A new central compact finite difference scheme with high spectral resolution for acoustic wave equation

Abstract

Based on the existing cell-node and cell-centered compact finite difference schemes, we developed a new central compact scheme with a high spectral resolution for the acoustic wave equation. In the new scheme, both the function values on the cell-nodes and cell-centers are used to compute the second-order spatial derivatives on the cell-nodes. The cell-centered values are stored and updated as independent variables in the modeling. The spatial derivatives on the cell-centers are evaluated by half shifting the indices in the formula designed for the cell-nodes. Compared to the conventional compact interpolation scheme, the proposed approach can avoid introducing transfer errors. Either Taylor-series expansion-based or optimized least-squares-based methods are used to calculate the finite difference coefficients. Theoretical analysis and synthetic examples demonstrate that the optimized least-squares-based method can provide higher accuracy than the Taylor-series expansion-based method. This new scheme is not a simple combination of the cell-node and cell-centered compact schemes and outperforms them in three scenarios. Firstly, it can promise higher accuracy considering the same formal truncation errors and model parameters. Thus, it can maintain superior precision while using a shorter spatial finite difference stencil. Secondly, compared to the cell-node compact scheme with half of grid spacing, the new scheme can yield equally as accurate results with less time consuming, together with saving approximately 25% and 29% of memory in 2D and 3D modeling, respectively. Finally, for similar memory requirements, the new method can more efficiently provide solutions with higher accuracy. The synthetic examples on the 2D homogeneous and the 3D horizontally-layered models demonstrate the advantages of the proposed scheme. The numerical simulations with 2D Marmousi model further validate its accuracy, efficiency and flexibility in complex media.