Based on the chaining of diffraction-stack migration and isochron-stack demigration, we derive a general true-amplitude Kirchhoff-type single-stack operator for 3D and 2.5D redatuming. It consists of performing a single weighted stack along adequately chosen stacking surfaces or lines. The corresponding traveltimes and weight functions can be calculated using quantities obtained from dynamic ray tracing. The operator simplifies when specified for zero-offset data. For simple types of media, we derive analytic expressions for the stacking lines and weight functions and demonstrate their functionality with numerical examples. © 2014 Elsevier B.V.105 95111Berryhill, J.R., Wave-equation datuming (1979) Geophysics, 44, pp. 1329-1344Berryhill, J.R., Wave equation datuming before stack (1984) Geophysics, 49 (11), pp. 2064-2067Bevc, D., (1995) Imaging Under Rugged Topography and Complex Velocity Structure, , (Ph.D. dissertation), Stanford UniversityBeylkin, G., Imaging of discontinuities in the inverse scattering problem by inversion of a generalized Radon transform (1985) J. Math. Phys., 26 (1), pp. 99-108Bleistein, N., (1984) Mathematical Methods for Wave Phenomena, , Academic Press, New YorkBleistein, N., Two-and-one-half dimensional in-plane wave propagation (1986) Geophys. Prospect., 34, pp. 686-703Bleistein, N., On the imaging of reflectors in the earth (1987) Geophysics, 52, pp. 931-942Červený, V., de Castro, M.A., Application of dynamic ray tracing in the 3-D inversion of seismic reflection data (1993) Geophys. J. Int., 113, pp. 776-779Hanitzsch, C., Schleicher, J., Hubral, P., True-amplitude migration of 2D synthetic data (1994) Geophys. Prospect., 42 (5), pp. 445-462Hubral, P., Krey, T., Interval velocities from seismic reflection time measurements (1980) Soc. Expl. Geophys., Tulsa, OK, , K. Larner (Ed.)Hubral, P., Schleicher, J., Tygel, M., Three-dimensional paraxial ray properties - part II. Applications (1992) J. Seism. Explor., 1 (4), pp. 347-362Hubral, P., Schleicher, J., Tygel, M., A unified approach to 3-D seismic reflection imaging - part I: Basic concepts (1996) Geophysics, 61 (3), pp. 742-758Martins, J., Schleicher, J., Tygel, M., Santos, L.T., 2.5-D true-amplitude Kirchhoff migration and demigration (1997) J. Seism. Explor., 6 (2-3), pp. 159-180Schleicher, J., Tygel, M., Hubral, P., 3-D true-amplitude finite-offset migration (1993) Geophysics, 58 (8), pp. 1112-1126Schleicher, J., Tygel, M., Hubral, P., (2007) Seismic True-amplitude Imaging. No. 12 in Geophysical Developments, , SEGSchneider, W.A., Phillip, L.D., Paal, E.F., Wave-equation velocity replacement of the low-velocity layer for overthrust-belt data (1995) Geophysics, 60, pp. 573-580Schuster, G.T., Zhou, M., A theoretical overview of model-based and correlation-based redatuming methods (2006) Geophysics, 71 (4), pp. SI103-SI110Sheriff, R.E., Factors affecting seismic amplitudes (1975) Geophys. Prospect., 23, pp. 125-138Tegtmeier, S., Gisolf, A., Verschuur, E., 3D sparse data Kirchhoff redatuming (2004) Geophys. Prospect., 52 (6), pp. 509-521Tygel, M., Schleicher, J., Hubral, P., Pulse distortion in depth migration (1994) Geophysics, 59, pp. 1561-1569Tygel, M., Schleicher, J., Hubral, P., Dualities involving reflectors and reflection-time surfaces (1995) J. Seism. Explor., 4, pp. 123-150Tygel, M., Schleicher, J., Hubral, P., A unified approach to 3-D seismic reflection imaging - part II: theory (1996) Geophysics, 61 (3), pp. 759-775Tygel, M., Schleicher, J., Hubral, P., Santos, L.T., 2.5D true-amplitude Kirchhoff migration to zero offset in laterally inhomogeneous media (1998) Geophysics, 63 (2), pp. 557-573Wapenaar, C.P.A., Kirchhoff-Helmholtz downward extrapolation in a layered medium with curved interfaces (1993) Geophys. J. Int., 115, pp. 445-455Wapenaar, C.P.A., Cox, H.L.H., Berkhout, A.J., Elastic redatuming of multicomponent seismic data (1992) Geophys. Prospect., 40 (4), pp. 465-482Wiggins, J.W., Kirchhoff integral extrapolation and migration of nonplanar data (1984) Geophysics, 49, pp. 1239-1248Yilmaz, O., Lucas, D., Prestack layer replacement (1986) Geophysics, 51, pp. 1355-1369