基于球谐变换及负荷响应解算地表三维形变
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P237

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四川大学社科研究项目


Calculating 3D Surface Deformation Based on Spherical Harmonic Transformation and Load Response
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    摘要:

    地表水储量发生大幅度迁移时会引起周边区域的地表形变,严重时导致地质灾害的发生,因此对地表形变的监测预测具有重要意义。针对该现象提出一种基于球谐变换及负荷响应理论解算由于水体大幅变化引起的地表三维形变的方法。模拟以水体为质量中心的载荷模型时,基于研究区域的DEM数据创建平均水厚栅格矩阵,其空间分辨率可精确至1.1km左右。基于负荷响应理论将平均水厚栅格矩阵进行球谐展开,通过保留更高阶次的谐波信息,解算出更精确的地表三维形变及其时间序列。以三峡水库为实例进行方法验证,反演过程中等效水高的误差率可降低至0.742%,且垂直形变时间序列的趋势与负荷格林方法的解算结果具有较好的一致性。

    Abstract:

    The large-scale migration of surface water reserves will cause surface deformation in the surrounding area, and cause geological disasters in severe cases. Therefore, the monitoring and prediction of surface deformation is of great significance. Aiming at this phenomenon, a method based on spherical harmonic transformation and load response theory is proposed to solve the three-dimensional surface deformation caused by the large change of water body. When simulating a load model with a water body as the center of mass, a grid matrix of average water thickness is created based on the DEM data of the study area, and its spatial resolution can be accurate to about 1.1km. Based on the load response theory, the average water thickness grid matrix is expanded in spherical harmonics. By retaining the higher-order harmonic information, a more accurate three-dimensional surface deformation and its time series can be calculated. Taking the Three Gorges Reservoir as an example, the error rate of the equivalent water height in the inversion process can be reduced to 0.742%, and the trend of the vertical deformation time series is in good agreement with the results of the load Green method.

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王希禾,陈雨,刘慧玲. 基于球谐变换及负荷响应解算地表三维形变[J]. 科学技术与工程, 2021, 21(28): 11963-11970.
Wang Xihe, Chen Yu, Liu Huiling. Calculating 3D Surface Deformation Based on Spherical Harmonic Transformation and Load Response[J]. Science Technology and Engineering,2021,21(28):11963-11970.

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  • 收稿日期:2021-05-11
  • 最后修改日期:2021-07-07
  • 录用日期:2021-06-16
  • 在线发布日期: 2021-09-29
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