This work is concerned with the estimation of radial velocities of sea surface elevations. The data, is a noisy along-track interferometric synthetic aperture radar (AT-INSAR) image. We assume the Velocity Bunching Model. This model relates the complex AT-INSAR image at a point in the image plane, with the radial velocity of a scatterer point in the sea surface. The relation is by means of a nonlinear integral operator mapping radial velocities into AT-INSAR images. Consequently, the estimation of radial velocities, amounts to the solution of nonlinear integral equations. Our proposal is to solve the latter by Newton's methods on function spaces, the optimize then discretize approach. We show that this continuous version is accurate, and faster than the classical discretize then optimize version. Also a physical comparison is carried out with the interferometric velocities.