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

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.