Abstract：Compared with the central finite difference (FD) scheme，the compact difference (CD) scheme has the advantages of high computational accuracy and simple boundary processing. Specifically，the fourth-order CD scheme based on a regular grid requires fewer computational nodes and has higher computational accuracy. However，it is required to solve large sparse diagonal matrix equations when using this scheme to solve the acoustic wave equation. When the model is large，the fourth-order CD scheme is less computationally efficient，and the memory requirement for storing and computing the diagonal matrix equations is large. The adaptive variable-grid strategy can improve computational efficiency and reduce memory consumption by optimizing the grid discretization and effectively reducing the number of grid points. This paper first derives a discrete scheme that uses the second-order FD scheme in time and the fourth-order CD scheme in space to solve the two-dimensional acoustic wave equation. Then the scheme is applied to forward modeling. As a result, the paper derives the modified acoustic wave equation based on the adaptive variable-grid strategy and develops a high-efficiency and high-accuracy reverse time migration method with adaptive variable-grid CD scheme. Numerical experiments show that the proposed method can image complex structures efficiently with high-resolution. Compared with the regular fine grid discretization method，the proposed method can improve the imaging efficiency of the Marmousi model by about 33.7% without accuracy loss.
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