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A K-Means-Based Least Squares Collocation Method and Its Application in High-Precision Fitting and Estimation of Large-Scale Crustal Velocity Fields
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Cheng WANG1, Wei QU1, 2, *, Jiuyuan LI1, Xingyou TANG1, Guangyao WANG1, Kai YANG1
Journal of Geodesy and Geodynamics | 2025, 45(12) : 1294 - 1303
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Journal of Geodesy and Geodynamics | 2025, 45(12): 1294-1303
A K-Means-Based Least Squares Collocation Method and Its Application in High-Precision Fitting and Estimation of Large-Scale Crustal Velocity Fields
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Cheng WANG1, Wei QU1, 2, *, Jiuyuan LI1, Xingyou TANG1, Guangyao WANG1, Kai YANG1
Affiliations
  • 1 School of Geological Engineering and Geomatics, Chang'an University, 126 Yanta Road, Xi'an 710054, China
  • 2 Key Laboratory of Western China's Mineral Resources and Geological Engineering, Ministry of Education, 126 Yanta Road, Xi'an 710054, China
  • WANG Cheng, postgraduate, majors in geodetic inversion of crustal deformation, E-mail:

About Author:

WANG Cheng, postgraduate, majors in geodetic inversion of crustal deformation, E-mail:

Published: 2025-12-15 doi: 10.14075/j.jgg.2024.11.525
Outline
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To address the issues of abnormal and non-smooth fitting results in sparse monitoring station areas and block margins when using the traditional least squares collocation (TLSC) algorithm for high-precision fitting of crustal motion velocity fields in large-scale regions, a K-means clustering-based least squares collocation method (KLSC) is developed by integrating the K-means clustering algorithm with the TLSC algorithm. The effectiveness of this method is validated using the GNSS-measured crustal motion velocity field on the Qinghai-Xizang plateau. The results show that: 1) Compared to the TLSC algorithm, the KLSC algorithm leverages the advantages of the K-means algorithm in unsupervised classification to first divide the study area into multiple sub-regions with similar velocities based on the inherent characteristics of the GNSS velocity field, and then applies TLSC for velocity field fitting within each sub-region, thereby avoiding the impact of local complex geological environments on the accuracy of regional velocity field fitting; 2) The KLSC algorithm selects fitting parameters based on the proximity of each grid point to the cluster centers, resolving the issue of poor fitting results in data-sparse areas; 3) By utilizing secondary nearest-neighbor fitting combined with convolution filtering, the KLSC algorithm effectively addresses the non-smooth fitting results at block margins; 4) The RMSE accuracy and correlation of the velocity fields fitted by the KLSC algorithm are superior to those of the TLSC algorithm, with improvements in RMSE accuracy of 37% to 48.2% and 52.1% to 67.2%, and increases in correlation of 24.1% to 24.7% and 4.7% to 5.2% for the eastward and northward fitted velocity fields, respectively.

GNSS velocity field  /  least squares collocation method  /  K-means algorithm  /  Qinghai-Xizang plateau  /  smoothed crustal velocity field
王程, 瞿伟, 李久元, 唐兴友, 王光耀, 杨凯. 一种基于K-means聚类的最小二乘配置法及在大尺度地壳速度场高精度拟合推估中的应用. 大地测量与地球动力学, 2025 , 45 (12) : 1294 -1303 . DOI: 10.14075/j.jgg.2024.11.525
Cheng WANG, Wei QU, Jiuyuan LI, Xingyou TANG, Guangyao WANG, Kai YANG. A K-Means-Based Least Squares Collocation Method and Its Application in High-Precision Fitting and Estimation of Large-Scale Crustal Velocity Fields[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (12) : 1294 -1303 . DOI: 10.14075/j.jgg.2024.11.525
  • National Natural Science Foundation of China(42174006)
  • Science Fund for Distinguished Young Scholars of Shaanxi Province(2022JC-18)
  • Fundamental Research Funds for the Central Universities, CHD(300102263201)
Year 2025 volume 45 Issue 12
43
19
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Article Info
doi: 10.14075/j.jgg.2024.11.525
  • Receive Date:2024-11-18
  • Online Date:2026-10-29
  • Published:2025-12-15
Article Data
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History
  • Received:2024-11-18
Funding
National Natural Science Foundation of China(42174006)
Science Fund for Distinguished Young Scholars of Shaanxi Province(2022JC-18)
Fundamental Research Funds for the Central Universities, CHD(300102263201)
Affiliations
    1 School of Geological Engineering and Geomatics, Chang'an University, 126 Yanta Road, Xi'an 710054, China
    2 Key Laboratory of Western China's Mineral Resources and Geological Engineering, Ministry of Education, 126 Yanta Road, Xi'an 710054, China
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表12种不同金属材料的力学参数
科
Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)
属
Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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