求解声波方程的径向基函数无网格法

地震勘探广泛应用于油气、煤田勘探。地震波场数值模拟是整个地震勘探数据处理技术的基石。将径向基函数（RBF）引入地震声波波场数值模拟中，在空间上用径向基函数无网格法来构造二阶导数，而在时间上采用简单的二阶差分公式，并重点讨论了形状参数c对该方法精度的影响，总结c经验取值范围为2~4倍平均数据点间距。设计不同模型，利用径向基函数无网格法进行声波波场模拟，并与空间四阶时间二阶的有限差分计算结果进行对比，结果表明：同样精度下，径向基函数每个波长所取的数据点数远小于空间四阶矩形网格有限差分每个波长所取的网格点数，即径向基函数的空间采样率更低，这表明径向基函数具有更小的数值频散。

Numerical solution of the acoustic wave equation using meshless method with radial basis functions

Seismic exploration has been widely used in oil and gas as well as coal exploration. Numeric modeling of the seismic wave field is the footstone of the overal seismic exploration technique. The paper, introducing the radial basis function(RDF) into the numeric modeling of seismic wave field, constructiong in space the second derivative by using the meshless method of the radial basis function, and in time domain using the simple second order difference formula, discussed emphatically the influence of the shape parameters(c) on the accuracy of the method, summed up the range of empirical value of c of 2~4 times of the avarage interval of data points. Different models were designed, sonic wave field was simulated by using meshless method of radial basis function, and compared with the calculation results of the finite difference in four order space and two order time. The results show that at the same accuracy the number of data points taken by each wave length of the radial basis function was much less than the mesh points taken by each wave length of finite difference of rectangular mesh of four order space, that is, the spatial sampling rate of the radial basis function was lower, suggesting that the radial basis function had smaller numerical dispersion.