The finite-difference (FD) scheme is extensively applied in seismic modelling, imaging and inversion due to its advantages of large-scale parallel computing and programming. However, numerical dispersion caused by using a difference operator in substitution for the differential operator is non-negligible, which reduces the accuracy of the modelling and can lead to some misinterpretations. In addition, the computing resources required by the FD scheme is highly demanding when dealing with large models, which limits its applicability. In this paper, a new optimised FD scheme is proposed, which is based on an improved particle swarm optimisation (PSO) algorithm. We improve the conventional PSO algorithm by introducing strategies related to local learning and global learning, which contribute to accelerating the convergence rate and effectively avoiding getting trapped in local extrema. Then, the improved PSO algorithm is used to improve the conventional FD scheme. Dispersion analysis and numerical modelling demonstrate that the low-order optimised FD scheme can achieve higher accuracy than a high-order conventional operator. Compared with the conventional FD scheme and a FD scheme based on the Remez exchange algorithm, the optimised FD scheme based on the improved PSO algorithm can more efficiently suppress numerical dispersion and increase computational efficiency.

有限差分（FD）方案由于其大规模并行计算和编程的优势，被广泛应用于地震建模、成像和反演。然而，使用差分算子代替差分算子引起的数值离散是不可忽略的，这降低了建模的准确性并可能导致一些误解。此外，FD方案在处理大型模型时对计算资源的要求很高，限制了其适用性。在本文中，提出了一种新的优化 FD 方案，该方案基于改进的粒子群优化 (PSO) 算法。我们通过引入与局部学习和全局学习相关的策略来改进传统的 PSO 算法，这有助于加快收敛速度​​并有效避免陷入局部极值。然后，改进的PSO算法被用来改进传统的FD方案。色散分析和数值建模表明，低阶优化的 FD 方案可以实现比高阶常规算子更高的精度。与传统FD方案和基于Remez交换算法的FD方案相比，基于改进PSO算法的优化FD方案可以更有效地抑制数值色散，提高计算效率。色散分析和数值建模表明，低阶优化的 FD 方案可以实现比高阶常规算子更高的精度。与传统FD方案和基于Remez交换算法的FD方案相比，基于改进PSO算法的优化FD方案可以更有效地抑制数值色散，提高计算效率。色散分析和数值建模表明，低阶优化的 FD 方案可以实现比高阶常规算子更高的精度。与传统FD方案和基于Remez交换算法的FD方案相比，基于改进PSO算法的优化FD方案可以更有效地抑制数值色散，提高计算效率。