The sensitivity of surface mass loading displacement response to perturbations in the elastic structure of the crust and mantle

Surface mass loads generate a rich spectrum of deformation responses in the solid Earth that might be exploited to probe the material properties of the crust and mantle. Here we present a detailed examination of load-induced surface displacements and their sensitivities to systematic perturbations in elastic Earth structure. We compute Love numbers and displacement load Green's functions (LGFs) by integrating the equations of motion for spheroidal deformation of a radially heterogeneous and self-gravitating Earth. Sensitivity kernels are derived for individual Love numbers numerically using finite differences and quasi-analytically using calculus of variations. We then generate sensitivity kernels for displacement LGFs by systematically perturbing the preliminary reference Earth model. We find that displacement LGFs are most sensitive to elastic structural perturbations within 500 km depth from the surface and for short source-receiver distances. For separate perturbations to the shear modulus, bulk modulus, and density within the crust and mantle, the sensitivity kernels exhibit unique patterns, consistent with the possibility to constrain the parameters independently given a spatially distributed set of sufficiently accurate loading response observations. The sensitivity to density structure, however, is generally weak in comparison to elastic structure. We also examine the sensitivity of surface displacements caused by M-2 ocean tidal loading (OTL) to systematic perturbations in the elastic moduli and density. Since OTL-induced surface displacements are load and site dependent, we focus on high-resolution profiles across Iceland as a case study. The sensitivity kernels constitute a key element in the formulation of the inverse problem with application to geodetic tomography.