Forward and inverse problems in towed cable hydrodynamics

This paper addresses the problem of reconstructing the velocities of the ocean currents impinging on a towed streamer cable during an offshore seismic survey. This study considers a two-dimensional model describing the motion of a flexible, inextensible cable in the presence of hydrodynamic drag forces in an incompressible fluid. In the first part the forward model is introduced and then solved to yield the cable's velocity, curvature and tension in the knowledge of the towing vessel motion and the hydrodynamic loads applied. In sequence, we formulate the inverse problem of inferring the ocean current velocities from discrete samples of the cable's shape and tension and show that this is rank deficient and ill-posed. In approaching the inverse problem a numerically stable algorithm is adopted based on generalized Tikhonov regularization, in the context of robust differentiation of discrete noisy signals. In order to demonstrate the practical performance of the scheme, some examples of ocean current reconstructions obtained using simulated noisy data are presented.