The Application Of Compressed Sensing In Seismic Wave Field Propagation

With the target of petroleum exploration changing gradually,the imaging precision of seismic imaging method has been required increasingly.As a high-precision imaging method,reverse-time migration has became the focus of research in petroleum exploration,which aims to solve the problem of conventional migration method can not image complex structural accurately,as well as to offer guarantee to the follow-on work of seismic data interpretation and oil reservoir accurate description.Reverse-time migration bases on forward modeling of acoustic wave equation,the simulation method of wave equation based on wave theory can accurately describe the characters of kinematics,therefore,accurately show the seismic wave propagation law.However,there is need of storing the forward prolongation wave field data and the reverse prolongation wave field data on every time point,the massive data storage is one of the major causes that restricts the widespread application of reverse-time migration.Compressed sensing as a new signal sampling and recovery theory attracts the attention of experts and scholars at home and abroad immediately,meanwhile,apply compressed sensing to seismic data processing is an important research interest of seismic exploration.This thesis uses compressed sensing algorithm to compress and to recover seismic wave field which is calculated by forward numerical simulation base on the research of reverse-time migration,and research the compressed sensing method which is appropriate for seismic wave field propagating.Reverse-time migration involves forward modeling,imaging conditions,migration noise suppression and other key issues.This thesis uses high-order staggered grid finite difference methods to calculate forward modeling wave field and researches the influence of difference order,wavelet frequency and grid spacing about numerical dispersion based on that.PML absorbing boundary condition is used in this thesis which has good result in absorbing reflected wave field resulted from boundary and effectively to avoid wave field interference caused by boundary reflection.In the process of imaging,using cross-correlation imaging condition and Laplace noising technology to finally image and suppress low-frequency noise.The result of model test indicates that the reverse-time migration algorithm introduced by this thesis acquires high-quality imaging effect.On the basis of studying the method of inverse time migration,two-dimensional discrete wavelet transform is used to construct the sparse representation of the seismic wave field,and a partial Hadamard observation matrix based on the orthogonal basis linear representation method is used to reduce the seismic wave field data so as to achieve a good wave field compression effect.In order to ensure the accuracy of inverse time migration imaging,this paper studies several seismic wave field reconstruction algorithms,and analyzes the reconstruction results of different algorithms.BFSSAMP algorithm with higher computational efficiency and reconstruction accuracy is used to reconstruct the seismic wave field accurately.Finally,the model tests show that the proposed compressing sensing algorithm can effectively compress and accurately reconstruct the forward seismic wave field,and solve the problem of huge data storage in the implementation of inverse time migration imaging method.