A Multiple 1D Earth Approach (M1DEA) to account for lateral viscosity variations in solutions of the sea level equation: An application for glacial isostatic adjustment by Antarctic deglaciation

The pseudo-spectral form of the sea level equation (SLE) requires the approximation of a radially-symmetric visco-elastic Earth. Thus, the resulting predictions of sea level change (SLC) and glacial isostatic adjustment (GIA) often ignore lateral variations in the Earth structure. Here, we assess the capabilities of a Multiple 1D Earth Approach (M1DEA) applied to large-scale ice load components with different Earth structures to account for these variations. In this approach the total SLC and GIA responses result from the superposition of individual responses from each load component, each computed globally assuming locally-appropriate 1D Earth structures. We apply the M1DEA to three separate regions (East Antarctica, West Antarctica, and outside Antarctica) to analyze uplift rates for a range of Earth structures and different ice loads at various distances. We find that the uplift response is mostly sensitive to the local Earth structure, which supports the usefulness of the M1DEA. However, stresses transmitted across rheological boundaries (e.g., producing peripheral bulges) present challenges for the M1DEA, but can be minimized under two conditions: (1) If the considered time period of ice loading for each component is consistent with the relaxation time of the local Earth structure. (2) If the load components can be subdivided according to the scale of the lateral variations in Earth structure. Overall, our results indicate that M1DEA could be a computationally much cheaper alternative to 3D finite element models, but further work is needed to quantify the relative accuracy of both methods for different resolutions, loads, and Earth structure variations.