Finite difference in the polar coordinate system with irregular topography

The finite difference method (FDM) is an important numerical tool in seismological research. The application of the traction free surface boundary condition is a key issue in the FDM. For the Cartesian coordinate system FDM, when irregular topography exists, the traction image method can satisfy the traction free condition with high accuracy and high efficiency. For seismic wave modeling on regional or global scales, the effect of Earth' s curvature must be considered. In this case, the polar coordinator system FDM is more convenience, but the existing method cannot calculate the effect of topography accurately. In this work we introduce a boundary confirm grid and a traction image method into the polar coordinate system FDM to solve this problem. Several numerical tests confirm the validity of our work.