sparse representation are the method in seismic signal processing,in which most of these algorithm are for two-dimensional seismic data,and no effective use of multi-dimensional seismic signals information,the recovery accuracy is not high,the reconstruction of a large number of missing data is not easy.The commonly used tensor decomposition method does not make good use of the redundancy in multidimensional seismic data.This thesis is response to these problems,using a new tensor decomposition method,the specific work is as follows:Firstly,for the singular value decomposition of matrix unable to recover the rule missing data and unideal suppressing noise,the thesis proposes a new method of seismic signal restoration based on Hankel tensor kernel norm regularization.The algorithm combines the Hankel matrix and the tensor kernel norm by a new tensor decomposition method,constructing a new objective function and solving the optimal solution of the variable by the method of multiplier.At the same time,the randomized tensor singular value decomposition is introduced to solve the problem that the time complexity is too high due to the introduction of the Hankel matrix.The damped truncation method is used to effectively reduce the error for the rank selection.The algorithm can suppress the random noise while effectively reconstructing missing seismic data.Secondly,for the matrix dictionary learning to restore the whole trace earthquake data missing appears fuzzy situation,the thesis proposes a new method of learningregularization sparse representation of tensor dictionary.The algorithm applies a new tensor product method to the tensor dictionary learning process,constructing a new target constraint function.The sparse coefficients are solved by the iterative algorithm,and the respective variables are solved in the time domain and frequency domain respectively.The Lagrange duality method is used to train the tensor dictionary,improving the calculation speed.Finally,the tensor dictionary and tensor sparse coefficients are updated iteratively to reconstruct the missing seismic signals.