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

Abstract

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 M2 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.

Deformation in the Northern Volcanic Zone of Iceland 2008–2014: An interplay of tectonic, magmatic, and glacial isostatic deformation

“…Insights can be gained from modeling results of the elastic response to surface loading. For the case of surface loads on a spherical Earth model, Martens et al [] show that Greens functions for vertical and horizontal surface displacements depend in a different manner on the Earth model and variations in its parameters. If a similar situation arises for the viscoelastic case, then a simplified Earth model fitting horizontal displacements may not necessarily fit equally well the vertical.…”

A comparison of predicted and observed ocean tidal loading in Alaska

“…Also of interest is using geodetic observations of OTL response to constrain allowable models for Earth structure (Ito & Simons 2011;Bos et al 2015;Martens et al 2016aMartens et al , 2019. The theory behind load-induced Earth deformation long predates the ability to measure deformation with sufficient accuracy (e.g.…”

“…Moreover, Martens et al (2016b) found similarities between predictions and observations even for the small-amplitude principal lunar fortnightly tide (M f ), although measurement uncertainties were larger in this frequency band than for the semidiurnal and diurnal tides. Sensitivity analyses of Earth's response to surface loading indicate peak sensitivities to structure within the crust and upper mantle (Ito & Simons 2011;Martens et al 2016a). As such, OTL-induced deformation provides a valuable opportunity to perform inversions for structure using geodetic data sets that are complementary to traditional seismic methods.…”

Downscaling Vertical GPS Observations to Derive Watershed‐Scale Hydrologic Loading in the Northern Rockies

“…Finally, we forward‐model load‐induced surface displacements using the LoadDef software (Martens, Simons, et al, ; Martens, Rivera, et al, ). The predicted displacements are generated by convolving a mass‐load model with load Green's functions that specify the response of a spherically symmetric, nonrotating, elastic, and isotropic Earth to a point‐load of unit mass (Farrell, ).…”