Passive Source Reverse Time Migration Of Converted Wave And Angle Domain Common Image Gather

The discovery of subsurface structure has always been the hot-discussed issue,the receiver function method is a popular method because of its practicality,which based on the hypothesis that subsurface structure is horizontally layered and teleseismic plane wave eject nearly vertically into surface,thus it is not applicable to the imaging of complex medium.The pre-stack depth migration based on exploration seismology suits this situation,however,in order to obtain accurate velocity model,it requires a suitable migration velocity.So we employ migration velocity analysis(MVA)in exploration seismology to build velocity model and realize accurate imaging.This paper have realized passive source converted wave reverse time migration(PS-RTM)and compared the imaging difference from two imaging condition for PS-RTM;we employ polarity-corrected scalar imaging condition to migration to realize fine structure characterization.However,pre-stack depth migration has high requirement for migration velocity model,therefore,we have developed passive source converted wave angle domain common image gather(ADCIG)extraction methods(wavefront vector method,local plane wave decomposition method and local shift method).to realize passive source converted wave migration velocity analysis(MVA)based on flattening common image gather.In order to explore the feasibility of this method,we have tested the behavior of passive source converted ADCIG to different velocity error.When either Vp or Vs is larger than the true value,CIG curve upward;When either Vp or Vs is lower than the true value,CIG curve downward,which is opposite to active source situation.When the one is larger than the true value and the other is lower,it is possible that CIG is still flat In evidence,it is not reliable that invert Vp and Vs simultaneously by passive source converted wave migration velocity analysis(MVA)based on flattening common image gather,therefore,we introduce the ratio of Vp to Vs to constraint inversion.Secondly,we extend three active source converted wave angle domain common image gather(ADCIG)-extracted methods to passive source situation.Considering both P-and S-wave are from receiver side,the behavior of passive source situation is different from active source situation.When the one of Vp and Vs is accurate,the other is higher than accurate velocity,passive source converted wave ADCIG curves upward;When the other is lower than accurate velocity,passive source converted wave ADCIG curves downward.Similar with active source situation,when the one is lower and the other is higher,it is possible that passive source converted wave ADCIG is flat.We find that there exists strong non-uniqueness in MVA of passive source converted wave to invert both Vp and Vs,therefore we introduce the ratio of Vp to Vs as prior information to constrain inversion.When solving inversion problem,first,we employ cross-correlation method to pick depth residual of common image gather(CIG),then define the least square norm of depth residual as objective function,in order to conveniently derive the gradient of objective function to velocity,we introduce connective function to link the depth residual with migration velocity and solve inversion problem with the adjoint state method.In this process,first,we utilize acoustic Born approximation and elastic wave scattering theory to calculate gradient with respect to Vp and Vs,and then back-project depth residuals to migration velocity with gradient.Second,solve step length by using parabolic fitting in line search methods.Finally,update migration velocity by using conjugate gradient method.Our method does not require source information,which can be used for earthquake,microseismic,induced earthquake,or artificial sources situation,Velocity models can be used for migration imaging(Moho and strong velocity discontinuities)or localization(earthquake,microseismic,induced earthquake localization).Velocity model obtained from the passive source migration velocity analysis can be used as the initial velocity model for the full waveform inversion of elastic waves to realize fine characterization of subsurface structure.