The Research Of Least-squares Split-step Fourier Migration

With increasing expectations for image accuracy and amplitude-preserving of seismic exploration,imaging problem has been posed as an inverse problem based on the minimization of a least-squares waveform error functional,and an alternative approach is least-squares migration(LSM),which consider imaging problem as a linear inverse problem,and it is well known for its good performance on image accuracy,amplitude preserving and image resolution.However,current LSM methods are all implicitly based on the assumption of consistent surface.In other word,shots and receivers are located on the same horizontal plane.In this case,LSM can accommodate well for marine seismic data and onshore seismic data with slight change for surface elevation,but cannot cope with seismic data recorded on irregular surface,especially for southern and western exploration surveys in China.In this paper,we firstly derive the expression of split-step Fourier propagator.Then,linear modelling formulation is obtained according to Born approximation,and we give migration and demigration operators with Green function constructed by split-step Fourier propagator,which are two fundamental elements to implement LSM.In order to suppress impacts from boundary reflection induced by artificial boundary and wraparound effect caused by DFT,we adopt cosine damping boundary.Finally,we employ split-step Fourier migration and demigration operators into the frame of LSM,achieving least-squares split-step Fourier migration by conjugate gradient method.Considering the influence of irregular surface,we utilize the strategy of “accumulating wavefields step by step” to continue the wavefield,which allows our method to deal with seismic data recorded on irregular surface directly.Both model trials and field data tests bring good results,which prove our method feasible,effective and practical.And we draw the following conclusion:(1)our method can recover the theoretic reflectivity model as the number of iteration increases,and improve both vertical and lateral amplitude preservation,especially for the deeper reflectors,and enhance image resolution to some extent;(2)our method can show more small-scale structures and local structural features,which plays an important role in identifying and determining an effective trap for oil and gas exploration.