On rewriting the imaging mechanism of underwater bottom topography by synthetic aperture radar as a Volterra series expansion

Ocean surface current gradients can be imaged by real and synthetic aperture radar (RAR/SAR) due to the so-called hydrodynamic modulation mechanism. This is the reason why underwater bottom topography and internal waves are visible on radar images. Several physical models exist for this imaging mechanism. When trying to obtain current information from SAR images, a problem arises: the imaging mechanism can be nonlinear. We propose to rewrite the classical modeling of the SAR underwater bottom topography imaging mechanism by using a Volterra series expansion. The Volterra model can be seen as a tool allowing us to study whether the imaging mechanism can be inverted or not. It is a transposition of a well-studied physical problem into a more explicit expression. The conditions for the inversion of the Volterra model are presented and a scheme for estimating the bathymetry from SAR images is described. The main property of the inversion algorithm is its independence from the physical model used for the mechanism.