Least-square Reverse Time Migration Based On Two-dimensional Acoustic Finite Difference Method

Due to adaptability to any complex models,reverse time migration(RTM)has become the most popular migration imaging method.On this basis,least-square reverse time migration(LSRTM)based on the idea of full waveform inversion(FWI)can further improve the imaging effect and preserve the amplitude.Therefore,it is of great significance to study LSRTM for inversion of geological structure and prediction of oilgas reservoir.Based on the two-way wave equation,RTM needs accurate wave equation solution and absorbing boundary conditions.In this paper,time-space domain finite difference(FD)method and hybrid absorbing boundary condition are introduced.Compared with traditional FD method,time-space domain FD method has higher accuracy and lower dispersion in calculating wavefield.The hybrid absorbing boundary condition is easy to achieve and perform perfect absorbing effect.In the RTM section,the paper describes the mathematical principle of RTM and the low-frequency noise problems.To remove the noise,some popular suppressing noise methods are introduced and a numerical case is given to compare the denoising effects.In addition,the deficiencies of the RTM,such as serious noise,insufficient illumination and low resolution,are summarized from the numerical example.In order to solve these problems,LSRTM based on the idea of FWI has been developed.In the LSRTM section,the mathematical principle of LSRTM is introduced,that is,the establishment of the objective function,and the use of Gauss Newton method to solve its gradient formula in the frequency domain.In order to accelerate the convergence of LSRTM,and take into account the efficiency and memory at the same time,a wavefield decomposition imaging method based on single forward modeling is introduced,and applied to the LSRTM.Finally,numerical examples of simple model and complex model show the effectiveness of our method.