A scheme to treat the singularity in global seismic wavefield simulation using pseudospectral method with staggered grids

The pseudospectral method has been applied to the simulation of seismic wave propagation in 2-D global Earth model. When a whole Earth model is considered, the center of the Earth is included in the model and then singularity arises at the center of the Earth where <i<r</i<=0 since the 1/<i<r</i< term appears in the wave equations. In this paper, we extended the global seismic wavefield simulation algorithm for regular grid mesh to staggered grid configuration and developed a scheme to solve the numerical problems associated with the above singularity for a 2-D global Earth model defined on staggered grid using pseudospectral method. This scheme uses a coordinate transformation at the center of the model, in which the field variables at the center are calculated in Cartesian coordinates from the values on the grids around the center. It allows wave propagation through the center and hence the wavefield at the center can be stably calculated. Validity and accuracy of the scheme was tested by compared with the discrete wavenumber method. This scheme could also be suitable for other numerical methods or models parameterized in cylindrical or spherical coordinates when singularity arises at the center of the model.