Residual time extrapolation operators for efficient wavefield construction

Solving the wave equation using nite-dierence approximations suers from dispersion and stability related issues that might limit ecient or proper extrapolation of high frequencies. Spectral-based time extrapolation methods tend to mitigate these problems, but at an additional cost to the extrapolation. I investigate the prospective of using a residual formulation of the spectral approach, along with utilizing Shanks transform based expansions, that adheres to the residual requirements, to improve accuracy and reduce the cost. Utilizing the fact that spectral methods excel (time steps are allowed to be large) in homogeneous and smooth media, the residual implementation allows for velocity discretization that optimizes the use of this feature.