A Dislocation Model of Seismic Wave Attenuation and Micro-creep in the Earth: Harold Jeffreys and the Rheology of the Solid Earth

Abstract

A microphysical model of seismic wave attenuation is developed to provide a physical basis to interpret temperature and frequency dependence of seismic wave attenuation. The model is based on the dynamics of dislocation motion in minerals with a high Peierls stress. It is proposed that most of seismic wave attenuation occurs through the migration of geometrical kinks (micro-glide) and/or nucleation/migration of an isolated pair of kinks (Bordoni peak), whereas the long-term plastic deformation involves the continuing nucleation and migration of kinks (macro-glide). Kink migration is much easier than kink nucleation, and this provides a natural explanation for the vast difference in dislocation mobility between seismic and geological time scales. The frequency and temperature dependences of attenuation depend on the geometry and dynamics of dislocation motion both of which affect the distribution of relaxation times. The distribution of relaxation times is largely controlled by the distribution in distance between pinning points of dislocations, L, and the observed frequency dependence of Q, Q ∝ w α, is shown to require a distribution function of P(L) ∝ L −m with m = 4 − 2α. The activation energy of Q −1 in minerals with a high Peierls stress corresponds to that for kink nucleation and is similar to that of long-term creep. The observed large lateral variation in Q −1 strongly suggests that the Q −1 in the mantle is frequency dependent. Micro-deformation with high dislocation mobility will (temporarily) cease when all the geometrical kinks are exhausted. For a typical dislocation density of ~ 108 m−2, transient creep with small viscosity related to seismic wave attenuation will persist up to the strain of ~10−6, thus even a small strain (~10−6 − 10−4) process such as post-glacial rebound is only marginally affected by this type of anelastic relaxation. At longer time scales continuing nucleation of kinks becomes important and enables indefinitely large strain, steady-state creep, causing viscous behavior.