Angle-domain least-squares reverse time migration through full-wave and ray-theory Hessian operators

Least-squares reverse time migration (LSRTM) is a powerful method for imaging complex subsurface structures. Traditional LSRTM implementations typically recover a stacked image interpreted as a velocity perturbation, which lacks any physical interpretation when analyzing angle-dependent responses. An angle-domain LSRTM framework is introduced to invert for angle-dependent reflectivity using full-wave and ray-theory Hessian operators. The method enables a computationally efficient strategy for LSRTM by assuming the angle-domain migration Hessian operator is a diagonally dominant banded matrix. The migration step follows a standard common-shot implementation of angle-domain reverse time migration, while the Hessian operator is explicitly computed using wave-equation-based amplitudes and traveltimes. Although the method requires additional finite-difference simulations at receiver positions, it remains computationally efficient and yields amplitude-preserving angle-dependent reflectivity images. Numerical experiments using both synthetic and field data are conducted to test the proposed algorithm and demonstrate the fidelity of AVA responses. Furthermore, our analysis demonstrates that the ray-theory angle-domain Hessian operator provides a physically justified, computationally efficient, and memory-efficient alternative to the full-wave operator for both modeling and inversion.