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/m2 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.
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Acknowledgments. We thank M. Beˇhounková and B. Kadlec for discussions, which have prompted us to look into viscous dissipation, and L. Yang for her drawing. Reviews by M. Nakada, M. Kameyama and B. Moore improved the manuscript significantly. The work has been supported by the Research Project DG MSM 113200004, by the Charles University Grant 238/2001/B-GEO/MFF, by the Czech Grant Agency Projects 205/00/D113 and 205/03/0778 and by the CSEDI and ITR programs of the National Science Foundation.
- Heat dissipation
- Postglacial rebound