求解声波方程的径向基函数无网格法  

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

作　　者：蒋婵君[1,2] 王有学[1,2] 李川[1] 曾高福[3] 贠鹏[1] JIANG Chanjun WANG Youxue LI Chuan ZENG Gaofu YUN Peng(College of Earth Science , Guilin University of Technology, Guilin 541006, China State Key Laboratory of Continental Tectonics and Dynamics, Beijing 100037, China China Nonferrous Metals（Guilin） Geology and Mining Co., Ltd.,Guilin 541004, China)

机构地区：[1]桂林理工大学地球科学学院,广西桂林541006 [2]大陆构造与动力学国家重点实验室,北京100037 [3]中国有色桂林矿产地质研究院有限公司,广西桂林541004

出　　处：《煤田地质与勘探》2016年第5期136-141,共6页Coal Geology & Exploration

基　　金：国家自然科学基金项目(41174077);大陆构造与动力学国家重点实验室开放基金项目(k201505)~~

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

关 键 词：径向基函数 声波方程 波场模拟 无网格法 

分 类 号：P631[天文地球—地质矿产勘探]