Earth Structure, Ice Mass Changes, and the Local Dynamic Geoid

Abstract:

Spherical Slepian localization functions are a useful method for studying regional mass changes observed by satellite gravimetry. By projecting data onto a sparse basis set, the local field can be estimated more easily than with the full spherical harmonic basis. We have used this method previously to estimate the ice mass change in Greenland from GRACE data, and it can also be applied to other planetary problems such as global magnetic fields.

Earth's static geoid, in contrast to the time-variable field, is in large part related to the internal density and rheological structure of the Earth. Past studies have used dynamic geoid kernels to relate this density structure and the internal deformation it induces to the surface geopotential at large scales. These now classical studies of the eighties and nineties were able to estimate the mantle's radial rheological profile, placing constraints on the ratio between upper and lower mantle viscosity.

By combining these two methods, spherical Slepian localization and dynamic geoid kernels, 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 on a regional basis. First-order differences of the regional mantle viscosity structure are accessible to this technique.

In this contribution we present our latest, as yet unpublished results on the geographical and temporal pattern of ice mass changes in Antarctica over the past decade, and we introduce a new approach to extract regional information about the internal structure of the Earth from the static global gravity field. Both sets of results are linked in terms of the relevant physics, but also in being developed from the marriage of Slepian functions and geoid kernels. We make predictions on the utility of our approach to derive fully three-dimensional rheological Earth models, to be used for corrections for glacio-isostatic adjustment, as necessary for the interpretation of time-variable gravity observations in terms of ice sheet mass-balance studies.