Treatment of ice-shelf evolution combining flow and flexure

We develop a two-dimensional, plan-view formulation of ice-shelf flow and viscoelastic ice-shelf flexure. This formulation combines, for the first time, the shallow-shelf approximation for horizontal ice-shelf flow (and shallow-stream approximation for flow on lubricated beds such as where ice rises and rumples form), with the treatment of a thin-plate flexure. We demonstrate the treatment by performing two finite-element simulations: one of the relict pedestalled lake features that exist on some debris-covered ice shelves due to strong heterogeneity in surface ablation, and the other of ice rumpling in the grounding zone of an ice rise. The proposed treatment opens new venues to investigate physical processes that require coupling between the longitudinal deformation and vertical flexure, for instance, the effects of surface melting and supraglacial lakes on ice shelves, interactions with the sea swell, and many others.

Rheology and thermal structure of the lithosphere beneath the Hawaiian Ridge inferred from gravity data and models of plate flexure

SUMMARY We examine the rheology and thermal structure of the oceanic lithosphere, expressed in situ by plate flexure beneath the Hawaiian Ridge, where volcanoes of variable sizes have loaded seafloor of approximately the same age, and thus where the lithosphere is expected to have had an approximately uniform age-dependent thermal structure at the time of loading. Shipboard and satellite-derived gravity, as well as multibeam bathymetry data are used in models of plate flexure with curvature-dependent flexural rigidity, the strength of which is limited, in the shallow lithosphere, by brittle failure, and in the deeper lithosphere, by low-temperature plasticity (LTP). We compute relative likelihoods and posterior probabilities for four model parameters: average crustal density ρc, friction coefficient for brittle failure ${\mu _f}$, a pre-exponential weakening factor F controlling the strength of LTP and lithospheric geotherm age t. Results show that if the lithosphere temperatures were as is expected for normal (t = ) 90-Myr-old seafloor at the time of volcano loading, the rheology must be significantly weaker than expected. Specifically, weak brittle strengths (μf ≤ 0.3) show relatively high probabilities for three of the six published LTP flow laws examined. Alternatively, moderate-to-large brittle strengths (μf ≥ 0.5) require all LTP flow laws to be substantially weakened with F = 102 to > 108 or, equivalently, activation energy reduced by 10–35 per cent. In contrast, if the lithosphere has been moderately reheated by the Hawaiian hotspot, represented by geotherms for t = 50–70 Myr, then the flow laws of Evans & Goetze, Raterron et al. and Krancj et al. require little or no weakening. Such modest thermal rejuvenation is allowed by heatflow constraints, supported by regional mantle seismic tomography imaging as well as compositions of mantle xenoliths, and reconciles previously noted discrepancies between the LTP strengths of lithosphere beneath Hawaii versus that entering the Pacific subduction zones.

The influence of plate strength on dynamic topography estimates

<p>A common method used to evaluate dynamic topography amplitudes begins with an estimate of Moho depth, usually from seismic data but sometimes - or also - from the inversion of gravity data. Then the principles of Airy isostasy are applied: surface topography is assumed to be in isostatic equilibrium, buoyantly supported by the displacement of high-density mantle material by the low-density crustal ‘root’ that compensates the surface topographic mass. Hence, the actual relief of the Moho yields an ‘isostatic topography’ which will depart from the actual, observed topography by a component that, in theory, must arise from convective support or subsidence. Notwithstanding the fact that the errors on the seismic Moho may be larger than the topography itself, there is another source of uncertainty, that of the flexural rigidity of the lithosphere. Airy isostasy is essentially an end-member of plate flexure models, one in which the flexural rigidity is zero. However there are very few places on Earth where the flexural rigidity, usually represented by its geometric analogue the effective elastic thickness (Te), is indeed zero. In most environments, the rigidity of the plate will act to resist flexure, with the implication that the ‘Airy isostatic topography’ and therefore the dynamic topography will be in error. Here several scenarios will be presented illustrating these issues, and paths for remediation recommended.</p>