Abstract. 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.

Abstract. This paper considers the problem of reconstructing the velocities of ocean currents impinging on a towed streamer cable sparsely equipped with steering elements. The study is based on a two-dimensional model describing the quasi-steady motion of the towed cable in the presence of hydrodynamic drag and steering forces that depend nonlinearly on the angle of attack. To derive the proposed methodology we firstly outline the hydrodynamic equations used in solving the forward problem by which the cable's velocity, curvature and tension are obtained in the knowledge of the towing vessel's motion, the ocean current velocities and the drag coefficient characteristics of the steering elements. In sequence we formulate the inverse problem of inferring the ocean velocities using a finite set of noise-infused positioning and tension measurements showing that this is nonlinear and ill-posed. To solve the inverse problem we adopt Newton's scheme for nonlinear convex problems in conjunction with generalized Tikhonov regularization. The problem under consideration bares significant differences from the linear non-steered formulation addressed in (12), due to the nonlinearity in the forward method as well as the discontinuities observed in the forward measurements due to the steering forces. A series of numerical simulation studies is subsequently presented in order to demonstrate the practical performance of the proposed technique in reconstructing the ocean currents velocity profile and angle of attack.

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