E3 Rheology of the Mantle and Crust

Topic

Rheology describes how materials deform when subjected to stress. Within the Earth, a single material can behave as an elastic solid when traversed by a seismic wave (over mere milliseconds), as a viscous material when responding to isostatic rebound (over thousands of years), or as a plastic material flowing almost like a liquid during mantle convection (over millions of years); which of these three behaviors dominates depends on how the process's timescale compares to the material's characteristic relaxation time—a value determined by the ratio of the material's viscosity to its elastic rigidity.

Solid-state creep in minerals such as olivine follows a well-established empirical law characterized by exponential temperature dependence: the higher the mineral's temperature and the smaller its grain size, the more easily the mineral flows—and, consequently, the more easily the mantle composed of that mineral flows.

The extraordinarily high viscosity of the upper mantle—on the order of $10^{21}$ Pascal-seconds—governs the rate of postglacial isostatic rebound; for instance, Scandinavia continues to rise today at a rate of nearly one centimeter per year—more than ten thousand years after the Pleistocene ice retreated from the region—with a characteristic relaxation time of approximately four and a half millennia. Lithospheric flexure, for its part, describes how the lithosphere bends under the weight of a topographic load—whether a mountain range, a volcano, or an accumulation of sediment. The wavelength of this deflection depends on the rigidity of the lithosphere itself, and that rigidity, in turn, depends on the lithosphere's effective elastic thickness at that point—a thickness ranging from five to one hundred and twenty kilometers, depending on the lithosphere's thermal age—thereby linking the distinct rheological behaviors mentioned at the beginning of this description with the specific way the lithosphere responds to the loads placed upon it.

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