Lowrank finite-differences and lowrank Fourier finite-differences for seismic wave extrapolation in the acoustic approximation

Conclusions

Explicit finite difference (FD) methods are the most popular and straightforward methods for seismic modeling and seismic imaging, particularly for reverse-time migration. Traditionally the coefficients of FD schemes are derived from a Taylor series expansion around the zero wavenumber. We present a novel FD scheme: Lowrank Finite Differences (LFD), which is based on the lowrank approximation of the mixed-domain space-wavenumber propagator. LFD uses compact FD schemes, which are more suitable for parallelization on multi-core computers than spectral methods that require FFT operations. This technique promises higher accuracy and better stability than those of the conventional, explicit FD method. We also propose to replace the 4th-order FD operator based on Taylor's expansion in Fourier Finite Differences (FFD) with an 8th-order LFD operator to reduce dispersion, particularly in the TTI case. Results from synthetic experiments illustrate the stability of the proposed methods in complicated velocity models. In TTI media, there is no coupling of qP-waves and qSv-waves by either method. Both methods can be incorporated in seismic imaging by reverse-time migration to enhance its accuracy and stability.

Lowrank finite-differences and lowrank Fourier finite-differences for seismic wave extrapolation in the acoustic approximation