GIA imaging of 3-D mantle viscosity based on palaeo sea level observations - Part I: Sensitivity kernels for an Earth with laterally varying viscosity.

A key initial step in geophysical imaging is to devise an effective means of mapping the sensitivity of an observation to the model parameters, that is to compute its Fréchet derivatives or sensitivity kernel. In the absence of any simplifying assumptions and when faced with a large number of free parameters, the adjoint method can be an effective and efficient approach to calculating Fréchet derivatives and requires just two numerical simulations. In the Glacial Isostatic Adjustment problem, these consist of a forward simulation driven by changes in ice mass and an adjoint simulation driven by fictitious loads that are applied at the observation sites. The theoretical basis for this approach has seen considerable development over the last decade. Here, we present the final elements needed to image 3-D mantle viscosity using a dataset of palaeo sea-level observations. Developments include the calculation of viscosity Fréchet derivatives (i.e. sensitivity kernels) for relative sea-level observations, a modification to the numerical implementation of the forward and adjoint problem that permits application to 3-D viscosity structure, and a recalibration of initial sea level that ensures the forward simulation honours present-day topography. In the process of addressing these items, we build intuition concerning how absolute sea-level and relative sea-level observations sense Earth's viscosity structure and the physical processes involved. We discuss examples for potential observations located in the near field (Andenes, Norway), far field (Seychelles), and edge of the forebulge of the Laurentide ice sheet (Barbados). Examination of these kernels: (1) reveals why 1-D estimates of mantle viscosity from far-field relative sea-level observations can be biased; (2) hints at why an appropriate differential relative sea-level observation can provide a better constraint on local mantle viscosity and (3) demonstrates that sea-level observations have non-negligible 3-D sensitivity to deep mantle viscosity structure, which is counter to the intuition gained from 1-D radial viscosity Fréchet derivatives. Finally, we explore the influence of lateral variations in viscosity on relative sea-level observations in the Amundsen Sea Embayment and at Barbados. These predictions are based on a new global 3-D viscosity inference derived from the shear-wave speeds of GLAD-M25 and an inverse calibration scheme that ensures compatibility with certain fundamental geophysical observations. Use of the 3-D viscosity inference leads to: (1) generally greater complexity within the kernel; (2) an increase in sensitivity and presence of shorter length-scale features within lower viscosity regions; (3) a zeroing out of the sensitivity kernel within high-viscosity regions where elastic deformation dominates and (4) shifting of sensitivity at a given depth towards distal regions of weaker viscosity. The tools and intuition built here provide the necessary framework to explore inversions for 3-D mantle viscosity based on palaeo sea-level data.

Geodynamically corrected Pliocene shoreline elevations in Australia consistent with midrange projections of Antarctic ice loss.

The Mid-Pliocene represents the most recent interval in Earth history with climatic conditions similar to those expected in the coming decades. Mid-Pliocene sea level estimates therefore provide important constraints on projections of future ice sheet behavior and sea level change but differ by tens of meters due to local distortion of paleoshorelines caused by mantle dynamics. We combine an Australian sea level marker compilation with geodynamic simulations and probabilistic inversions to quantify and remove these post-Pliocene vertical motions at continental scale. Dynamic topography accounts for most of the observed sea level marker deflection, and correcting for this effect and glacial isostatic adjustment yields a Mid-Pliocene global mean sea level of +16.0 (+10.4 to +21.5) m (50th/16th to 84th percentiles). Recalibration of recent high-end sea level projections using this revised estimate implies a more stable Antarctic Ice Sheet under future warming scenarios, consistent with midrange forecasts of sea level rise that do not incorporate a marine ice cliff instability.

Exceptionally stable preindustrial sea level inferred from the western Mediterranean Sea.

An accurate record of preindustrial (pre-1900 CE) sea level is necessary to contextualize modern global mean sea level (GMSL) rise with respect to natural variability. Precisely dated phreatic overgrowths on speleothems (POS) provide detailed rates of Late Holocene sea-level rise in Mallorca. Statistical analysis indicates that sea level rose locally by 0.12 to 0.31 m (95% confidence) from 3.26 to 2.84 thousand years (ka) ago (2σ) and remained within 0.08 m (95% confidence) of preindustrial levels from 2.84 ka to 1900 CE. This sea-level history is consistent with glacial isostatic adjustment models adopting relatively weak upper mantle viscosities of ~1020 Pa s. There is virtual certainty (>0.999 probability) that the average GMSL rise since 1900 CE has exceeded even the high average rate of sea-level rise between 3.26 and 2.84 ka inferred from the POS record. We conclude that modern GMSL rise is anomalous relative to any natural variability in ice volumes over the past 4000 years.

Rapid postglacial rebound amplifies global sea level rise following West Antarctic Ice Sheet collapse.

Geodetic, seismic, and geological evidence indicates that West Antarctica is underlain by low-viscosity shallow mantle. Thus, as marine-based sectors of the West Antarctic Ice Sheet (WAIS) retreated during past interglacials, or will retreat in the future, exposed bedrock will rebound rapidly and flux meltwater out into the open ocean. Previous studies have suggested that this contribution to global mean sea level (GMSL) rise is small and occurs slowly. We challenge this notion using sea level predictions that incorporate both the outflux mechanism and complex three-dimensional viscoelastic mantle structure. In the case of the last interglacial, where the GMSL contribution from WAIS collapse is often cited as ~3 to 4 meters, the outflux mechanism contributes ~1 meter of additional GMSL change within ~1 thousand years of the collapse. Using a projection of future WAIS collapse, we also demonstrate that the outflux can substantially amplify GMSL rise estimates over the next century.