李贤炮, 钟波, 刘滔. GNSS垂直位移反演区域地表质量变化的模拟分析[J]. 武汉大学学报 ( 信息科学版), 2022, 47(1): 45-54. DOI: 10.13203/j.whugis20190257
引用本文: 李贤炮, 钟波, 刘滔. GNSS垂直位移反演区域地表质量变化的模拟分析[J]. 武汉大学学报 ( 信息科学版), 2022, 47(1): 45-54. DOI: 10.13203/j.whugis20190257
LI Xianpao, ZHONG Bo, LIU Tao. Simulation Analysis of Inverting Regional Surface Mass Variations Using GNSS Vertical Displacement[J]. Geomatics and Information Science of Wuhan University, 2022, 47(1): 45-54. DOI: 10.13203/j.whugis20190257
Citation: LI Xianpao, ZHONG Bo, LIU Tao. Simulation Analysis of Inverting Regional Surface Mass Variations Using GNSS Vertical Displacement[J]. Geomatics and Information Science of Wuhan University, 2022, 47(1): 45-54. DOI: 10.13203/j.whugis20190257

GNSS垂直位移反演区域地表质量变化的模拟分析

Simulation Analysis of Inverting Regional Surface Mass Variations Using GNSS Vertical Displacement

  • 摘要: 连续密集的全球导航卫星系统(global navigation satellite system, GNSS) 地表形变监测为反演精细的区域地表质量变化提供了有效技术手段。针对格林函数方法反演区域地表质量变化的病态问题,给出了一种改进的正则化拉普拉斯约束矩阵,讨论了广义交叉检验(generalized cross-validation, GCV)方法在病态法方程正则化参数选取中的适应性,并通过数值模拟分析了GNSS垂直位移的噪声水平和测站数量及分布对反演结果的影响。结果表明:(1)给出的正则化拉普拉斯矩阵相比传统的拉普拉斯矩阵能更有效抑制边缘效应的影响;(2)GCV方法可以有效地确定最优正则化参数,其反演结果与均方根误差(root mean square error, RMSE)最小方法的反演结果符合较好;(3)GNSS垂直位移的噪声水平越小, 测站数越多,反演结果越好,并且在测站数达到一定的条件下,均匀分布测站与随机分布测站的反演结果精度相当。

     

    Abstract:
      Objectives  Continuous and dense global navigation satellite system (GNSS) surface deformation data provide an effective tool to invert refined regional surface mass variations. However, the factors influencing the reliability of GNSS inversion results need to be further studied, such as regularization (includ‍ing the construction of regularization matrix and determination of optimal regularization parameter), observation noise and distribution of GNSS stations.
      Methods  First, we proposed an improved regularized Laplacian constraint matrix and discussed the adaptability of the generalized cross-validation (GCV) method in selecting the regularization parameter of ill-posed equations for inversion of regional surface mass variations based on the loading Green's function theory. Second, we compared the effects of different constraint matrices and constraint methods on the GNSS inversion results. Third, we further investigated the influ‍enc‍es of different noise levels of GNSS vertical displacement, the number and distribution of GNSS stations on the inversion results.
      Results  (1) The regularized Laplacian matrix in this paper can better suppress the edge effects than the traditional Laplacian matrix. (2) The GCV method can effectively determine the optimal regularization parameter, and the inversion results are in good agreement with those solved by the root mean square error (RMSE) criterion. (3) If there are enough GNSS stations and the observation accuracy is high enough in the studied area, the inversion results will be more reliable. Meanwhile, the accuracy of inversion results for uniformly distributed stations is comparable to that of randomly distributed stations when the number of stations is large enough.
      Conclusions  The improved regularized Laplacian matrix and the GCV method can improve the reliability of GNSS inversion results, which can guide the inversion of surface mass variations using measured GNSS data.

     

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