Development of a High-Precision Deep-Sea Seabed Terrain Model Through Frequency Domain Weighted Fusion of Multi-Source Data: A Case Study in the Southern Waters of Greenland
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摘要: 融合卫星重力反演、船载声呐测深等多源数据是构建大范围深海高精度地形模型的核心技术途径。然而，当前方法通常难以兼顾局部地形细节和全局整体趋势，为此本文提出了一种基于多源数据频率域加权融合的深海高精度海底地形模型构建方法。首先，对多源数据进行数据格式转换、数据清洗与基准统一等预处理；然后，分别对测区对应的6个全球地形模型进行分频处理与加权融合，以局部船测地形与融合后模型的水深偏差为约束条件，迭代优化融合权重并得到初始融合结果；最后，联合局部船测地形与初始融合结果进行局部地形细节构建，从而实现大范围测区高精度地形模型重构。以格陵兰岛南部局部区域深海地形重构为例，结果表明：相比最邻近插值、反距离加权、自然邻近插值、克里金插值以及移去-恢复法等经典方法，本文方法构建的海底地形模型的均方根误差分别降低了17.15%、16.50%、16.63%、16.67%、9.99%，与IBCAO5.0模型之间的决定系数R2分别提高了约8.82%、8.27%、8.27%、8.41%、16.09%，地形整体趋势与局部细节信息均得到有效保证。Abstract: The fusion of multi-source data, such as satellite gravity inversion and shipboard sonar bathymetry, is the core technology for constructing large-scale high-precision deep-sea topographic models. However, existing methods are usually difficult to consider the local topographic details and global trends, so this paper proposes a method for constructing a high-precision seafloor topographic model of the deep sea based on the weighted fusion of multi-source data in the frequency domain. First, data format conversion, data cleaning and datum unification are performed on the multi-source data; then, the six global terrain models corresponding to the survey area are processed by frequency division and weighted fusion, and the fusion weights are iteratively optimized to obtain the initial fusion results with the constraints of the bathymetric deviation of the local ship's measured terrain and the fused model; finally, the local terrain details are constructed by combining the local ship's measured terrain and the initial fusion results, so as to realize the construction of a high-accuracy seabed topographic model over a wide range of survey areas. A case study in the southern part of Greenland Island was presented, and the results showed that the root-mean-square error (RMSE) of the seafloor topography model constructed by the proposed method significantly decreased, with RMSE 17.15%, 16.50%, 16.63%, 16.67%, and 9.99% lower than that of the nearest-neighbor interpolation, inverse-distance-weighted, natural-neighbor interpolation, kriging interpolation methods, and the remove-and-recovery method, respectively. The improvement in the coefficient of determination R2 with the IBCAO5.0 model was about 8.82%, 8.27%, 8.27%, 8.41% and 16.09%, respectively, and the information of the overall trend of the terrain and the local details are effectively guaranteed.
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图 2 研究区域对应的各个DBMs水深图
Fig. 2 Bathymetric map of various DBMs corresponding to the research area
图 6 不同小波基函数与分解层数下地形加权融合结果评价指标变化
Fig. 6 Changes in evaluation indicators for terrain weighted fusion results under different wavelet basis functions and decomposition levels
图 7 IBCAO4.0 (a)和IBCAO5.0 (b)水深图
Fig. 7 Bathymetric maps of IBCAO4.0 (a) and IBCAO5.0 (b)
图 8 不同方法构建的海底地形模型：a最近邻插值，b反距离加权，c自然邻近插值，d克里金插值，e移去-恢复法，f 本文方法
Fig. 8 Seafloor terrain models constructed by different methods: a Nearest neighbor interpolation, b Inverse distance weighting, c Natural neighbor interpolation, d Kriging interpolation, e Removal-recovery method, f This paper's method
图 9 不同方法构建的海底地形与IBCAO5.0之间水深偏差的分布统计
Fig. 9 Statistic of depth biases distribution between the seafloor topography model constructed by different methods and IBCAO5.0
图 11 本文方法构建的海底地形模型与各DBMs产品地形剖面对比
Fig. 11 Seabed profile comparison between the seafloor topographic model constructed by the proposed method and the different DBMs product
