基于球谐变换及负荷响应解算地表三维形变  

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

作　　者：王希禾 陈雨[1] 刘慧玲 WANG Xi-he;CHEN Yu;LIU Hui-ling(College of Electronics and Information, Sichuan University, Chengdu 610065, China)

机构地区：[1]四川大学电子信息学院,成都610065

出　　处：《科学技术与工程》2021年第28期11963-11970,共8页Science Technology and Engineering

基　　金：四川大学社科研究项目(skbm201915)。

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,基于研究区域的数字高程模型(digital elevation model,DEM)数据创建平均水厚栅格矩阵,其空间分辨率可精确至1.1 km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。The large-scale migration of surface water reserves cause surface deformation in the surrounding area,and cause geolo-gical 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 was 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 was created based on the digital elevation model(DEM)data of the study area,and its spatial resolution can be accurate to about 1.1 km.Based on the load response theory,the average water thickness grid matrix was 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.

关 键 词：球谐函数 垂直形变 水平形变 负荷响应 数字高程模型(DEM)数据 

分 类 号：P237[天文地球—摄影测量与遥感]