Convection and the Constant Q-Mechanism

Abstract

IT has been argued¹ that the data on the Q value of the Earth's mantle do not militate against convection currents because the range of frequency over which Q has been proved constant in the laboratory (10⁻⁴<f<10⁶ Hz) does not lie entirely within that which can be explained by the Lomnitz law² of creep in rocks (10⁻⁸<f<1 Hz). The Lomnitz law is characterized by a decreasing rate of creep that forbids convection and McCann rightly points out that according to this law the mechanism which accounts for the constant Q over the laboratory proven range is inexplicable and so convection is, in fact, allowed as the law is not representative of rocks thought to make up the Earth's interior. There are several comments to be made on this reasoning. (i) The processes responsible for damping in the mantle are not the same as those dominant in the laboratory. Experiments made at atmospheric pressure are dominated by microcracks, as noted by Anderson³ and Orowan⁴. These cracks are closed by pressures of only 2 or 3 kbar, corresponding to a depth of approximately 10 km. Thus, laboratory data that show a wide range of frequency-independent Q are not of any use at depth unless special experimental arrangements are made. (ii) Most experiments on damping are inherently unsatisfactory because they are made on the width of the damping peak in amplitude, that is liable to be broadened by numerous effects (ref. 2, page 334). (iii) Lomnitz⁵ in his original work used a torsion method to investigate the anelastic response of rocks to a suddenly applied stress, P, and arrived at the law where ε is the strain at time t, μ is the rigidity, and q, a are constants. It is an empirical creep law, and needs connecting with an explicitly stated damping process before any fundamental connexion between the two can be attempted⁶. Indeed, there may well be no connexion between the creep processes and the damping processes operative in the Earth, as they are rate-controlled in different ways on an atomic scale.