Creep Of Olivine Research Articles

Reply [to “Comment on ‘Brittle failure in the upper mantle during extension of continental lithosphere’ by Dale S. Sawyer”

ence on the stress required to deform the lithosphere at a given strain rate (equation (8), hereinafter called the strength of the lithosphere) of cooling the ductile portion of the lithosphere during extension. I concluded that for slow enough strain rates (< 10- ½ s-), cooling during extension, and the consequent increase in the strength of the lithosphere, could provide a limit to extension. In contrast, Sawyer [1985] contends that when brittle deformation of the lithosphere is considered, the correct conclusion should be that the rheological properties of the lithosphere cannot limit its extension under any circumstances. The purpose of this comment is to point out that Sawyer's conclusion is based on the results of calculations using a single, probably inappropriately cool, continental geotherm and that it is not justifiable to generalize these results to all reasonable continental geotherms. The earlier paper employed the slab model [Parsons and Sclater, 1977] for the initial thermal conditions of the continental lithosphere and assumed that the strength of lithosphere was dominated by the power law creep of olivine. Increase in the strength of the lithosphere then follows from temperature changes in the mantle due to thermal diffusion during extension; the magnitude of these changes is scaled by the temperature at the base of the lithosphere, but no significance is attached to absolute values of the temperature because of the simplicity of the model. This approach has the advantage of describing the system in terms of a few parameters, at the expense of neglecting factors such as brittle failure, high-stress plasticity of olivine [Goetze, 1978; Brace and Kohlstedt, 1980], the strength of the crust, and the influence of radioactivity on the continental geotherm. Sawyer [1985] advocates using a more realistic model and so incorporates the effect of brittle failure; however, he neglects the other simplifications, with misleading results: Because of the strong dependence of the strength of earth materials on temperature, any refinement to the simple model of England [1983] that attaches significance to absolute values of stress must also attach significance to absolute values of temperature. It is unfortunate, then, that Sawyer's paper deals exclusively with the development of a continental lithosphere having an oceanic geotherm. In addition, emphasis on the magnitude of the strength of the lithosphere ought to be matched by emphasis on the likely magnitudes of the stresses available to drive extension. It is hard to disagree with the conclusion that if the Moho were at a temperature of 340oC, then the upper mantle of a lithosphere straining at 2.5 X 10 -6 S - would probably be in the brittle field [Sawyer,

The strength of intraplate lithosphere

The deformation of intraplate lithosphere in response to laterally applied stress has been investigated using a mathematical model of the elastic, brittle and viscous response of the lithosphere. Fundamental to the model is the conservation of the horizontal force associated with the applied stress and the redistribution of stress within the lithosphere after stress release by ductile or brittle failure. Ductile deformation is assumed to be controlled by dislocation creep in quartz in the crust and by dislocation and Dorn law creep in olivine in the mantle. Brittle failure is predicted using Griffith theory. The redistribution of stress after brittle and ductile deformation results in large levels of stress in the middle and lower crust immediately above the elastic-ductile or brittle-ductile transition. Lithosphere deformation is controlled critically by the lithosphere thermal structure of which surface heat flow, q, is taken as a convenient indicator. For hotter lithosphere, stress release by ductile deformation in the middle and lower lithosphere is more extensive and rapidly leads to larger levels of stress in the upper lithosphere. For sufficiently large levels of applied stress, or sufficiently hot lithosphere, complete failure ( Whole Lithosphere Failure of the lithosphere occurs by ductile and brittle deformation resulting in geologically significant strains. Critical levels of applied stress required to produce Whole Lithosphere Failure have been computed as a function of the lithosphere surface heat flow. The predicted strength of the lithosphere has been compared with expected levels of intraplate stress arising from plate boundary forces and isostatically compensated loads. The model predicts significant extensional intraplate deformation in regions of moderate heat flow with q > 60 m W m −2. For compressional deformation, however, a hotter lithosphere is required with q > c. 75 m W m −2. The model predictions are in general agreement with the comparatively widespread occurrence of extensional intraplate deformation and the restricted occurrence of compressional deformation. The model has also been used to investigate the relationship between the depth of the brittle-ductile transition and lithosphere temperature structure. The brittle-ductile transition depth is shown to become shallower with increasing heat flow, in good agreement with seismic evidence.

