Short time-scale heating of the Earth’s mantle by ice-sheet dynamics

Abstract

We have studied the possibility of short time-scale energy transfer from the ice sheet loading and unloading processes to the Earth's interior via viscous dissipation associated with the transient viscoelastic flow in the mantle. We have focussed on the magnitude of glacially induced deformations and the corresponding shear heating for an ice sheet of the spatial extent of Laurentide region in Maxwellian viscoelastic compressible models with a Newtonian viscosity. We have used a discretization method based on the method of lines for integrating the time-dependent evolutionary equations of self-gravitational, viscoelastic flow. We have found that shear heating from the transient viscoelastic flow can represent a non-negligible mantle energy source with cryogenic origins. Volumetric heating by viscous deformation associated with these flows can be locally greater than chondritic heating by radioactivity. In the presence of an abrupt change in the ice loading history, the time average of the integral of the dissipation over depth corresponds to a mantle heat flow of the order of magnitude of mW/m 2 below the periphery of ancient ice sheets or below their central areas. However, the peak values of this integral in time are almost two orders higher. Our results would suggest that some degree of volcanism may be associated with dramatic episodes in ice loading.

Effects of mantle rheologies on viscous heating induced by Glacial Isostatic Adjustment

“…The results for models with uniform mantle are summarized in Table 3 which show that compressibility almost doubles the peak viscous heating when the rheology is linear. This is in line with the finding of Hanyk et al (2005). The reason is that the 162 von Mises stress τ in the upper mantle increases with compressibility.…”

“…This confirms the finding of the simple ice deglaciation models of Hanyk et al (2005). In addition, the sharp decline of viscous heating after 13 kBP means that the effect is localized in time, thus the effects of previous glacial cycles are small and can be neglected in our computation.…”

“…Unlike the simple ice sheet model used in Hanyk et al (2005), the ice model used here is the realistic global ICE6G model of Peltier et al (2015). Since ICE6G provides ice thickness history from 26 kBP to the present, we assume that the ice thickness increased linearly from zero at 108 kBP to the ice thickness at 26 kBP.…”

“…From the stress output at any time step, the local viscous heating for each element can be computed using eqs (4a) or (4b). In this paper, viscous heating is normalized by the chondritic radiogenic heating of 3 × 10 −9 W m −3 (Hanyk et al 2005).…”

“…The link between them is generally attributed to decompression (Jull & McKenzie 1996;Slater et al 1998), but volcanism can also be triggered by viscous heating induced by Glacial Isostatic Adjustment (GIA) of the Earth in response to cycles of ice and ocean loading. Hanyk et al (2005) modeled viscous heating due to GIA using simple ice load histories on a spherical Earth with linear rheology. They found that viscous heating can generate observable transient heat flux on the surface of the Earth.…”