质量负荷引起地表形变的格林函数和球谐函数方法对比研究

Comparative Study of Green's Function and Spherical Harmonic Function Methods on Surface Deformation Caused by Mass Loading

固体地球对地表质量负荷响应,一般采用格林函数或球谐函数方法来计算。两者在数学上是等价的,在实际计算中存在差异。应用地表流体质量负荷变化数据,定量分析了二者在计算地表位移时的精度。结果表明,同一负荷作用下对单点地表位移的计算,两者的精度在误差水平上是一致的,其计算效率也是一致的;但在计算全球1°规则网格站点时,球谐函数方法要比格林函数方法在计算效率上快近100倍。对地表流体质量变化而言,2°空间网格的分辨率一般可满足改正GPS位移数据的精度,且地表流体引起的站点垂直位移变化可解释超过50%的GPS观测方差。

The response of the solid Earth＇s crust to mass loading on the Earth＇s surface usually can be computed by Green＇s Function or Spherical Harmonic Function methods.The two methods are equivalent in mathematics,but will give different crustal deformation results from the same surface loading.We thus use surface fluid mass change data to quantitatively analyze the precision of the two methods＇ results in calculating the crustal deformation on the Earth＇s surface.The results indicate that the crustal deformation precisions of both methods,in the level of observed GPS error,are consistent.The two methods also have the same calculation efficiency for single station crustal deformation.However,in calculating the crustal deformations of global 1°×1°grid sites,the efficiency of the spherical harmonic function method is nearly 100 times faster than that of Green＇s function method.For the surface fluid change data,only using 2°×2°spatial grid data will have enough accuracy to correct the crustal deformation of GPS stations.The vertical crustal deformation caused by surface fluid changes can explain more than 50% variance of that of GPS stations globally.