ON LATERAL VISCOSITY CONTRAST IN THE MANTLE AND THE RHEOLOGY OF LOW-FREQUENCY GEODYNAMICS

Mantle-wide heterogeneity is largely controlled by deeply penetrating thermal convective currents. These thermal currents are likely to produce significant lateral variation in theology, and this can profoundly influence overall material behaviour. How thermally related lateral viscosity variations impact models of glacio-isostatic and tidal deformation is largely unknown. An important step towards model improvement is to quantify, or bound, the actual viscosity variations that characterize the mantle. Simple scaling of viscosity to shear-wave velocity fluctuations yields map-views of long-wavelength viscosity variation. These give a general quantitative description and aid in estimating the depth dependence of theological heterogeneity throughout the mantle. The upper mantle is probably characterized by two to four orders of magnitude variation (peak-to-peak). Discrepant time-scales for rebounding Holocene shorelines of Hudson Bay and southern Iceland are consistent with this characterization. Results are given in terms of a local average viscosity ratio, Delta ($) over bar eta(i), of volumetric concentration, phi(i). For the upper mantle deeper than 340km the following reasonable limits are estimated for Delta ($) over bar eta approximate to 10(-2): 0.01 less than or equal to phi less than or equal to 0.15. A spectrum of ratios Delta ($) over bar eta(i) < 0.1 at concentration level phi(i) approximate to 10(-6)-10(-1) in the lower mantle implies a spectrum of shorter time-scale deformational response modes for second-degree spherical harmonic deformations of the Earth. Although highly uncertain, this spectrum of spatial variation allows a purely Maxwellian viscoelastic theology simultaneously to explain all solid tidal dispersion phenomena and long-term rebound-related mantle viscosity. Composite theory of multiphase viscoelastic media is used to demonstrate this effect.