顾及海底地形非线性项的最小二乘配置反演方法

doi:10.11947/j.AGCS.2021.20200341

测绘学报 ›› 2021, Vol. 50 ›› Issue (7): 953-971.doi: 10.11947/j.AGCS.2021.20200341

顾及海底地形非线性项的最小二乘配置反演方法

范雕^1,2, 李姗姗², 欧阳永忠³, 孟书宇⁴, 陈成⁵, 邢志斌⁶, 张驰²

1. 地理信息工程国家重点实验室, 陕西西安 710054;
2. 信息工程大学地理空间信息学院, 河南郑州 450001;
3. 南京信息工程大学遥感与测绘工程学院, 南京 210044;
4. 32022部队, 湖北武汉 430074;
5. 海军工程大学导航工程系, 湖北武汉 430074;
6. 航天工程大学, 北京 102206

收稿日期:2020-07-22 修回日期:2021-02-10 发布日期:2021-08-13
通讯作者: 李姗姗 E-mail:zzy_lily@sina.com
作者简介:范雕(1991-),男,博士,研究方向为物理大地测量和空间化海洋测绘工程。E-mail:fandiao2311@mails.jlu.edu.cn
基金资助:
国家自然科学基金（41774021；41774018；41574020；41504018；41674026；41674082）；国家重点研发计划（2016YFB0501702）；地理信息工程国家重点实验室开放基金（SKLGIE2019-M-1-3）

Seafloor topography inversion using least square collocation considering nonlinear term

FAN Diao^1,2, LI Shanshan², OUYANG Yongzhong³, MENG Shuyu⁴, CHEN Cheng⁵, XING Zhibin⁶, ZHANG Chi²

1. State Key Laboratory of Geo-Information Engineering, Xi'an 710054, China;
2. Institute of Geospatial Information, Information Engineering University, Zhengzhou 450001, China;
3. School of Remote Sensing & Geomatics Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China;
4. Troops 32022, Wuhan 430074, China;
5. Department of Navigation, Naval University of Engineering, Wuhan 430033, China;
6. Space Engineering University, Beijing 102206, China

Received:2020-07-22 Revised:2021-02-10 Published:2021-08-13
Supported by:
The National Natural Science Foundation of China(Nos. 41774021;41774018;41574020;41504018;41674026;41674082);The National Key Research and Development Program of China(No. 2016YFB0501702);The State Key Laboratory of Geo-Information Engineering(No. SKLGIE2019-M-1-3)

摘要/Abstract

摘要： 针对目前常用的反演海底地形方法主要考虑海底地形和卫星测高重力数据线性趋势项而忽略非线性项影响现状，提出了顾及海底地形非线性项的最小二乘配置反演方法。选择日本海某海域作为目标海区，利用卫星测高重力异常和重力异常垂直梯度数据作为输入源进行了方法试算并构建了相应的海深模型，然后以实际船测海深作为外部检核参考，评估了反演模型效能，同时分析了反演模型频谱特征。目标海区试验结果表明：相较于本文仅仅考虑海底地形和重力数据线性趋势项采用最小二乘方法建立的海深模型，基于最小二乘配置方法，利用相同重力异常和重力异常垂直梯度数据获得的目标海区反演海深模型检核精度最低分别提高了大约2.5倍和3.5倍，相对精度最高分别提升了9.76%和13.07%，极大地提升了海底地形建模质量；采用本文方法建立的海底地形模型在研究海域表现良好，反演模型与S&S V18.1、ETOPO1、GEBCO和BAT_VGG模型在研究海域相关系数均达到了0.95以上；在研究海区本文模型检核精度与S&S V18.1相当，远远优于ETOPO1等海深模型；本文模型可有效改善船测海深相关波段信息（本文反演波段范围为15~160 km），其中重力异常垂直梯度构建的海深模型相比重力异常为输入源建立的海深模型改善船测海深相关波段信息更为明显，验证了本文方法的可行性和有效性。

关键词: 海底地形, 最小二乘配置, 重力异常, 重力异常垂直梯度, 非线性项

Abstract: The linear term of seafloor topography and satellite altimetry gravity data draws much attention and non-linear term tends to be ignored in current seafloor topography inversion. We proposed to use least square collocation (LSC) to estimate the linear term and non-linear term of seafloor topography and gravity data. A certain area in the sea of Japan was selected as the target sea area and corresponding bathymetry models were constructed by vertical gravity gradient anomaly (VGG) and gravity anomaly (GA) as the input data based on LSC. The accuracy of the inversion models was evaluated using shipboard sounding data as external checking points, and the spectral characteristics of the inversion models were analyzed. The results in the study area showed that the accuracy of the inversion models derived by the same GA and VGG based on LSC was improved by 2.5 times and 3.5 times at least, the relative accuracy was improved by 9.76% and 13.07%, compared with the least-square bathymetry models which only consider the linear term of seafloor topography and gravity data in the paper, which indicated that LSC greatly improved the quality of bathymetry inversion. The correlation coefficients between the inversion models and some other models, i. e. S&S V18.1, ETOPO1, GEBCO and BAT_VGG, were all above 0.95, which verifies the validity of the method (LSC) in the study area. The accuracy of the models by LSC was similar to S&S V18.1 and much higher than ETOPO1 and other bathymetry models in the study area. The inversion models could improve the relevant band information of ship measuring data effectively. The bathymetry models derived by VGG improved the relevant band information of shipboard sounding data more obviously than the bathymetry models by GA (the range of inversion waveband was 15 km to 160 km). In summary, the results in the study area verified the LSC’s feasibility and effectiveness.

Key words: seafloor topography, least square collocation, gravity anomaly, vertical gravity gradient anomaly, nonlinear term

中图分类号:

P229

范雕, 李姗姗, 欧阳永忠, 孟书宇, 陈成, 邢志斌, 张驰. 顾及海底地形非线性项的最小二乘配置反演方法[J]. 测绘学报, 2021, 50(7): 953-971.

FAN Diao, LI Shanshan, OUYANG Yongzhong, MENG Shuyu, CHEN Cheng, XING Zhibin, ZHANG Chi. Seafloor topography inversion using least square collocation considering nonlinear term[J]. Acta Geodaetica et Cartographica Sinica, 2021, 50(7): 953-971.

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顾及海底地形非线性项的最小二乘配置反演方法

Seafloor topography inversion using least square collocation considering nonlinear term

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