A Model of Dislocation-Controlled Rheology for the Mantle

Abstract

The dislocation microstructure of mantle materials can account simultaneously for long-term steady-state creep, and for stress wave attenuation at seismic frequencies. The hypothesis that a single microstructural model explains the rheology for characteristic times ranging from 1 to 10^(10) seconds can be used to restrict the class of permissible rheological models for the mantle. We review steady-state dislocation damping models in order of increasing complexity, and reject those which do not satisfy laboratory data or geophysical constraints. This elimination procedure leads us to consider an organized microstructure, in which most dislocations are found inside subgrain walls. The cells contain relatively few dislocation links. These are free to bow under small, i.e. seismic, stresses. The time constant of this mechanism is controlled either by the diffusion of kinks or of point defects bound to the dislocation line. The glide of intragrain dislocations explains the magnitude and frequency range of seismic attenuation. Steady-state creep is governed by recovery through climb and annihilation in cell walls. Under conditions of jog undersaturation, climb is controlled by jog formation in addition to self-diffusion, and the model requires a higher creep activation energy than for self-diffusion, in agreement with observations on olivine. Quantitative agreement with laboratory data is achieved if the density of cell-wall dislocations is one to two orders of magnitude higher than the density of intracell dislocations. Self-diffusion is probably controlled by silicon diffusion at low pressure and by oxygen diffusion at high pressure. The long-term tectonic stress is the dominant factor determining scale lengths; as a result, the total strength of the relaxation associated with bowing of intracell dislocation links is fixed by the geometry and is of the order of 10%. This limits the width of the seismic absorption band to 2-3 decades in frequency for each mantle mineral. The actual position of the seismic absorption band is determined primarily as a result of a trade-off between temperature, pressure and tectonic stress. This model provides a physical framework within which the quality factor Q and viscosity are related via the dislocation microstructure.

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