Fourier prestack migration is reformulated through a change of variables, from offset wavenumber to a new equivalent wavenumber, which makes the migration phase shift independent of horizontal wavenumber. After the change of variables, the inverse Fourier transform over horizontal wavenumber can be performed to create unmigrated, but fully horizontally positioned, gathers at each output location. A complete prestack migration then results by imaging each gather independently with a poststack migration algorithm. This equivalent wavenumber migration (EWM) is the Fourier analog of the space‐time domain method of equivalent offset migration (EOM). The latter is a Kirchhoff time‐migration technique which forms common scatterpoint (CSP) gathers for each migrated trace and then images those gathers with a Kirchhoff summation. These CSP gathers are formed by trace mappings at constant time, and migration velocity analysis is easily done after the gathers are formed. Both EWM and EOM are motivated by the algebraic combination of a double square root equation into a single square root. This result defines equivalent wavenumber or offset. EWM is shown to be an exact reformulation of prestack f-k migration. The EWM theory provides explicit Fourier integrals for the formation of CSP gathers from the prestack data volume and the imaging of those gathers to form the final prestack migrated result. The CSP gathers are given by a Fourier mapping, at constant frequency, of the unmigrated spectrum followed by an inverse Fourier transform. The mapping requires angle‐dependent weighting factors for full amplitude preservation. The imaging expression (for each CSP gather) is formally identical to poststack migration with the result retained only at zero equivalent offset. Through a numerical simulation, the impulse responses of EOM and EWM are shown to be kinematically identical. Amplitude scale factors, which are exact in the constant velocity EWM theory, are implemented approximately in variable velocity EOM.
A scaling-less Newton-Raphson pipelined implementation for a fixed-point inverse square root operator