Lowrank Finite-differences and Lowrank Fourier Finite-differences for Seismic Wave Extrapolation

We introduce a novel finite-difference approach for seismic wave extrapolation in time. We derive the coefficients of the finite-difference operator from a lowrank approximation of the space-wavenumber, wave-propagator matrix. Numerical examples confirm the validity of the proposed technique. Based on the technique of lowrank finite-differences, we also improve the finite difference scheme of the two-way Fourier finite differences (FFD). We call the new operator: lowrank Fourier finite differences (LFFD). Both the lowrank FD and lowrank FFD method can be applied to enhance accuracy in seismic imaging by reverse-time migration.