Dynamics of crustal compensation and its influences on crustal isostasy

Deviation from isostasy is commonly believed to be caused by the strength of the Earth's lithosphere. An analysis of crustal compensation dynamics suggests that the deviation may have a dynamic origin. The analysis is based on analytic models that assume that (1) the medium is incompressible and has a layered and linear viscoelastic rheology and (2) the amplitude of topography is small compared with its wavelength. The models can describe topographic relaxation of different density interfaces at both small (e.g., postglacial rebound) and large time‐scales. The models show that for a simple crust‐mantle system with topography at the Earth's surface and Moho representing the only mass anomalies, while the crust always approaches the isostatic state at long wavelengths (>800 km), crustal isostasy may not be an asymptotic limit at short wavelengths, depending on crustal and lithospheric rheology. For a crust with viscosity smaller than lithospheric viscosity, at wavelengths comparable with widths of orogenic belts (i.e., <300 km), the crust tends to approach a state with significant overcompensation (i.e., excess topography at the Moho) within a timescale of about 107 years, and this characteristic time depends on wavelengths and crustal viscosity. This overcompensation is greater for weaker crust and stronger lithosphere. A thicker crust or lithosphere also enhances this overcompensation. If crustal and lithospheric viscosities are both large and comparable, the asymptotic state for the crust displays a slight undercompensation. For an elastic and rigid upper crust, the crust eventually becomes undercompensated after a characteristic decay time of topography at the Moho. The characteristic time is dependent on viscosity and thickness of the lower crust. The deviation from isostasy arises because these viscosity structures result in a ratio of vertical velocity at the surface to vertical velocity at the Moho which in the asymptotic state for short wavelengths differs from the ratio of density contrast at the Moho to that at the surface.