Revisiting acoustic true-amplitude seismic imaging: Asymptotic linearized inversion, reverse-time migration, and their interrelations

Abstract

True-amplitude migration is essential for quantitative seismic imaging because it preserves the amplitude information required for reliable inversion and interpretation. Ray-theoretical formulations, beginning with asymptotic linearized inversion, establish migration as the adjoint of the Born operator and achieve amplitude fidelity through pseudo-differential analysis. In contrast, wave-equation-based methods such as reverse-time migration (RTM) are widely applied in practice, but their crosscorrelation implementations do not, in general, ensure amplitude correctness. This raises a fundamental question of consistency: under what conditions does RTM recover the same amplitude-correct image as asymptotic linearized inversion? In this study, we develop a unified framework for true-amplitude migration in acoustic media, valid in $R^n$ ($n\ge 2$). Using scattering-angle-domain decompositions of the Born operator, we analyze the stationary-phase structure of the single-scattering Hessian and construct a Beylkin-type migration operator within a least-squares framework. By explicit evaluating the Jacobian factors that map acquisition surface coordinates into angle-domain coordinates at the imaging point, and further examining the asymptotic behavior of forward- and backward-propagated wavefields, we demonstrate that angle-restricted RTM recovers the same true-amplitude scaling as the derived Beylkin-type operator. This result reconciles ray-theoretical and wave-equation-based perspectives, showing that amplitude corrections, traditionally associated with ray-based methods, can be systematically and naturally incorporated in RTM through geometrical-spreading analysis. Numerical demonstrations confirm that the proposed formulation yields angle-domain common image gathers with accurate amplitude behavior, validating the theoretical consistency and providing a robust foundation for amplitude-variation studies and quantitative inversion in complex acoustic media.