Conclusions

The fast marching method of solving the eikonal equation is both unconditionally stable and extremely efficient. Both features are well demonstrated on the SEG/EAGE salt-dome model for both the Cartesian and spherical coordinate implementation of the fast marching method. However, the spherical-coordinate version provides more accurate direct-wave traveltimes than the Cartesian coordinate implementation. The only arrivals that suffer in the spherical-coordinate implementation are head-waves, which are not useful for imaging. Head-waves and fast-traveling salt penetrating waves are dominant in the traveltime solutions of the eikonal equation for the salt body model. These arrivals cause problems in imaging data above and beneath the salt in this medium.

 

errplhead Figure 8 Vertical section of the traveltime contour map resulted from solving the Spherical-coordinate fast marching method superimposed on a slice of the error field associated with the spherical-coordinate implementation (like Figure .

 

headwaves
Figure 9 Two-dimensional contour maps of the traveltime with sections of the velocity field displayed in the background and the salt body structure. Left: a semi-top view with the arrow pointing a head-wave. Right: a bottom view with arrows pointing to the portion of the wavefront that traveled through the salt, and thus has weak energy. Both waves, because of their first-arrival nature, have replaced the more useful direct waves.