Small-scale Convection and the Evolution of the Lithosphere

In this thesis we calculate the effect of small-scale convection on the thickness and temperature structure of the lithosphere for three cases where geophysical and geological data may allow us to see these effects. The problems are: (1) the cooling of the oceanic lithosphere; (2) the cooling of a passive rift temperature structure; and (3) the rate of thinning of lithosphere which has been thickened in a continental convergence zone. In all these cases the convection is driven by the temperature gradients at the base of the lithosphere and the key to the interaction between the lithosphere and the flow in the asthenosphere is the viscosity relation we assume. It is very likely that the viscosity of the mantle depends on temperature and we take that to be the case. Viscosity which also depends on pressure and stress is also considered in these calculations. We study all these problems using finite difference numerical methods and, where possible, we derive general relations between the model parameters and predicted data. For the problem of the cooling of the oceanic lithosphere we find that a linear relation is predicted between the subsidence of the ocean floor and (time) 11/ 2 , even after small-scale convection has begun. The slope of this plot depends on the viscosity structure of the convecting region, and its magnitude is less than the corresponding subsidence for purely conductive cooling. Small-scale convection can begin to affect the subsidence age relation after only a few million years of lithospheric cooling. Convection which begins under lithosphere of this age can produce vertical deformations of the surface of the sea floor, which should produce a detectible gravity signal. Previous workers have shown that small-scale convection beneath the moving oceanic plates should have the orientation of two-dimensional rolls with axes aligned parallel to the direction of plate motion. In that case the gravity signals produced by the convection should be aligned in the direction of plate motion and so may account for signals with this orientation which have been observed over several areas of the oceans in Seasat altimeter data. We suggest that the short wavelength (<300 km) topography produced by the convection is "frozen in" by the elastic lithosphere as the plate cools. For convection to be sufficiently vigorous under the young lithosphere to produce the topographic and gravity signals, before the elastic lithosphere is so thick as to damp out these signals, requires minimum asthenospheric viscosities less than 1018 Pa-s. Such values are consistent with estimates of average mantle viscosity if a pressure dependence of viscosity is included. Another body of data which may reflect the effects of small-scale convection under the oceanic plates concerns the offset of the geoid height across fracture zones. This data reflects the difference in lithospheric thickness across fracture zones. The convective models considered here can account for the trend and most of the magnitude of the data. Conductive thermal models cannot. Including lateral flow across the fracture zone may account for the data variations not matched here. We are able to use theoretical relationships between the heat flux out of a convecting region and the viscosity parameters which describe the rheology of that region to study the problem of the cooling of the oceanic lithosphere. This allows us not only to elucidate the features of our models which are important to the physics of the cooling of the lithosphere, but also allows us to define general reltionships between the predicted subsidence, geoid height and heat flow, and the model parameters. We use the mathematical formulation of the Stefan problem to describe the temperatures in the lithosphere with time given the variations predicted for the heat transport across the convecting region. We find that one parameter (X) describes the changes in the temperatures and thickness of the model lithosphere caused by small-scale convection, which is driven by cooling from above. This parameter can be related directly to the average viscosity of the convecting asthenosphere and to the temperature and pressure dependence of the viscosity. The parameter X varies nearly linearly with the log of the average viscosity of the convecting region. For a change in the average viscosity of a factor of ten, X changes by about 20%. Several geophysically interesting model predictions can be related to the parameter X. The predicted subsidence varies linearly with X and the isostatic geoid height varies approximately with X2 while, the surface heat flux goes like 1/X. Subsidence variations for different areas of the oceans can be related to the differences in the asthenospheric viscosities and presumably temperatures (through the temperature dependence of viscosity) using the derived relationships. The asthenospheric temperatures can be estimated using seismic methods, and then compared to the estimates based on subsidence data using this model. To deal with the problem of calulating the flow induced by the large horizontal temperature gradients under a rift we developed a simple finite difference method for approximating a curved, no-slip boundary called the "repeated corner approach". It is valid because the viscosities decrease rapidly going away from a boundary in this problem, so the flow rates near the boundary are much less than further away. It is shown that the effects of convection induced by a passive rift temperature structure can explain data on the uplift of the flanks of rifts and details of the subsidence history of rifted continental margins. Uplift of the flanks of about 1 km is shown to be consistent with the lateral transfer of heat beneath a rift, caused by a combination of conduction and convection. The amount of uplift depends on the viscosities assumed, but they must be low to match observed uplifts (a minimum of about 1018 Pa-s is required for 1 km of uplift). The stress dependence of viscosity also contributes to the uplift of the flanks. Also, we find that the narrower the rift, the greater the uplift. Finally, we test the hypothesis that small-scale convection under lithosphere, which has been thickened in a convergence zone, can thin "normal" lithosphere in only a few tens of millions of years. This is required to explain the high surface heat flux in convergence zones if the lithosphere is thickened along with the crust. If the visosity depends on temperature through laboratory estimated parameters, we find that the rate of thinning of the lithosphere is not significantly increased by the instability of the thickened boundary layer at the base of the lithosphere. In Tibet, the crust was thickened within the past 40 m.y., but the surface heat fluxes are presently higher than normal. This leads us to suggest that the mantle lithosphere was not thickened along with the crust in that region, but was subducted in a manner similar to that observed for oceanic lithosphere. Thesis Advisor: M. Nafi Toksoz Professor of Geophysics Title: