A new computationally efficient symplectic algorithm for forward modeling and attenuation-compensated reverse time migration

Abstract The Earth medium exhibits characteristics beyond pure elasticity, with widespread viscosity leading to wave propagation attenuation. In seismic imaging methodologies such as reverse time migration (RTM), it becomes imperative to consider viscosity and accurately account for attenuation. This study aims to propose an RTM method with attenuation compensation specifically tailored for visco-acoustic models. Achieving successful RTM hinges on utilizing a stable and highly accurate forward numerical solver with minimal numerical dispersion. We address this need by formulating the visco-acoustic wave equation as a Birkhoffian system and introducing the stereo-modeling (STEM) operator. This enables the development of a novel symplectic algorithm, NSM-STEM, designed for the visco-acoustic wave equation. Numerical examples demonstrate that, in comparison to conventional finite difference methods, NSM-STEM effectively suppresses numerical dispersion and maintains energy and stability over extended simulations. Furthermore, we incorporate NSM-STEM into an RTM framework with attenuation compensation. Numerical examples highlight the method's capability to mitigate artifacts introduced by numerical dispersion, resulting in superior imaging quality, particularly in the deep regions of the model where conventional RTM is notably affected by attenuation effects.