S U M M A R YThe rapid melting of the Earth's ice reservoirs will produce geographically distinct patterns of sea level change that have come to be known as sea level fingerprints. A basic, gravitationally self-consistent theory for computing these patterns appeared in the 1970s; however, recent, highly discrepant fingerprint calculations have led to suggestions that the algorithms and/or theoretical implementation adopted in many previous predictions is not robust. We present a suite of numerical predictions, including benchmark comparisons with analytic results, that counter this argument and demonstrate the accuracy of most published predictions. Moreover, we show that small differences apparent in calculations published by some groups can be accounted for by subtle differences in the underlying physics. The paper concludes with two sensitivity analyses: (1) we present the first-ever calculation of sea level fingerprints on earth models with 3-D variations in elastic structure and density, and conclude that this added complexity has a negligible effect on the predictions; (2) we compare fingerprints of polar ice sheet mass flux computed under the (very common) assumption of a uniform melt distribution to fingerprints calculated using melt geometries constrained by analysing recent trends in GRACE gravity data. Predictions in the near field of the ice sheets are sensitive to the assumed melt geometry; however, this sensitivity also extends to the far field, particularly in the case of Antarctic mass changes, because of the strong dependence of the rotational feedback signal on the melt geometry. We conclude that inferences of ice sheet mass flux based on modern sea level constraints should consider these more realistic melt geometries.

S U M M A R YWe describe and present results from a finite-volume (FV) parallel computer code for forward modelling the Maxwell viscoelastic response of a 3-D, self-gravitating, elastically compressible Earth to an arbitrary surface load. We implement a conservative, control volume discretization of the governing equations using a tetrahedral grid in Cartesian geometry and a low-order, linear interpolation. The basic starting grid honours all major radial discontinuities in the Preliminary Reference Earth Model (PREM), and the models are permitted arbitrary spatial variations in viscosity and elastic parameters. These variations may be either continuous or discontinuous at a set of grid nodes forming a 3-D surface within the (regional or global) modelling domain. In the second part of the paper, we adopt the FV methodology and a spherically symmetric Earth model to generate a suite of predictions sampling a broad class of glacial isostatic adjustment (GIA) data types (3-D crustal motions, long-wavelength gravity anomalies). These calculations, based on either a simple disc load history or a global Late Pleistocene ice load reconstruction (ICE-3G), are benchmarked against predictions generated using the traditional normal-mode approach to GIA. The detailed comparison provides a guide for future analyses (e.g. what grid resolution is required to obtain a specific accuracy?) and it indicates that discrepancies in predictions of 3-D crustal velocities less than 0.1 mm yr −1 are generally obtainable for global grids with ∼3 × 10 6 nodes; however, grids of higher resolution are required to predict large-amplitude (>1 cm yr −1 ) radial velocities in zones of peak postglacial uplift (e.g. James bay) to the same level of absolute accuracy. We conclude the paper with a first application of the new formulation to a 3-D problem. Specifically, we consider the impact of mantle viscosity heterogeneity on predictions of present-day 3-D crustal motions in North America. In these tests, the lateral viscosity variation is constructed, with suitable scaling, from tomographic images of seismic S-wave heterogeneity, and it is characterized by approximately 2 orders of magnitude (peak-to-peak) lateral variations within the lower mantle and 1 order of magnitude variations in the bulk of the upper mantle (below the asthenosphere). We find that the introduction of 3-D viscosity structure has a profound impact on horizontal velocities; indeed, the magnitude of the perturbation (of order 1 mm yr −1 ) is as large as the prediction generated from the underlying (1-D) radial reference model and it far exceeds observational uncertainties currently being obtained from space-geodetic surveying. The relative impact of lateral viscosity variations on predicted radial motions is significantly smaller.

We perform joint nonlinear inversions of glacial isostatic adjustment (GIA) data, including the following: postglacial decay times in Canada and Scandinavia, the Fennoscandian relaxation spectrum (FRS), late‐Holocene differential sea level (DSL) highstands (based on recent compilations of Australian sea level histories), and the rate of change of the degree 2 zonal harmonic of the geopotential, J2. Resolving power analyses demonstrate the following: (1) the FRS constrains mean upper mantle viscosity to be ∼3 × 1020 Pa s, (2) postglacial decay time data require the average viscosity in the top ∼1500 km of the mantle to be 1021 Pa s, and (3) the J2 datum constrains mean lower mantle viscosity to be ∼5 × 1021 Pa s. To reconcile (2) and (3), viscosity must increase to 1022–1023 Pa s in the deep mantle. Our analysis highlights the importance of accurately correcting the J2 observation for modern glacier melting in order to robustly infer deep mantle viscosity. We also perform a large series of forward calculations to investigate the compatibility of the GIA data sets with a viscosity jump within the lower mantle, as suggested by geodynamic and seismic studies, and conclude that the GIA data may accommodate a sharp jump of 1–2 orders of magnitude in viscosity across a boundary placed in a depth range of 1000–1700 km but does not require such a feature. Finally, we find that no 1‐D viscosity profile appears capable of simultaneously reconciling the DSL highstand data and suggest that this discord is likely due to laterally heterogeneous mantle viscosity, an issue we explore in a companion study.

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A gravitationally self-consistent, global sea level model with 3D viscoelastic Earth structure is interactively coupled to a 3D dynamic ice sheet model, and the coupled model is applied to simulate the evolution of ice cover, sea level changes, and solid Earth deformation over the last deglaciation, from 40 ka to the modern. The results show that incorporating lateral variations in Earth’s structure across Antarctica yields local differences in the modeled ice history and introduces significant uncertainty in estimates of both relative sea level change and modern crustal motions through the last deglaciation. An analysis indicates that the contribution of glacial isostatic adjustment to modern records of sea level change and solid Earth deformation in regions of Antarctica underlain by low mantle viscosity may be more sensitive to ice loading during the late Holocene than across the last deglaciation.