Dynamics of crustal compensation and its influences on crustal isostasy

Abstract

Abstract. 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 theology 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 timescales. 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 theology. 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.

Long‐wavelength topographic relaxation for self‐gravitating planets and implications for the time‐dependent compensation of surface topography

“…By assuming that viscoelastic properties within each layer are uniform and time-invariant, we can use a propagator matrix method to solve the equations, as is done for elastic displacement or pure viscous flow problems [e.g., Hager and O'Connell, 1981]. However, in our formulation, special treatment will be required to account for the nature of symbolic solutions in a Laplacian space [Zhong, 1997]. By solving equations (1) -(4) with multiple-layer viscoelastic structure and free surface boundary conditions (see Appendices A, B, and C for solution approaches), we can obtain solutions for the time evolution of interface relief at the surface, crust-mantle interface (i.e., Moho), and coremantle boundary (CMB) for a given initial relief at any of these density interfaces.…”

“…Our models also include a crust-mantle crust and upper mantle with distinctive mechanical properties. density interface that allows us to examine the dynamics of The viscosity for both the mantle and crust is described by a crustal compensation in association with the relaxation of temperature-and depth-dependent NewtonJan rheology surface or internal loads [Zhong, 1997].…”

New constraints on the thermal and volatile evolution of Mars

“…For this reason, we will distinguish only three stages of 312 relaxation in our results: no relaxation, partial relaxation and complete relaxation, even though 313 our technique provides more precise results. Despite the challenges inherent in analytic models 314 of viscosity evolution, our approach newly includes the time evolution of viscosity and elastic 315 thickness, and is therefore better suited for modeling of the effects of cooling of the lithosphere 316 than the other studies (Zhong, 1997;Nimmo and Stevenson, 2001;Nimmo, 2005). 317…”

Crustal compensation during mountain‐building

“…Our analysis represents the further development of a previous crustal compensation formalism [Zhong, 1997] …”

“…Gravity, topography, and seismic observations indicate that regions of active orogeny including the Himalayas/Tibetan plateau and Tian Shan are approximately isostatically compensated [Jin et al, 1996;Burov et al, 1990] while many tectonically stable and old orogenic belts including the southern Appalachians [McNutt, 1980] and Caledonia [Kusznir and Matthews, 1988] show significant isostatic gravity anomalies. Deviations from local isostasy for inactive orogenic belts can be attributed to the combined effects of dynamic compensation processes immediately following orogeny that lead to non-isostatic states [Zhong, 1997] and subsequently increased lithospheric strength which is capable of supporting deviatoric stresses indefinitely on a regional scale [Daly, 1940].…”