FD methods and spectral methods are the two most popular wavefield extrapolation approaches for seismic modeling and seismic wavefield imaging. To handle variable density and velocity in seismic modeling or RTM, we have proposed SGL method by applying lowrank decomposition to first-order
-space propagation operators on a staggered grid. The cost of the new method amounts to using a small number of FFTs, which corresponds to the approximation rank. On the basis of the SGL method, we have also designed the SGLFD method, which extends the lowrank finite-differences from a case of constant density to one of variable density. This approach promises higher accuracy and better stability than those of the traditional, explicit staggered grid finite-difference methods. We tested the proposed methods using the MMS solutions and concluded that they retained high accuracy for large temporal and spatial intervals or high frequency sources. Results for synthetic models illustrate that our proposed methods are highly accurate for heterogeneous media and can handle sharp velocity and density variations. Although the proposed methods are focused on the acoustic case, they can also be extended in principle to elastic, anisotropic or attenuating media. The methods can be used for seismic modeling or RTM.
Lowrank seismic wave extrapolation on a staggered grid