A New Class of Central Compact Finite-difference Scheme with High Spectral Resolution for Acoustic Wave Equation

Based on the existing cell-node and cell-centre compact finite difference (FD) schemes, we have developed a new central compact scheme with high spectral resolution for acoustic wave equation. In the new scheme, both the values on cell nodes and cell-centres are used to compute the second-order spatial derivatives on nodes. The spatial derivatives on cell-centres are evaluated by half shifting the indices in the formula for derivatives on nodes. The values on cell-centres are stored as independent variables during modelling. The unknown coefficients are determined by optimization method, and the optimization problem is solved with least squares. The new scheme outperforms the traditional cell-node and cell-centre compact schemes at the following aspects: (1) the new scheme can promise a higher accuracy than the conventional cell-node and cell-centre compact schemes for the same formal truncation errors and model parameters, and it can maintain higher accuracy while using a shorter spatial stencil; (2) for the similar level of accuracy, the new scheme requires less time cost and memory. The synthetic examples on the 2D homogeneous media, the 3D horizontal-layered model and the 2D Marmousi model demonstrate the advantages of the proposed scheme.