Eikonal solvers in the Cartesian coordinates often suffer from source singularity due to the plane-wave assumption for the wavefront near the source point. Traveltime errors induced by the source singularity near the source point will spread to the whole domain and reduce the accuracy of subsequent traveltimes. The source singularity can be avoided if the eikonal equation is formulated and solved in the polar/spherical coordinates. However, the grid in the polar/spherical coordinates will cause sparse non-uniform resampling in the region far away from the source point after the traveltime is transformed back to the Cartesian mesh, hence reducing the uniform accuracy in this region. To deal with the source singularity and maintain uniform accuracy, we introduce a hybrid fast sweeping method that computes the traveltime near the source in the polar/spherical coordinates and computes the traveltime far away from the source in the Cartesian coordinates. The source singularity near the source point is resolved in the polar/spherical coordinates, and the uniform accuracy is achieved by switching to the Cartesian coordinates away from the source point. Numerical examples are presented to demonstrate the method.

由于源点附近波前的平面波假设，笛卡尔坐标中的 Eikonal 求解器经常遭受源奇异性的影响。源点附近的源奇点引起的走时误差会扩散到整个域，降低后续走时的准确性。如果在极坐标/球坐标中制定和求解 eikonal 方程，则可以避免源奇异性。但是，极/球坐标中的网格在将走时转换回笛卡尔网格后，会在远离源点的区域造成稀疏的非均匀重采样，从而降低该区域的均匀精度。为了处理源奇异性并保持一致的精度，我们引入了一种混合快速扫描方法，该方法在极坐标/球坐标中计算源附近的走时，并在笛卡尔坐标中计算远离源的走时。源点附近的源奇点在极坐标/球坐标中得到解决，通过切换到远离源点的笛卡尔坐标来实现统一的精度。给出了数值例子来演示该方法。