Spatial variation in sound speed causes aberration in medical ultrasound imaging. Although our previous work has examined aberration correction in the presence of a spatially varying sound speed, practical implementations were limited to layered media due to the sound speed estimation process involved. Unfortunately, most models of layered media do not capture the lateral variations in sound speed that have the greatest aberrative effect on the image. Building upon a Fourier split-step migration technique from geophysics, this work introduces an iterative sound speed estimation and distributed aberration correction technique that can model and correct for aberrations resulting from laterally varying media. We first characterize our approach in simulations where the scattering in the media is known a-priori. Phantom and in-vivo experiments further demonstrate the capabilities of the iterative correction technique. As a result of the iterative correction scheme, point target resolution improves by up to a factor of 4 and lesion contrast improves by up to 10.0 dB in the phantom experiments presented.