Earth Structure and the Dynamic Geoid: Beyond One-Dimensional Sensitivity Kernels

Earth's geoid betrays the signature of its viscosity and density structure through its response to internal and surface forces. Solving a simplified set of conservation equations, dynamic geoid kernels represent the geopotential and interface deformation resulting from an arbitrary internal density distribution. With a mantle density structure indirectly derived from seismological observations, the now classical studies of the eighties and nineties were able to estimate the mantle's radial rheological profile, comparing the observed geoid and the dynamic geoid resulting from the calculated internal flow globally. Undoubtedly, mantle rheology is not only a function of radius, but varies laterally as well. Using spherical Slepian localization functions we have created local dynamic geoid kernels which are sensitive only to density variations within an area of interest. With these kernels we can estimate the approximate local radial rheological structure that best explains the locally observed geoid. Although this technique is not sensitive to absolute viscosity, the best-fit ratio between upper and lower mantle viscosity can be determined on a region-by-region basis. First-order differences of the regional mantle viscosity structure should be accessible to this technique. In this contribution we present our new approach to extracting regional information about the internal structure of the Earth from the global gravity field in combination with tomographic earth models. We evaluate the nature and size of the remaining uncertainty, and make predictions on the utility of our approach to derive three-dimensional Earth models that can be used to make corrections for glacio-isostatic adjustment, as necessary for the interpretation of time-variable gravity observations in terms of ice sheet mass balance studies.