Angle Gathers Extraction From Reverse Time Migration And Wave-equation Migration Velocity Analysis In Acoustic Medium

With the development of seismic exploration,there has a shift from seismic imaging to parameter inversion.How to obtain the physical properties of the subsurface in details(e.g.,velocity,density,anisotropy,etc.)has become a major problem in exploration seismology.There are mainly two ways to obtain the subsurface physical properties.The first method includes three parts: the pre-stack depth migration(PSDM),migration velocity analysis(MVA),and amplitude-related analysis methods(such as AVO/AVA).The second approach is the full waveform inversion(FWI).Both methods try to obtain the broadband properties,and we can carry out the geological interpretation of the reservoir subsequently.Although FWI is the most attractive technique to rebuild the subsurface velocity,due to the nature of strong nonlinear,the inverted results strongly depend on the user-defined initial model.An accurate initial model is one of the key factors for a successful FWI workflow.Wave-equation migration velocity analysis(WEMVA)which is based on a two-way wave operator uses the reflected data to estimate the macro velocity in the image domain automatically.This approach updates the velocity by measuring the coherence(e.g.,flatness or focusing)of migrated image gathers.But there are some problems with this approach:(1)The conventional reverse time migration(RTM)suffers artifacts that affect the quality of the image.These artifacts also can lead to an improper interpretation;(2)The computation cost of angle gathers extraction from RTM is time-consuming,and it is difficult to extend 2D to real 3D case;(3)The differential-semblance-optimization-based(DSO)WEMVA is sensitive to noise,and the gradient artifacts will come up when the data suffers from noise.Aiming at these problems,the researches on how to obtain the migrated images with high quality,how to generate the image gathers from RTM efficiently and how to construct the MVA objective function with convex behavior are necessary.With the imaging framework of the reflected dataset,in order to obtain the subsurface reflectivity and background velocity,firstly,high-quality imaging results(image gathers)are obtained by RTM,and then the macro velocity is obtained by WEMVA with the migrated images iteratively.Under the assumption of the acoustic medium,the research mainly focuses on two aspects: imaging gather extraction from RTM and the WEMVA workflow.The first is the research on the cause of diving wave artifacts in reverse-time migration and its removal.The second is the research on the efficient method of angle gathers extraction from RTM in isotropic and VTI media.The third is the research on the WEMVA via the optimal-transport-based objective function.Through a series of work in image-domain based on acoustic RTM,we try to give a reasonable and good initial model for subsequent waveform inversion in the data domain,and provide a low-wavenumber part for velocity building.The main research achievements of the thesis include five aspects:(1)Based on the wavefield-decomposition imaging condition,the thesis analyzes the causes of low-frequency artifacts and diving wave artifacts in RTM,and compares the advantages and disadvantages of different removal methods.For the diving wave artifact in RTM,the decomposition method based on analytical wavefield is used to remove the artifacts.Meanwhile,a method of diving wave artifact removal based on a wavelength-dependent smoothing operator is proposed.By smoothing the velocity model,the propagation characteristics of the wavefield in the areas with strong velocity gradient are similar to the ones in the true velocity.Numerical tests show that the proposed wavelength-dependent smoothing algorithm can suppress the diving wave artifacts,and retain the imaging ability for steep structures.This method can be performed in the imaging framework of the conventional RTM.(2)For different strategies of angle gather extraction,like local plane-wave decomposition,extended imaging conditions,and direction-based vector method,the advantages,and disadvantages of different strategies are analyzed.The thesis proposes an efficient and stable angle gather extraction method based on traveltime gradient.Compared with the local slowness analysis method,it shows that the traveltime gradient can give accurate and stable source-side propagation direction,and the reflection/azimuth angle can be obtained by combining the reflector normal direction with the source-side propagation.The synthetic and real data show that this method can generate the angle gathers efficiently.(3)The pure quasi-P(qP)wavefield propagator is used for the RTM in VTI media,and the angle gather extraction from RTM based on traveltime gradient is extended from isotropic to VTI media.Compared with the anisotropic elastic wave equation,this method does not need the P-S mode separation.Through the analysis of source-side propagation direction,it shows that the traveltime gradient of the VTI medium can also give an accurate and stable propagation direction.The synthetic data results show that the angle gather extraction strategy based on traveltime gradient is feasible for the VTI medium.(4)The DSO-based objective function for WEMVA is implemented.Compared with the traditional MVA,inversion velocity analysis(IVA)replaces the adjoint of the Born modeling operator with its approximate inverse.This method can generate the higherquality image gathers,remove the artifacts in the gradient and accelerate the inversion convergence.(5)The optimal transport theory is applied to the objective function construction in WEMVA,and the thesis proposes the WEMVA via the optimal-transport-based objective function.Through the numerical analysis of the proposed objective function,it shows that the objective function has good convexity even over a large velocity range.The synthetic and real data show that this method can give a better macro velocity model and provide a good initial velocity for the subsequent FWI.The innovation points of the thesis include three aspects:(1)The thesis proposes an effective method of eliminating the diving wave artifacts in RTM based on a wavelength-dependent smoothing operator.This method does not need wavefield decomposition.By introducing the wavelength-dependent smoothing operator,the propagation characteristics of the wavefield in the strong velocity gradient are similar to the one in the true velocity.Then the diving wave artifacts are suppressed.This method is efficient and retains the ability to imaging steep structures.(2)The thesis proposes an efficient and stable method of angle gather extraction from RTM based on traveltime gradient.Firstly,the stable source-side local plane-wave propagation direction is obtained by using the traveltime gradient.Secondly,the normal direction of the reflector can be estimated from the stable imaging result.Thirdly,the scattering/azimuth angle is obtained by combining the source-side propagation direction with the reflector normal direction.Finally,the angle gathers are generated by using the excitation-criteria-based imaging conditions in the angle domain.(3)The thesis proposes the WEMVA via optimal-transport-based objective function.The optimal transport theory is applied to construct the objective function for MVA in the image domain.Firstly,the imaging gathers are transformed into the probability distribution to satisfy the requirements of optimal transport theory.Secondly,the objective function is constructed by measuring the difference of the probability distribution corresponding to the adjacent traces in the angle gathers by Wasserstein distance.The objective function tries to reduce the influence of amplitude,and exhibits good convexity and unimodal property over a large velocity range which helps the inversion to avoid falling into local minimum.