18. 3D VTI Eikonal Solver for Efficient Acoustic Travel-Time Computation

Abstract

Travel-time computation is efficiently achieved through direct numerical resolu- tion of the eikonal equation on a 3D computational grid. Efficiency may even be improved when solving the eikonal equation using an appropriate transformation called transforma- tion in the celerity domain. Neglecting the effects of anisotropy in the calculation of travel- time maps leads inevitably either to incorrect focusing or positioning of seismic events during the seismic imaging process. Thus, in the present paper, we propose to extend effi- cient P-wave travel-time computation to the simplified case of Vertical Transverse Iso- tropic (VTI) media, which is nevertheless of the most interest in surface reflection seismic. Based on an acoustic explicit eikonal equation for VTI media, the calculation of quasi-P travel times with our numerical resolution method in the celerity domain proves to be par- ticularly efficient, stable and accurate. In line with seismic contractor needs, we propose a parameterization, which is based on anisotropy effects, for the quasi-P VTI model used by the eikonal solver. The three independent anisotropic parameters are the NMO velocity as- sociated with short-spread curvatures, an ellipticity parameter equivalent to the ratio be- tween vertical and NMO velocities, and finally the well-known anellipticity parameter η, governing the long offset behavior of NMO curves.