Factored singularities and high-order Lax-Friedrichs sweeping schemes for point-source traveltimes and amplitudes

In the high frequency regime, the geometrical-optics approximation for the Helmholtz equation with a point source results in an eikonal equation for traveltime and a transport equation for amplitude. Because the point-source traveltime field has an upwind singularity at the source point, all formally high-order finite-difference eikonal solvers exhibit first-order convergence and relatively large errors. In this paper, we propose to first factor out the singularities of traveltime, takeoff angles, and amplitudes, and then we design high-order Lax-Friedrichs sweeping schemes for pointsource traveltimes, takeoff angles, and amplitudes. Numerical examples are presented to demonstrate the performance of our new method.