Study On Acoustic And Elastic Reverse Time Migration In Transversely Isotropic Media

The most widely used anisotropic model in seismic exploration is transversely isotropic(TI)media.In past decade,reverse time migration(RTM)based on coupled pseudo-acoustic wave equations in acoustic TI media developed rapidly.However,TI RTM for tilted transversely isotropic(TTI)media suffers from numerical instabilities and shear wave artifacts due to the coupling of the P-wave and SV-wave modes in the TTI coupled equations.Besides,the TI elastic RTM for multicomponent seismic data is in the early stages of development,and there are lots of things remains to be further investigated.So in this paper,we focus our work on the study of the TI acoustic and elastic RTM methods.Starting from qP-and q SV-wave dispersion in in vertical transversely isotropic(VTI)media,a systemic instruction of various acoustic approximations is presented in this paper,including the detailed derivation of these acoustic approximations,comparative analysis of their accuracy and the corresponding numerical methods.We found the Harlan's approximation,widely used in pure P-wave modeling in TI media,has lower accuracy among these approximations in a medium with strong anisotropy.So in this paper,we present a method to improve its accuracy by modifying the anelliptic(fractional)term and obtained three modifications.Based on the highest accurate phase velocity approximation of these three modifications,we further derived an improved TTI pure P-wave equation,which is exploited to construct source and reciver wavefields in our TTI RTM.The decoupled pure P-wave equations involves pseudo-differential operators which are difficult to be calculated by using finite-difference(FD)method alone.One can use pseudospectral(PS)method to implement these equations.However,it is computationally expensive due to many fast Fourier transforms(FFTs)in wavefield extrapolation at each time step.For the numerilca implement issue,in this paper,a hybrid PS/FD scheme to solve the decoupled pure Pwave equations for numerical efficiency and accuracy is introduced and developed.We test the stability,accuracy and efficiency of proposed TTI RTM algorithm with various kinds of TTI models.Following the isotropic elastic RTM,we propose two TI elastic RTM methods for multicomponent seismic data.The first one is based on the polarization vector projection method to separate anisotropic elastic wavefields.To reduce the storage memory requirements of space-domain separation operators and improve the efficiency of wavefield separation,the polarization-vector-projection-based RTM utilizes lowrank SVD decomposition method to approximate spatial-domain separation operators.For PS image polarity reversal problem,the isotropic shot-domain polarity correction method is introduced to solve this problem.The second TI elastic RTM is based on the anisotropic elastic decoupled P-and S-wave equations to separate the vector wavefield.The output separated wavefields are both vectorial.To obtain the scalar images,we propose a new imaging condition in which the scalar product of two vector wavefields is exploited to produce scalar images in elastic RTM.At last,simple flat layer models and complex models are used to test these two anisotropic elastic RTM algorithms,and to demonstrate the potential of the proposed methods.