Visualiztion of Viscous Heating in the Earth's Mantle Induced by Glacial Loading

We have studied the a possible mechanism of transferring gravitational potential energy into viscous heating in the mantle via glacial loading during the ice ages. Shear heating associated with the transient flow occurring over a short timescale on the order of tens of thousand of years can cause a non-negligible amount of heat production in the mantle. We have applied our initial-value approach to the modelling of viscoelastic relaxation of spherical compressible self-gravitating Earth models with a linear viscoelastic Maxwellian rheology. We have focussed on the magnitude of deformations, stress tensor components and corresponding dissipative heating for ice sheets of the size of the Laurentide ice mass and cyclic loading with a fast unloading phase two orders of magnitude less than that associated with mountain building and vertical tectonics. Much to our surprise, we have found that this kind of internal heating can represent a non-negligible internal energy source with, however, an exogenic origin. The volumetric heating by this fast rate of deformation can be locally higher than the chondritic radiogenic heating during peak events with short timescales. In the presence of an abrupt change in the ice-loading, its time average of the integral over the depth corresponds to equivalent mantle heat flow of the order of magnitude of milliwatts per m² below the periphery of ancient glaciers or below their central areas. However, peak heat-flow values in time are almost by about two orders higher. On the other hand, nonlinear rheological models can potentially increase the magnitude of localized viscous heating. To illustrate the spatial distribution of the viscous heating for various Earth and glacier models, we have employed the powerful 3-D visualization system Amira. ( www.amiravis.com ). With this type of data format we can animate very easily the temporal evolution of the data fields on a moving curvilinear mesh, which spreads over outer and inner mantle boundaries and mantle cross-sections. Amira movies can reveal the complex nature of dissipative heating of the PREM model with a lower-mantle viscosity hill at the end of the recent Pleistocene ice age. This viscoelastic model can be employed in other dynamical situations with fast dynamical timescales, such as the aftermath of a meteoritic impact or other global cryospheric events.