Least-Squares Gaussian Beam Migration in the VTI Media With a Cauchy Constrain

Due to finite acquisition aperture, limited frequency bands, and unbalanced illumination, conventional migration often fails to generate high-quality reflectivity images. In contrast, least-squares migration (LSM) can produce high-resolution and amplitude-preserved images by solving a linear inverse problem. Although LSM has been implemented by ray-based and wave-equation propagators, its application has primarily been limited to isotropic media, thereby restricting its ability to handle anisotropy. To mitigate this issue, we propose a least-squares Gaussian beam migration (LSGBM) method for vertical transverse isotropic (VTI) media. Based on an efficient VTI ray tracing, we first derive the Born modeling and adjoint migration operators, and then iteratively update the reflectivity model. To suppress data overfitting artifacts, a multiplicative Cauchy constraint is introduced in the LSGBM to promote a sparse inversion result. Additionally, an approximate diagonal Hessian is employed as a preconditioner to accelerate convergence. Numerical experiments demonstrate that the proposed VTI LSGBM can correct anisotropic effects, enhance spatial resolution, and improve amplitude fidelity, producing high-quality images.