Elastic simulation method in an irregular polar coordinate system

When simulating the propagation of seismic waves in some special structures, such as tunnels and boreholes, finite difference forward modeling in the polar system has higher accuracy than the traditional Cartesian system. In actual situations, the polar space is the most irregular. To solve this problem, a forward modeling method for an irregular polar coordinate system is proposed to improve the simulation accuracy. First, an irregular surface of the polar space was meshed into an irregular polar system. After the transformation, the undulating surface was mapped into a plane one, and the wavefield was then computed in an irregular polar system. The Lebedev staggered grid was used to solve the wave equations in the irregular polar system. In addition, the artificial absorption boundary, cylindrical free boundary, and circumferential boundary conditions were used to absorb the boundary reflection. We selected three polar space models to demonstrate the new method in this study. The results show that the proposed elastic simulation method in an irregular polar coordinate system can produce more accurate and stable simulation results when modeling seismic wave propagation in an irregular polar space. Elastic full waveform inversion further shows that the irregular polar system elastic simulation method can accurately simulate the wavefield in an undulating polar space.