Green's function at depth of borehole observation required for precise estimation of the effect of ocean tidal loading near coasts

Abstract

SUMMARY We calculated Green's functions of displacements and strains caused by a surface load in surface and subsurface observations. Green's functions of displacements and strains at depth became different from those at the surface for a range of angular distances less than 0.01–0.1°. These Green's functions closely agree with the corresponding Boussinesq approximations for tidal loading at angular distances of less than about 0.01–0.001°. We examined the difference between the ocean tidal loading effect estimated by Green's functions at the surface and the effect for subsurface observations, and found a non-negligible difference when the ratio of distance between the coast and observatory to the deployment depth is smaller than 20. We compared amplitudes and phase shifts of areal and shear strains in the M2 tidal constituent observed by borehole strainmeters at 11 observatories with the theoretical strains using the Green's functions at the deployment depth and those at the surface. The theoretical strains using Green's function at the deployment depth are much closer to the observed strains than theoretical strains at the surface at four observatories where the ratios of distance from the coast to the observatories to the deployment depth are small. These results suggest that Green's functions at the deployment depth are needed to estimate theoretical strains precisely near the coast.