A Hybrid Harmonic Curve Model for Multi-Streamer Hydrophone Positioning in Seismic Exploration

Towed streamer positioning is a vital and essential stage in marine seismic exploration, and accurate hydrophone coordinates exert a direct and significant influence on the quality and reliability of seismic imaging. Current methods predominantly rely on analytical polynomial models for towed streamer positioning; however, these models often produce significant errors when fitting to streamers with high curvature, particularly during turning scenarios. To address this limitation, this study introduces a novel multi-streamer analytical positioning method that uses a hybrid harmonic function to model the three-dimensional coordinates of streamers. This approach mitigates the substantial modeling errors associated with polynomial models in high-curvature conditions and better captures the dynamic characteristics of streamer fluctuations. Firstly, the mathematical model for the hybrid harmonic function is constructed. Then, the algorithmic implementation of the model is detailed, along with the derivation of the error equation and the multi-sensor fusion solution process. Finally, the validity of the model is verified using both simulated and field data. The results demonstrate that, in the turning scenario without added error, the proposed harmonic model improves simulation accuracy by 35.5% compared to the analytical polynomial model, and by 27.2% when error is introduced. For field data, accuracy improves by 18.1%, underscoring the model's effectiveness in significantly reducing errors associated with polynomial models in turning scenarios. The performance of the harmonic function model is generally comparable to that of the polynomial model in straight scenarios.