Fast marching methods (FMM), with unconditonal stability and high efficiency, has become one of the most prevalent algorithms for traveltime computation. However, finite-difference (FD) schemes adopted by the existing FMMs define the velocity and traveltime on the same grid system, which doesn’t conform to the physical process of ray propagation.

In this article, by defining the traveltime and velocity on two sets of staggered grid system, we construct a new rotated staggered-grid FD schemes to approximate the eikonal equation. FMM with this staggered-grid FD schemes (RSFMM) can archive higher accuracy than classical FMM with 1st-order and 2nd-order FD schemes. Furthermore, RSFMM calculates the traveltime with the velocity at the centre of grid points involved in the FD operator, which perfectly conforms to the physical process of ray propagation. Therefore, RSFMM has better applicability in complex medium. Considering the Spherical wave characteristics in the vicinity of the source point, we apply a combination scheme of spherical approximation method (SAM) and RSFMM (SAM+RSFMM) to further improve the accuracy. Numerical experiments on homogeneous, layered and Marmousi model approve the high accuracy and applicability in complex media of RSFMM and SAM+RSFMM.


Article metrics loading...

Loading full text...

Full text loading...


  1. Faria, E. & Stoffa, P.
    1994. Traveltime computation in transversely isotropic media. Geophysics59, 272–281.
    [Google Scholar]
  2. Hassouna, M.S. & Farag, A.A.
    2007. Multi-stencils fast marching methods: a highly accurate solution to the eikonal equation on cartesian domains. IEEE Trans Pattern Anal Mach Intell29, 1563–1574.
    [Google Scholar]
  3. Popovici, A.M. & Sethian, J.A.
    2002. 3‐D imaging using higher order fast marching traveltimes. Geophysics67, 604–609.
    [Google Scholar]
  4. Schneider, W., Ranzinger, K., Balch, A. & Kruse, C.
    1992. A dynamic programming approach to first arrival traveltime computation in media with arbitrarily distributed velocities. Geophysics57, 39–50.
    [Google Scholar]
  5. Sethian, J.A.
    1996. A fast marching level set method for monotonically advancing fronts. Proceedings of the National Academy of Sciences93, 1591–1595.
    [Google Scholar]

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error