Characterization of Viscous Dissipative Heating in the Earth's Mantle Caused by Surface Forces

Abstract

AbstractViscous dissipative heating has long been discussed as a heat source in solid celestial bodies experiencing exogenic forces such as tidal forcing or surface loading. We examine the characteristics of viscous dissipative heating in a Newtonian, Maxwell viscoelastic solid in a 2D Cartesian box subjected to a surface load. The solutions are analyzed to understand the general controls on the energetics of planetary mantle that are associated with exogenic forcing. We find that work done at the surface is partitioned between dissipative and elastic terms depending on mantle viscosity, loading period, and loading wavelength. For viscosity structures with a weak upper mantle layer, dissipation is spatially concentrated in the upper mantle for short loading periods, implying that exogenic forces may play a role in the generation of weak upper mantle layers. The results are also scaled to estimate how much energy is dissipated in Earth's mantle, both present and past, during surface mass movement processes and tidal forcing. We find that the dissipation from glacial loading cycles since Mid‐Pleistocene at a period of 100,000 years might contribute ∼3 mW/m2 heat flux in the formerly glaciated regions, but for glacial cycles with a period of 40,000 years during the Early Pleistocene, the heat flux may have been 3 times larger at ∼9 mW/m2. We find that tidal forcing for the early Earth at 4 Ga may have contributed ∼30 TW of heat to the upper mantle, suggesting that exogenic forces have the capacity to contribute significantly to early Earth's energy budget.