  We mainly concerned with a decoupled fractional Laplacian wave equation in
this paper. A new time-space domain radial basis function (RBF) collocation
method is introduced to solve the fractional wave equation, which describes
seismic wave propagation in attenuation media. The directional fractional
Laplacian is adopted to cope with the fractional Laplacian of RBFs. In order to
increase the computational efficiency, we introduced the quasi-uniform nodes
configuration scheme, which is suitable for mesh-free discretization of wave
equations. The comparison between the new method and the commonly-used
pseudo-spectral method are implemented on square homogeneous models with
different model size. The CPU time and relative errors of different methods
show that the quasi-uniform configuration scheme provides better performance
and the calculation efficiency advantage is significantly prominent as the
computation domain increases. The relative errors indicate that the RBF
collocation method with quasi-uniform configuration could improve the
computational efficiency effectively and provide satisfactory accuracy. This
advantage was especially highlighted in complex models, where the new approach
achieved the same accuracy with only a half number of points. The
implementation on the 2D complex model further demonstrated the accuracy,
efficiency, and flexibility of the proposed new method.
