Inversion of seafloor topography in Emperor Seamount sea area by combined gravity anomalies and vertical gravity gradient anomalies data
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摘要: 海底地形对开展海洋科学调查和研究十分重要。以多波束为主的回声测深技术测量成本高且效率低，几十年来仅实现了全球约20%的海床测绘。对于空白区（特别是深海区域），可以借助重力异常和重力垂直梯度异常进行回归分析反演得到，但该方法得到的比例因子鲁棒性不强。为了解决这一问题，同时考虑到两种重力数据在表征海底地形长短波长的不同优势，本文结合滑动窗口赋权和稳健回归分析来反演海底地形。在太平洋皇帝山海域（35°～45°N，165°～175°E）的实验结果表明：在船测检核点处，本文构建模型的标准差为61.02 m，相比于单一重力数据反演模型，精度分别提高了14.92%（重力异常）和2.08%（重力垂直梯度异常），能较好地反映皇帝海山链的地形走势。Abstract: The topography of the seafloor is extremely important for marine scientific surveys and research. Echo-sounding technology, represented by multi-beam sounding, is costly and inefficient, and has only achieved about 20% of the world’s seabed mapping for decades. For the remaining void area, especially the deep ocean, it can be obtained by regression analysis using gravity anomalies and vertical gravity gradient anomalies, but the robustness of scale factor is poor. To address this issue, and considering the different advantages of the two kinds of gravity data in the characterization of the long and short wavelengths of the seafloor topography, a method which combining sliding window weighting and robust regression analysis was introduced in this paper. The experimental results in the Emperor Seamount in the Pacific Ocean (35°−45°N, 165°−175°E) indicate that: taking the ship test data as the checking condition, the standard deviation of the constructed model is 61.02 m, compared with the single gravity data inversion model, the accuracy was improved 14.92% (gravity anomalies) and 2.08% (vertical gravity gradient anomalies), which can better reflect the topographic trend of the Emperor Seamount Chain.
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图 4 反演波段重力数据与残余海深线性拟合结果
Fig. 4 Results of linear fitting between gravity data of inversion band and residual sea depth
图 5 重力垂直梯度异常模型权值xi分配示意图，相应的，重力异常模型的权值分配为1−xi
Fig. 5 The schematic diagram of weight distribution xi of vertical gravity gradient anomalies model. Accordingly, the weight distribution of gravity anomalies model is 1−xi
图 9 检核点处差值结果统计直方图
Fig. 9 Statistical histogram of the difference results at the check point
图 10 异常点空间位置分布图（黑色圆点代表异常点位）
Fig. 10 Spatial distribution map of outliers (black dots represent outliers)
表 1 海底地形模型与多波束数据差值统计结果
Tab. 1 Difference statistics of seafloor topographic model with multibeam data
模型 平均值/m 标准差/m 相关系数 SGA 166.54 462.98 0.948 3 SVG 128.76 402.27 0.956 1 MGM_LS 159.01 421.55 0.949 7 MGM 139.09 393.89 0.961 1 
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表 2 海底地形模型在检核点处差值统计结果
Tab. 2 Difference statistics of seafloor topographic model at check point
模型 最大值/m 最小值/m 平均值/m 标准差/m 相关系数 MGM 942.65 –895.09 0.64 61.02 0.998 0 DTU18 1 560.31 –1 110.94 7.74 95.41 0.996 6 V23.1 1 697.41 –2 148.33 10.46 95.52 0.996 6
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