Preconditioned prestack plane-wave least squares reverse time migration with singular spectrum constraint

Least squares migration can eliminate the artifacts introduced by the direct imaging of irregular seismic data but is computationally costly and of slow convergence. In order to suppress the migration noise, we propose the preconditioned prestack plane-wave least squares reverse time migration （PLSRTM） method with singular spectrum constraint. Singular spectrum analysis （SSA） is used in the preconditioning of the take-off angle-domain common-image gathers （TADCIGs）. In addition, we adopt randomized singular value decomposition （RSVD） to calculate the singular values. RSVD reduces the computational cost of SSA by replacing the singular value decomposition （SVD） of one large matrix with the SVD of two small matrices. We incorporate a regularization term into the preconditioned PLSRTM method that penalizes misfits between the migration images from the plane waves with adjacent angles to reduce the migration noise because the stacking of the migration results cannot effectively suppress the migration noise when the migration velocity contains errors. The regularization imposes smoothness constraints on the TADCIGs that favor differential semblance optimization constraints. Numerical analysis of synthetic data using the Marmousi model suggests that the proposed method can efficiently suppress the artifacts introduced by plane-wave gathers or irregular seismic data and improve the imaging quality of PLSRTM. Furthermore, it produces better images with less noise and more continuous structures even for inaccurate migration velocities.

Fast least-squares prestack time migration via accelerating the explicit calculation of Hessian matrix with dip-angle Fresnel zone

Amplitude versus offset analysis is a fundamental tool for determining the physical properties of reservoirs but generally hampered by the blurred common image gathers(CIGs).The blurring can be optimally corrected using the blockwise least-squares prestack time migration(BLS-PSTM),where common-offset migrated sections are divided into a series of blocks related to the explicit offsetdependent Hessian matrix and the following inverse filtering is iteratively applied to invert the corresponding reflectivity.However,calculating the Hessian matrix is slow.We present a fast BLS-PSTM via accelerating Hessian calculation with dip-angle Fresnel zone(DFZ).DFZ is closely related to optimal migration aperture,which significantly attenuates migration swings and reduces the computational cost of PSTM.Specifically,our fast BLS-PSTM is implemented as a two-stage process.First,we limit the aperture for any imaging point with an approximated the projected Fresnel zone before calculating the Hessian matrix.Then,we determine whether a seismic trace contributes to the imaging point via DFZ during calculating the Hessian matrix.Numerical tests on synthetic and field data validate the distinct speedup with higher-quality CIGs compared to BLS-PSTM.