Wavefield reconstruction by interpolating significantly decimated boundaries

Many practical seismic applications such as reverse time migration (RTM) and full-waveform inversion (FWI) are usually computation and memory intensive. To perform crosscorrelation in RTM or build the gradient for FWI, it is mandatory to access the forward and adjoint wavefields simultaneously. To do this, there are three methods: One is to read the stored forward wavefield from the disk, the second is using the final snapshot and the stored boundaries via reverse propagation, and the third is remodeling using checkpointing from stored state to another state. Among these techniques, wavefield reconstruction by reverse propagation appears to be a quite straightforward approach; however, it suffers a stringent memory bottleneck for 3D large-scale imaging applications. The Courant-Friedrichs-Lewy (CFL) condition is a fundamental criterion to determine temporal sampling to achieve stable wavefield extrapolation. The injection of the boundary sequence in time is essentially determined by Nyquist sampling principle, rather than the time interval given by CFL, which is much smaller than the Nyquist requirement. Based on this recognition, we have developed three boundary interpolation techniques, such as the discrete Fourier transform (DFT) interpolation, Kaiser windowed sinc interpolation, and Lagrange polynomial interpolation, for wavefield reconstruction to move from CFL to the Nyquist limit. Wavefield reconstruction via DFT interpolation can be implemented by folding and unfolding steps in the forward simulation and backward reconstruction on the fly. Compared with the DFT interpolation, the wavefield reconstruction methods using Kaiser windowed sinc interpolation and Lagrange polynomial interpolation have better efficiency while remaining a competitive accuracy. These methods allow us to dramatically decimate the boundary without significant loss of information, and they nicely reconstruct the boundary elements in between the samples, making the in-core memory saving of the boundaries feasible in 3D large-scale imaging applications.