表 1 船测数据信息
Tab. 1 Information on ship survey data
序号 航次 调查年份 多波束仪器型号 航线总长（km） 调查船 1 EW9607 1996 Atlas Hydrosweep DS 11500 Maurice Ewing 2 KN158L5 1998 SeaBeam 2112 3565 Knorr 3 MSM43 2015 Simrad EM122 7661 Maria S. Merian 4 AT30-01 2015 Kongsberg EM122 2495 Atlantis 5 AR35-04 2019 Kongsberg EM122; Kongsberg EM710 15778 neil_armstrong 6 AR46 2020 Kongsberg EM122 2466 neil_armstrong 
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表 2 各DBMs基本信息
Tab. 2 Basic information of each DBMs
数据集 组织机构 国家 更新时间 分辨率 水平和垂直基准 数据来源 ETOPO2022 NCEI USA 2023 15″ WGS84 MSL https://www.ncei.noaa.gov/products/etopo-global-relief-model ETOPO1 NGDC USA 2009 1′ WGS84 MSL https://www.ngdc.noaa.gov/mgg/global GEBCO_2024 The Nippon
Foundation GEBCOUK-Japan 2024 15″ WGS84 MSL https://www.gebco.net/data_and_products/gridded_bathymetry_data/ SRTM15_V2.5.5 SIO USA 2019 15″ WGS84 MSL https://topex.ucsd.edu/pub/srtm15_plus/ SRTM30_PLUS SIO USA 2014 30″ WGS84 MSL https://topex.ucsd.edu/pub/srtm30_plus/ TOPO25.1 SIO USA 2023 1′ WGS84 MSL https://topex.ucsd.edu/pub/global_ topo_1min/
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表 3 船测水深数据与DBMs的空间相关矩阵
Tab. 3 The spatial correlation matrix between ship-measured bathymetry data and DBMs
ETOPO1 ETOPO2022 GEBCO_2024 船测水深 SRTM15_V2.5.5 SRTM30_PLUS TOPO25.1 ETOPO1 1.00 0.84 0.81 0.77 0.84 0.89 0.88 ETOPO2022 0.84 1.00 0.98 0.92 0.97 0.95 0.96 GEBCO_2024 0.81 0.98 1.00 0.93 0.96 0.94 0.95 船测水深 0.77 0.92 0.93 1.00 0.91 0.88 0.90 SRTM15_V2.5.5 0.84 0.97 0.96 0.91 1.00 0.96 0.99 SRTM30_PLUS 0.89 0.95 0.94 0.88 0.96 1.00 0.96 TOPO25.1 0.88 0.96 0.95 0.90 0.99 0.96 1.00
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表 4 不同DBMs与实测水深数据的定量评价 m
Tab. 4 Quantitative evaluation of different DBMs with measured bathymetric data m
序号 模型 最大值 最小值 平均值 标准差(SD) 平均绝对值(MAE) 均方根误差（RMSE） 决定系数（R2） ① ETOPO_2022 396.634 −708.507 −3.991 64.778 35.787 64.900 0.795 ② ETOPO1 523.911 − 1002.336 −3.895 103.392 65.520 103.466 0.410 ③ GEBCO2024 387.406 −700.447 −7.691 59.895 31.461 60.386 0.813 ④ IBCAO5.0 365.996 −689.815 2.210 59.082 30.830 60.067 0.815 ⑤ IBCAO4.0 347.352 −789.955 17.413 68.780 43.113 70.950 0.779 ⑥ SRTM15_V2.5.5 347.352 −789.955 17.412 68.780 43.113 70.950 0.779 ⑦ SRTM30_PLUS 456.037 −747.088 −5.658 76.649 46.116 76.857 0.721 ⑧ TOPO_25.1 344.422 −681.350 −6.577 71.505 40.634 71.807 0.702
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表 5 不同方法构建的海底地形模型定量评价 m
Tab. 5 Quantitative evaluation of seafloor topographic models constructed by different methods m
序号 方法 最大值 最小值 平均值 标准差（SD） 平均绝对值（MAE） 均方根误差（RMSE） 决定系数（R2） 1 最近邻 368.034 −695.890 −13.542 56.024 36.191 57.638 0.782 2 反距离加权 364.755 −688.920 −13.550 55.567 35.566 57.195 0.786 3 自然邻 368.681 −688.567 −13.481 55.674 35.769 57.283 0.786 4 克里金 369.137 −688.811 −13.571 55.680 35.848 57.310 0.785 5 移去-恢复 346.130 −232.950 −27.383 45.446 38.371 53.058 0.733 6 本方法 626.480 -689.820 6.229 47.338 26.749 47.755 0.851
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表 6 不同方法构建海底地形模型无实测多波束区域定量评价 m
Tab. 6 Quantitative evaluation of different methods to construct a seafloor topographic modelwithout measured multibeam areas m
序号 方法 最大值 最小值 平均值 标准差（SD） 平均绝对值（MAE） 均方根误差（RMSE） 决定系数（R2） 1 最近邻 346.131 −232.951 −27.150 45.3574 38.137 52.862 0.737 2 反距离加权 346.131 −232.951 −27.150 45.357 38.137 52.862 0.737 3 自然邻 346.131 −232.952 −27.107 45.407 38.147 52.883 0.737 4 克里金 346.131 −232.951 −27.150 45.357 38.137 52.862 0.737 5 移去-恢复 346.131 −232.951 −27.556 45.537 38.566 53.226 0.731 6 本方法 626.484 −143.509 9.844 28.641 21.473 30.286 0.914
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