We explicit a forward time domain WKBJ approximation of the wave equation such that the gradient of the associated data misfit function yields the classical Kirchhoff migration formula, up to a positive migration weight. As a by product of this elementary derivation, we find the optimal prefiltering of the data, and a set of optimal migration weights such that the corresponding Kirchhoff migrated sections are as close as possible to inverted sections. We propose a cooperative iterated Kirchhoff migration algorithm which illustrate the possibilities opened by this gradient approach to Kirchhoff migration.