Local wavefield refinement using Fourier interpolation and boundary extrapolation for finite-element method based on domain reduction method

Abstract

The domain reduction method based on the finite-element method (FEM) is promising for multiscale seismic wave simulations for local complex structures and rough topography. However, a transition region is required to refine the wavefields from coarse to fine grids, which may lead to strong artifacts. Traditional wavefield interpolation methods can only handle a small upsampling ratio due to their low accuracy. Here, we propose a high accuracy upsampling method using Fourier interpolation and boundary extrapolation. It requires that the wavefield in the transition region is evenly sampled, which may slightly reduce the flexibility of FEMs. Fortunately, this constraint only exists in two layers of nodes, in which the coarse and fine grids are collocated. To further apply our interpolation method to the wavefield upsampling on the nonuniform grid, we adopt cubic interpolation within the local region of interest, which is adequate in accuracy for regularizing the wavefield on the fine nonuniform grid. For a topographic surface, we perform wavefield extrapolation on the ground surface to avoid abnormal amplitude variations below and beyond the surface, which can greatly reduce potential artifacts caused by the Fourier interpolation. Numerical experiments find that our method is superior to traditional interpolation methods in accuracy, especially for large upsampling ratios. Its relative error is less than 2% even for a 40-time upsampling; in contrast, the relative error of linear and cubic interpolation is up to 90% and 41% in the same situation, respectively. We further verify the feasibility of our method for 3D heterogeneous models with rough topography, multilayer heterogeneity, and random perturbations of background models. The proposed method yields a significant speeding of the multiscale seismic simulation using the FEM for 3D models with complex local structures and topographies while being highly accurate.