Mitigating Velocity Errors in Least-Squares Imaging Using Angle-Dependent Forward and Adjoint Gaussian Beam Operators

Compared with traditional adjoint-based migration, least-squares migration (LSM) can reduce finite-frequency effects, remove acquisition footprints and improve spatial resolution by solving a linear inverse problem for subsurface reflectivity. One important requirement for the success of LSM is having an accurate migration velocity model. Because of low signal-to-noise ratio (SNR), inaccurate traveltime picking, lack of low-frequency signals and limited acquisition aperture, it is still challenging to build an accurate velocity model using ray-based tomography or full waveform inversion. LSM with large velocity errors results in erroneous reflector locations, strong swing artifact and even non-convergence. To mitigate these issues, we develop a novel least-squares imaging framework in the subsurface half-opening angle domain. Instead of using high-wavenumber velocity perturbations as the reflectivity model as in traditional LSM, we parameterize the wave equation with an angle-dependent reflectivity, and derive the corresponding linearized forward modeling and adjoint migration operators. Because Gaussian Beam migration naturally incorporates propagation directions in wavefield extrapolation, we compute the Green's function using the Gaussian beam summation method. To improve the common-image gather (CIG) quality for low-fold and low-SNR data, a shaping regularization over the half-opening angles is introduced in the conjugate gradient scheme to iteratively update the angle-dependent reflectivity model. A flattening-enhanced summation is used to compute the stacked images by accounting for the depth moveout of CIGs caused by velocity errors, and produces constructive stacking results. Numerical experiments for benchmark models and a land survey demonstrate that the proposed method can improve LSM convergence and produce high-quality angle-dependent and stacked images even with inaccurate migration velocity models.

Automated summary

Least-squares migration (LSM) can reduce finite-frequency effects, remove acquisition footprints and improve spatial resolution by solving a linear inverse problem for subsurface reflectivity. A novel imaging framework in the subsurface half-opening angle domain has been developed to mitigate velocity model inaccuracies in LSM.