A discontinuous Galerkin method on triangular meshes for first-arrival traveltime and its extension to reflected PP/PS waves

Summary Accurate numerical computation of traveltimes is essential for seismic applications, including traveltime tomography and seismic imaging. Most existing numerical methods have been developed on rectangular grids, whose regular structure limits their ability to capture rugged topography and irregular subsurface interfaces. To address this limitation, we develop a fast sweeping method (FSM) combined with the discontinuous Galerkin (DG) method to efficiently calculate traveltimes on triangular meshes. In the proposed method, the FSM offers an efficient Gauss–Seidel iterative framework, whereas the DG method solves the eikonal equation with second-order accuracy. The combination of these two techniques enables efficient computation of transmitted-wave traveltimes in models with complex geometries. After computing the transmitted-wave traveltimes, those at the reflection interfaces are employed as the initial conditions to further compute the traveltimes of reflected PP and PS waves in the elastic medium. Numerical simulations confirm the validity and accuracy of the proposed method in handling models with complex geometry.