Second-order interpolation of later-arrival traveltimes

The performance of a 3D prestack migration of the Kirchhoff type can be significantly enhanced if the computation of the required stacking surface is replaced by an efficient and accurate method for the interpolation of diffraction traveltimes. Thus, input traveltimes need only be computed and stored on coarse grids, leading to considerable savings in CPU time and computer storage. However, interpolation methods based on a local approximation of the traveltime functions fail in the presence of triplications of the wavefront or later arrivals. This paper suggests a strategy to overcome this problem by employing the coefficients of a hyperbolic traveltime expansion to locate triplications and correct for the resulting errors in the interpolated traveltime tables of first and later arrivals.