基于海洋声速剖面数据的多插值方法拟合及误差分析
Research on Fitting Degree and Error Analysis of Multi-Interpolation Method Based on Ocean Sound Velocity Profile Data
DOI: 10.12677/ams.2025.124025, PDF,   
作者: 孙月明：海军大连舰艇学院军事海洋与测绘系，辽宁 大连
关键词: 声学剖面数据；插值方法；误差分析；Acoustic Profile Data； Interpolation Method； Error Analysis
摘要: 本文基于某次海试测点CTD获得的声速剖面数据，利用拉格朗日插值、最优点插值、样条插值和kriging插值法，得到某测点的声剖曲线，与实测数据进行拟合，通过拟合曲线误差分析，得到各插值法处理海洋声剖数据的优缺点。拉格朗日插值易在跃层区过拟合，偏离实测值。最优点插值法通过增加龙格现象抑制，能有效减少振荡。样条插值法中B样条更适配浅水区，线性与三次样条可兼顾全水深，最近邻样条平滑性最差。kriging插值拟合的声速剖面曲线整体分布上表现更均匀，出现极端误差值的概率最低，但其局部精确度上弱于其他插值方法，累计误差高且均匀分布于各个深度。
Abstract: Based on the sound speed profile data obtained by CTD at a certain sea trial station, this study employs Lagrange interpolation, optimal point interpolation, spline interpolation, and Kriging interpolation to generate sound speed profile curves for the station. These curves are fitted with the measured data, and the advantages and disadvantages of each interpolation method in processing marine sound speed profile data are derived through fitting curve error analysis. Lagrange interpolation is prone to overfitting in the thermocline region, leading to deviations from the measured values. The optimal point interpolation method can effectively reduce oscillations by adding Runge phenomenon suppression. Among spline interpolation methods, B-spline is more suitable for shallow water areas, linear and cubic splines can balance the entire water depth, and nearest neighbor spline has the poorest smoothness. The sound speed profile curves fitted by Kriging interpolation show a more uniform overall distribution and the lowest probability of extreme error values, but their local accuracy is weaker than that of other interpolation methods, with high cumulative errors evenly distributed across all depths.
文章引用：孙月明. 基于海洋声速剖面数据的多插值方法拟合及误差分析[J]. 海洋科学前沿, 2025, 12(4): 238-247. https://doi.org/10.12677/ams.2025.124025

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