Robust and efficient upwind finite-difference traveltime calculations in three dimensions

First‐arrival traveltimes in complicated 3-D geologic media may be computed robustly and efficiently using an upwind finite‐difference solution of the 3-D eikonal equation. An important application of this technique is computing traveltimes for imaging seismic data with 3-D prestack Kirchhoff depth migration. The method performs radial extrapolation of the three components of the slowness vector in spherical coordinates. Traveltimes are computed by numerically integrating the radial component of the slowness vector. The original finite‐difference equations are recast into unitless forms that are more stable to numerical errors. A stability condition adaptively determines the radial steps that are used to extrapolate. Computations are done in a rotated spherical coordinate system that places the small arc‐length regions of the spherical grid at the earth’s surface (z = 0 plane). This improves efficiency by placing large grid cells in the central regions of the grid where wavefields are complicated, thereby...