Reverse Time Migration with Modified Nearly Analytical Discretization: Efficient Large-Scale High-Resolution Imaging and Aliasing Suppression

Abstract

Reverse time migration (RTM) requires numerically solving the partial differential wave equation because analytical solutions are infeasible. A significant challenge in numerical methods arises from inaccuracies in derivatives approximation, making the numerical wave velocity frequency-dependent and causing numerical dispersion. It is an unphysical artifact that degrades modeling and imaging, particularly at higher frequencies and over time. Avoiding numerical dispersion requires finer spatial grids, which substantially increase computational costs to achieve high-resolution imaging results. The modified nearly analytical discretization (MNAD) method reduces numerical dispersion by incorporating additional analytical relations through simultaneous numerical solutions of the wavefield and its spatial gradient fields, employing them in higher-order derivative approximations, and improving spatial derivative estimation via energy conservation optimization. MNAD is introduced for RTM in large-scale studies, where leveraging compact stencils and coarser spatial and temporal grids enables high-resolution imaging with substantially lower computational and memory costs compared to conventional finite difference (FD) methods. Furthermore, adjoint-state imaging is enhanced with a novel data boundary condition interpolation using MNAD gradient fields, mitigating aliasing effects in recovered images from data recorded at half the Nyquist rate, enabling imaging with fewer required number of sources/receivers and alleviating acquisition costs. Synthetic experiments validate the method’s performance in modeling and imaging on coarser grids than FD methods and in maintaining stability over longer propagation times. Further, the MNAD-based RTM application to ocean bottom seismometer (OBS) data in a large-scale study confirms its capability to achieve high-resolution images with reduced computational costs. Finally, imaging with data sampled at half the Nyquist rate highlights the potential of the proposed approach for minimizing acquisition costs without sacrificing resolution and suffering from aliasing. These findings affirm MNAD as a robust and efficient alternative to FD methods for large-scale, high-resolution imaging, offering significant advantages in computation, storage, and acquisition efficiency.