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

Authors:
Songting Luo;Jianliang Qian
Affiliations:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA;Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Venue:
Journal of Computational Physics
Year:
2011

Citing 9
Cited 1

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Abstract

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 traveltimes, takeoff angles, and amplitudes, and then we design high-order Lax-Friedrichs sweeping schemes for point-source traveltimes, takeoff angles, and amplitudes. Numerical examples are presented to demonstrate the performance of our new method.