We propose an iterative method for the linearized prestack inversion of seismic profiles based on the asymptotic theory of wave propagation. For this purpose, we designed a very efficient technique for the downward continuation of an acoustic wavefield by ray methods. The different ray quantities required for the computation of the asymptotic inverse operator are estimated at each diffracting point where we want to recover the earth image. In the linearized inversion, we use the background velocity model obtained by velocity analysis. We determine the short wavelength components of the impedance distribution by linearized inversion of the seismograms observed at the surface of the model. Because the inverse operator is not exact, and because the source and station distribution is limited, the first iteration of our asymptotic inversion technique is not exact. We improve the images by an iterative procedure. Since the background velocity does not change between iterations, there is no need to retrace rays, and the same ray quantities are used in the iterations. For this reason our method is very fast and efficient. The results of the inversion demonstrate that iterations improve the spatial resolution of the model images since they mainly contribute to the increase in the short wavelength contents of the final image. A synthetic example with one-dimensional (1-D) velocity background illustrates the main features of the inversion method. An example with two-dimensional (2-D) heterogeneous background demonstrates our ability to handle multiple arrivals and a nearly perfect reconstruction of a flat horizon once the perturbations above it are known. Finally, we consider a seismic section taken from the Oseberg oil field in the North Sea off Norway. We show that the iterative asymptotic inversion is a reasonable and accurate alternative to methods based on finite differences. We also demonstrate that we are able to handle an important amount of data with presently available computers.