As the key point of full-waveform inversion (FWI), numerical solution of wave equation is required to simulate the forward propagated and adjoint wavefield. When traditional regular grids are used for forward modelling, scattering artifacts may occur due to the stepped approximation of layer interfaces and rugged topography. Unstructured mesh or irregular grids method can achieve certain geometric flexibility, however, its algorithm is quite complex. Mesh-free FWI can effectively reduce the scattered artifacts under regular grids and avoid the extra computation in the process of irregular grids generation. For the implementation of mesh-free FWI method, an algorithm with fast generation of node distributions is used to discretize the velocity model, radial-basis function generated finite difference is used to realise seismic wave propagation numerical simulation, and Limited-memory BFGS (L-BFGS) algorithm is used for iteration. The mesh-free FWI method we proposed achieves flexibility of simulation region and abundant wavefield information. It reduces the storage required for FWI and illustrates the applicability of high-precision reconstruction of underground velocity in the case of rugged topography, which can provide more accurate velocity information for oil and gas exploration under complex geological conditions.

作为全波形反演（FWI）的关键点，需要通过波动方程的数值解来模拟正向传播和伴随波场。当使用传统的规则网格进行正向建模时，由于层界面的阶梯式近似和崎岖的地形，可能会出现散射伪影。非结构化网格或不规则网格方法可以实现一定的几何灵活性，但其算法相当复杂。无网格 FWI 可以有效减少规则网格下的散乱伪影，避免不规则网格生成过程中的额外计算。为了实现无网格 FWI 方法，采用快速生成节点分布的算法对速度模型进行离散化，利用径向基函数生成的有限差分实现地震波传播数值模拟，并采用有限记忆BFGS（L-BFGS）算法进行迭代。我们提出的无网格FWI方法实现了模拟区域的灵活性和丰富的波场信息。减少了FWI所需的存储量，说明了在崎岖地形情况下高精度重建地下速度的适用性，可为复杂地质条件下的油气勘探提供更准确的速度信息。