Isostatic rebound and power‐law flow in the asthenosphere

Summary Laboratory experiments indicate that the asthenosphere probably deforms as a power‐law fluid. The experimental flow law for high‐temperature peridotite and olivine is Cė ‐1/ n = s̀ where ė is strain‐rate, s̀ deviatoric stress, n the power (observed to be about 3), and C a proportionality constant which is a function of composition, temperature, and confining pressure. However, most theoretical treatments of isostatic rebound have assumed that the asthensophere deforms as a Newtonian fluid. In this paper, numerical solutions are found for the relaxation of a sinusoidal surface deflection above a power‐law medium. These solutions are applied to an analysis of isostatic rebound data. First, following Post & Griggs (1973), it is shown by dimensional analysis that the rate of maximum uplift of a surface depression should be proportional to the maximum amount of remaining depression raised to the power n , where n is the power of the flow law. The rebound data from Fennoscandia and Canada yield in‐situ estimates of n between 2 and 4, in good agreement with the experimental results. Second, using the finite‐difference method, the proportionality constant is determined which relates the rate of uplift to the amount of remaining depression. Using this constant and assuming n = 3, the rebound data from Fennoscandia, Canada, and Lake Bonneville yield in‐situ estimates of about 10 10 Ns 1/3 m ‐2 for the creep coefficient C in the flow law. This is consistent with laboratory measurements for the creep of dry olivine at 1200°C. However, all three rebound areas give different values for C . Reasonable lateral temperature and compositional differences in the asthenosphere can explain the observed variations, but it is noticed that the estimates of C increase with increasing width of the rebound area. This suggests that the value of C increases with depth in the asthenosphere. Two models of increase of C with depth are examined and it is found that both can explain the rebound data without invoking lateral variations in the asthenosphere. First, if the asthenosphere has a rigid base, that base is at a depth of about 170 km below the lithosphere. Second, if C increases exponentially with depth, it increases by a factor of e every 135 km. An exponential increase of this magnitude is expected from the increase in confining pressure with depth.