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To carry out a 3D prestack migration of the Kirchhoff type is still a task of enormous computational effort. Its efficiency can be significantly enhanced by employing a fast traveltime interpolation algorithm. High accuracy can be achieved if second‐order spatial derivatives of traveltimes are included in order to account for the curvature of the wavefront. We suggest a hyperbolic traveltime interpolation scheme that permits the determination of the hyperbolic coefficients directly from traveltimes sampled on a coarse grid, thus reducing the requirements in data storage. This approach is closely related to the paraxial ray approximation and corresponds to an extension of the well‐known method to arbitrary heterogeneous and complex media in 3D. Application to various velocity models, including a 3D version of the Marmousi model, confirms the superiority of our method over the popular trilinear interpolation. This is especially true for regions with strong curvature of the local wavefront. In contrast to trilinear interpolation, our method also provides the possibility of interpolating source positions, and it is 5–6 times faster than the calculation of traveltime tables using a fast finite‐difference eikonal solver.

Multiparameter stacking is an important tool to obtain a first reliable time image of the subsurface. In addition, it provides wavefield attributes, which form the basis for many important applications. The quality of the image and the attribute estimates relies heavily on the accuracy of the traveltime moveout description. The commonly used hyperbolic common-reflectionsurface (CRS) operator reduces to the NMO hyperbola in the common-midpoint gather. Its accuracy, however, depends on the curvature of the reflector under consideration. The conventional multifocusing (MF) operator, a time-shifted doublesquare-root expression, leads to good results for high reflector curvatures and moderate inhomogeneities of the overburden.We used a new implicit CRS formulation that combines the robustness of CRS regarding heterogeneities with the high sensitivity to curvature of the MF approach. It assumes reflectors to be locally circular and can be applied in an iterative fashion. For simple but common acquisition and subsurface configurations, the new traveltime expression reduces to familiar formulas. Quantitative studies revealed that the new operator performs equally well over the full range of curvatures even in the presence of strong heterogeneities, while providing higher accuracy than the conventional CRS and MF methods. In addition, its application resulted in more reliable attribute estimates and an improved time-migrated section. Comparison of stacking and migration results for the complex synthetic Sigsbee 2a data set confirmed the potential of the suggested approach.

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