An efficient hybrid mesh method for seismic traveltime computation with irregular surfaces

Accurate and efficient traveltime computation with irregular surfaces is a prerequisite for traveltime tomography, seismic location, and seismic exploration in mountainous areas. The eikonal equation method is computationally favourable and has gained increasing popularity for obtaining traveltime in recent years. Nowadays most algorithms that can solve eikonal equation with irregular surfaces are based on fully unstructured triangular mesh or surface-fitting mesh. However, these methods have poor performance in terms of computational cost and accuracy. To cope with this problem, we develop a hybrid mesh method based on fast-sweeping-based eikonal solver with rectangular and unstructured triangular mesh for obtaining traveltime with irregular surfaces. In other words, we propose to divide the model into several different regions, which are discretized by rectangular mesh and unstructured triangular mesh respectively. Near the irregular surfaces of model, we use fast sweeping method based on unstructured triangular mesh which releases the full potential of unstructured triangular mesh's flexibility in accurately describing the irregular geometry of computation domain. For the rest part of the model, we adopt rectangular mesh to make full use of high efficiency of the corresponding high-order fast sweeping algorithm. At the interface of two types of mesh, we need interpolate the known nodes's traveltimes to get the boundary condition of another mesh, so as to start the fast sweeping method therein. It is found that the accuracy of hybrid mesh method can be increased by 83%, the computation time is reduced by 72%, and the storage requirement is reduced by 72%, compared with the fast sweeping method with full triangular mesh, when the rectangular mesh proportion is 80% in our model. Therefore, this proposed hybrid mesh method can greatly enhance the computational efficacy and serve as an potential forward engine in seismic inversions.