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.