Creep in the Earth and Planets (Invited Lecture)

Abstract

An outstanding problem is to reconcile the Moon's rotation with the persistence of its non-hydrostatic dynamical ellipticities. The first requires imperfection of elasticity under strains of order 10−7; the second apparently little under larger ones.Lomnitz gave experimental evidence that creep is linear at elastic shears from 10−5to 10−4, indicating that a linear rule could be right at still smaller values. Positive evidence for the Earth comes from the damping of the 14-monthly nutation, which has a relaxation time of the order of 30 yr. Most work on imperfect elasticity has assumed that under constant shear stress the strain increases with time either liket(elasticoviscosity) or like logt.If the result from the 14-monthly nutation, with elasticoviscosity, is applied to the Moon, the dynamical ellipticities would have subsided considerably in the last 200 yr. With the logarithmic rule anSpulse at 80° would have its beginning spread out over about 70 s and be unreadable. These contradictions are avoided if the increase under constant stress is about liket0.2. The resulting law involves two constants. Without change of these, applications are made to other phenomena. The rotations of the Moon and of other satellites whose rotations are known are explained; so is the persistence of the Moon's dynamical ellipticities; also the failure to detect three free oscillations that might theoretically exist. Elasticoviscosity would imply rapid disappearance of the non-hydrostatic second and third harmonics in the Earth's gravitational field; this is avoided with the new law. Study of damping of free vibrations of the Earth (including surface waves) has usually assumed the logarithmic law, but it appears that the new law fits the data at least as well, and that it may also explain those that have been interpreted in favour of layers of low velocity. It appears that the damping at depths up to 400 km or so is much more severe than the average for the Earth's shell, and more evidence for shorter periods is much needed.Any law with an index less than 1 would forbid thermal instability (convection) and continental drift.