## 4 Conclusions  
In this study, the time partial derivative of the elastic wave equation was discretized using the central difference scheme, and the spatial partial derivative was discretized using a meshless GFDM. When realizing the elastic wave numerical simulation via the GFDM  
Figure 14: Shot record of fault model: (**a**) SGFD X component; (**b**) SGFD Z component; (**c**) 4 th-order GFDM X component; (**d**) 4 th-order GFDM Z component.  
Figure 13: Fault model with irregular boundary: (**a**) model structure; (**b**) model parameters.  
in the time domain, the Poisson disk node generation algorithm and the centroid Voronoi node adjustment algorithm were combined to obtain an even and random distribution of nodes, and the Cerjan damping boundary condition was introduced. Through numerical calculation, the following understandings and conclusions were obtained:  
1. The GFDM is a meshless numerical calculation method based on scattered node approximation; it overcomes the dependence of traditional methods on grids, and can lay nodes in the simulation area in a flexible manner;
2. When using the GFDM for forward modeling, the nodes can be rendered consistent with the real velocity interface by generating a suitable distribution of nodes, so that the velocity interface can be accurately depicted, avoiding the situation where the grid and velocity interface cannot be aligned in the conventional finite difference forward modeling; thus eliminating the diffraction problems due to a stepped grid, and the record time error caused by an inaccurate description of the interface position;
3. One of the main problems in the GFDM forward modeling is in how to best discretize the model. The node discretization scheme used in this study is applicable to a model with gentle changes in lateral velocity. For models with sharp changes in lateral velocity, the simulation stability will be affected, so it would be necessary to explore a more stable and applicable node discretization scheme;
4. The 2 nd-order GFDM has high computational efficiency, but low accuracy. The 4 th-order GFDM is unstable when using a \"star\" composed of fewer points (for example, 13 points), therefore it can only use a \"star\" composed of more calculation nodes (21 nodes were used in this study), causing the calculation efficiency to be greatly reduced. To improve computing efficiency, high-performance computing can be considered to enable better efficiency;
5. Compared with SGFD, the GFDM requires some preprocessing before forward modeling can be applied, including calculation of the node distribution and the difference stencil, which makes GFDM more complicated in practical application.  
Conceptualization, S.L. and Z.Z.; methodology, S.L.; software, S.L.; validation, S.L.; formal analysis, W.Z.; review and editing, W.Z. and Z.Z.; supervision, Z.Z. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Fundamental Research Funds for the Central Universities of Central South University 2019 ZZTS300.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
We are grateful for technical support from the High-Performance Computing Center of Central South University. We gratefully acknowledge the editors and reviewers for providing thoughtful and useful suggestions.  
The authors declare no competing financial interests.