Fluid dynamics of layered systems in the field of gravity, a theoretical basis for certain global structures and isostatic adjustment

Abstract

The theory of fluid dynamics has been applied on unstable layering in the field of gravity, the instability being in the form of low-density layers overlain by more dense strata. Several models are analysed, viz. two infinite half spaces joined along a horizontal (isopotential) surface; layer of finite thickness overlain by infinite half space; infinite half space overlain by layer with finite thickness; and layer with finite thickness overlain by finite layer with free surface. Conditions of welded contacts as well as free slip along contacts are treated. When one layer or both layers have finite thickness the spontaneous rise of the buoyant medium is in the form of waves whose wavelength depends upon the thickness of the layers and on their rheological properties, [eqs. (4.4), (5.4), (6.4), (7.13) and (7.18). Waves with lengths either larger or smaller than the characteristic wavelength for the system rise less rapidly and are gradually “absorbed” by the fast growing waves. The theory, which is supported by simple tests, is applicable to the evolution of salt tectonics (especially salt domes), to the rise of granitic and gneissic batholithes and domes, to the upheaval of basement massives in orogenic belts, and in general the theory gives insight in the process of differentiation of the earth in the field of gravity. The above equations are also applicable to the process of isostatic adjustment of a layered earth. With the known postglacial rate-of-rise data from Scandinavia the viscosities have been calculated for two models, viz. 1) a uniform earth with uniform viscosity (giving μ = 1.25 · 10 22 poises), and 2) a low-viscosity layer 180 km thick overlain by a high-viscosity ( μ = 10 25 poises) crust 20 km thick and resting on a mantle with viscosity 10 26 poises. Model 2 gave μ = 7 · 10 20 poises for the low-viscosity layer. The deflection of the lower boundary of the crust, e.g. the Moho, is given as a function of the deflection of the free surface during isostatic adjustment.