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

ABSTRACT Least-squares reverse time migration (LSRTM) is a powerful method for imaging complex subsurface structures. Traditional LSRTM implementations typically recovered a stacked image interpreted as a velocity perturbation, which lacked a physical interpretation when analyzing angle-dependent responses. An angle-domain LSRTM framework was introduced to invert for angle-dependent reflectivity using full-wave and ray-theory Hessian operators. The method enabled a computationally efficient strategy for LSRTM by assuming that the angle-domain migration Hessian operator was a diagonally dominant banded matrix. The migration step followed a standard common-shot implementation of angle-domain reverse time migration, whereas the Hessian operator was explicitly computed using wave-equation-based amplitudes and traveltimes. Although the method required additional finite-difference simulations at receiver positions, it remained computationally efficient and yielded amplitude-preserving angle-dependent reflectivity images. Numerical experiments using both synthetic and field data were conducted to test the proposed algorithm, demonstrating the fidelity of amplitude variation with angle responses. Furthermore, our analysis demonstrated that the ray-theory angle-domain Hessian operator provided a physically justified, computationally efficient, and memory-efficient alternative to the full-wave operator for modeling and inversion.