A Spline Curve Fitting Model for Towed Streamer Positioning in Marine Seismic Exploration

The shape and position information of towed streamers is crucial for both implementing marine seismic exploration operations and analyzing exploration data. Streamer positioning accuracy directly impacts the quality and reliability of seismic imaging. Existing polynomial curve models exhibit deviations between the calculated and actual shapes during streamer turning. This paper proposes a segmented fitting positioning model based on spline curves. It is mathematically rigorous and applicable to complex scenarios. First, the specific function expression of the spline curve model is constructed. Then, using a cubic spline as an example, the segmented fitting method is explained, incorporating smoothness constraints at the connection points. The error equations for positioning observations and the calculation processes for curve parameters and hydrophone coordinates are derived. Finally, the model is verified through simulations and field tests. The experimental results show that, compared with the polynomial curve model, the spline curve model improves positioning accuracy by 47.1% in simulations involving six streamers and by 20.0% and 35.0% in field tests with six and ten streamers, respectively. In straight scenarios, both models perform similarly. Thus, the spline model can effectively reduce the modeling errors of the polynomial curve model under high-curvature conditions.