Reverse-time migration is a well-known method based on single-scattering approximation and designed to obtain seismic images in the case of a complex sub-surface. It can however be a very time consuming task as the number of computations is directly proportional to the number of processed sources. In the context of velocity model building, iterative approaches require to derive a series of migrated sections for different velocity models. We propose to replace the summation over sources by a summation over time delays. For that, we provide a new relationship between two migrated sections obtained for two different velocity models: starting from one of the two migrated images, we show how the second section can be correctly and efficiently obtained. In practice, for each time delay, we compute a generalized source term by extending the concept of exploding reflector to non-zero offset. The final migrated section is obtained by solving the same wave equation in the perturbed model with the modified source term. We illustrate the methodology on a 2D synthetic data set, in particular when the initial and perturbed velocity models largely differ.