2-D fast sweeping method for the factored Eikonal equation and its improvement on inversion accuracy

Abstract

Curvature of wavefront is very large near source point. However, plane wavefront assumption is adopted when calculating traveltimes by use of finite-difference scheme. Therefore, source singularity problem exists for all finite-difference based eikonal solvers. Traveltime error caused by the source singularity can spread from source to the whole computational domain, and make traveltimes inaccurate. The factored eikonal equation can deal with source singularity very well. The fast sweeping method (FSM) is chosen to solve the factored eikonal equation in this article (factored FSM). In principle, it decomposes solution of general eikonal equation into product of two factors. The first factor can be calculated analytically or numerically, while the second factor is the underlying function. Eikonal solver plays a significant role in velocity inversion. An accurate and efficient eikonal solver can improve the effect of tomogram. The factored FSM is adopted in the following velocity inversion. Three evaluation criteria are defined to test accuracy and convergence of velocity inversion. The first method is the root-mean-square (RMS) of traveltime residuals. The second method is the percentage perturbation of inverted agaist initial velocity model. The third method is the percentage ratio of inverted against real velocity model. When inversion incorporating with the factored FSM, numerical examples show that: (1) RMS of traveltime residuals can converge to a smaller level, (2) percentage perturbation of inverted against initial velocity model is also smaller, (3) percentage ratio of inverted against real velocity model can reach up to a greater value.