κ$\kappa$ ‐Generalized Least‐Squares Reverse Time Migration

Abstract

Least‐squares reverse time migration (LSRTM) is a powerful seismic imaging technique that estimates reflectivity models by iteratively minimizing the discrepancy between observed and modelled data, using the first‐order scattering approximation of the wave equation. However, because LSRTM relies on Gaussian statistical assumptions, it is susceptible to non‐Gaussian noise, which is frequently encountered in seismic datasets. To overcome this limitation, we introduce a robust generalization of LSRTM based on κ$\kappa$ ‐generalized statistics, termed κ$\kappa$ ‐LSRTM. We formulate a generalized objective function based on the maximum‐likelihood principle that enhances robustness to erratic data while maintaining the computational efficiency of adjoint‐based gradient optimization. Numerical experiments using a complex deep‐water pre‐salt model indicate that the κ$\kappa$ ‐LSRTM framework yields higher‐resolution seismic images with improved geological continuity, especially in deeper subsurface regions, even when Gaussian noise is present. In scenarios with non‐Gaussian noise, κ$\kappa$ ‐LSRTM substantially outperforms conventional LSRTM by providing more accurate reflectivity estimates and achieving faster convergence. These findings demonstrate the practical value of κ$\kappa$ ‐LSRTM for industrial‐scale seismic imaging in environments characterized by challenging noise and complex subsurface structures.