High-pressure recovery of olivine: implications for creep mechanisms and creep activation volume

High-temperature and high-pressure recovery experiments were made on experimentally deformed olivines at temperatures of 1613–1788 K and pressures of 0.1 MPa to 2.0 GPa. In the high-pressure experiments, a piston cylinder apparatus was used with BN and NaCl powder as the pressure medium, and the hydrostatic condition of the pressure was checked by test runs with low dislocation density samples. No dislocation multiplication was observed. The kinetics of the dislocation annihilation process were examined by different initial dislocation density runs and shown to be of second order, i.e. dρ dt = −p 2 K 0 exp[−( E ∗+PV ∗ RT ] where ρ is the dislocation density, k 0 is a constant, E ∗ and V ∗ are the activation energy and volume respectively, and P, R and T are pressure, gas constant and temperature, respectively. Activation energy and volume were estimated from the temperature and pressure dependence of the dislocation annihilation rate as E ∗=389±59 kJ mol −1 and V ∗=14±2 cm 3 mol −1 , respectively. The diffusion constants relevant to the dislocation annihilation process were estimated from a theoretical relation k= αD where k=k 0 exp [−(E ∗ + PV ∗)/RT], D is the diffusion constant and α is a non-dimensional constant of ca. 300. The results agree well with the self-diffusion constant of oxygen in olivine. This suggests that the dislocation annihilation is rate-controlled by the (oxygen) diffusion-controlled dislocation climb. The mechanisms of creep in olivine and dry dunite are examined by using the experimental data of static recovery. It is suggested that the creep of dry dunite is rate-controlled by recovery at cell walls or at grain boundaries which is rate-controlled by oxygen diffusion. Creep activation volume is estimated to be 16±3 cm 3 mol −1.

Creep of olivine during hot-pressing

The densification curves for the hot-pressing of pure olivine powders were obtained as a function of grain size (5 μ–2000 μ), temperature (1000–1600°C), and compacting stress (166–298 bars). This range of variables was found to straddle two fields of hot-pressing behavior, one dominated by power-law creep, one by Coble creep. The time required to density a powder to 99% of the single crystal density could be represented by the shorter of the two times: t 1 = 2.2 · 10 3σ −3.4 exp(85,000/RT) t 2 = 1.3 · 10 4σ −1.5(G) +3 exp(85,000/RT) where the compacting stress or pressure, σ, is given in bars and the grain size, G, in centimeters. It was also possible to estimate the parameters appropriate to Coble creep in a solid polycrystalline aggregate from the hot-pressing data; and these were: ϵ ̇ Coble = (3 to 10) · 10 −4(σ 1 − σ 3) 1 (G) −3 exp(85,000/RT) The strain rates computed from this formula are close to those predicted by Stocker and Ashby (1973) and those found by Twiss (1976).

The mechanisms of creep in olivine

We summarize the progress made in providing experimental verification for the deformation map of polycrystalline olivine published by Stocker &amp; Ashby in 1973 ( Rev. Geophys . 11, 391). Porosity-free polycrystalline deformation data, applicable to the mantle, were found to be obtainable only from high-pressure deformation studies. Combination of the results of such studies with hardness measurements and single crystal deformation studies on olivine provides narrow constraints on the flow of olivine resulting from dislocation mechanisms from room temperature to the melting point along a band of experimentally accessible strain rates. A good fit is obtained combining a Dorn law above 2 kbar differential stress, e/s -1 =5.7x10 11 ex{-128kcal/mol/RT (1-cr 1 -cr 2 /85000) 2 }, with a power law below 2 kbar, e = 70(cr 1 —cr 3 ) exp{— 122(kcal/mol)/RT}, where stress is measured in bars ( l bar = 10 5 Pa). Indirect data on a mechanism phenomenologically resembling the Goble creep regime are now available from two sources. The observed strain rates are only slightly faster than those predicted by Stocker &amp; Ashby (1973). The ' wet’ data, previously believed to show hydrolytic weakening, are found to fall within this Coble field. The asthenosphere is still expected to deform by the dislocation mechanism summarized by the two formulae given above, but higher stress deformation within the lithosphere is almost certainly dominated by this Coble creep regime once dynamic recrystallization sets in.

Nonlinear stress propagation in the Earth's upper mantle

This paper consists of two parts. The first is theoretical and extends Elsasser's theory of stress propagation in the upper mantle to an asthenosphere with nonlinear rheology. Exact solutions of the nonlinear equations are found for two geologically important problems. The second part uses these theoretical results as the basis for a measurement of the rheology of the asthenosphere. The seaward migration pattern of aftershocks from the February 4, 1965, Rat Island earthquake is analyzed, and strong evidence for a non-Newtonian stress-strain relation in the asthenosphere is presented. It is found that an individual large earthquake can influence the regional stress pattern only to a distance of about 300 km perpendicular to the line of rupture. Excellent agreement is found between the stress propagation coefficient calculated from the aftershock migration pattern and that calculated from laboratory measurements of high-temperature creep in olivine. We thus arrive at a picture of stress propagation in the upper mantle which is consistent both with theoretical expectation and with observational evidence.