D. L. Kohlstedt

Water in the oceanic upper mantle: implications for rheology, melt extraction and the evolution of the lithosphere

Abstract The influence of water on the dynamics of the oceanic upper mantle is re-evaluated based on recent experimental constraints on the solubility of water in mantle minerals and earlier experimental studies of olivine rheology. Experimental results indicate that the viscosity of olivine aggregates is reduced by a factor of ∼ 140 in the presence of water at a confining pressure of 300 MPa and that the influence of water on viscosity depends on the concentration of water in olivine. The water content of olivine in the MORB source is estimated to be810±490H10/6 Si, a value greater than the solubility of water in olivine at a confining pressure of 300 MPa (∼ 250H10/6 Si). We therefore conclude that the viscosity of the mantle in the MORB source region is 500±300 times less than that of dry olivine aggregates. The dependence of the solubility of water in olivine on pressure and water fugacity is used in conjunction with other petrological constraints to estimate the depth at which melting initiates beneath mid-ocean ridges. These calculations indicate that melting begins at a depth of ∼ 115 km, consistent with other geochemical observations. Owing to the relatively small amount of water present in the MORB source, only ∼ 1–2% melt is produced in the depth interval between the water-influenced solidus and the dry solidus. A discontinuity in mantle viscosity can develop at a depth of ∼ 60–70 km as a result of the extraction of water from olivine during the MORB melting process. In the mid-ocean ridge environment, the mantle viscosity at depths above this discontinuity may be large enough to produce lateral pressure gradients capable of focusing melt migration to the ridge axis. These observations indicate that the base of an oceanic plate is defined by a compositional rather than thermal boundary layer, or at least that the location of the thermal boundary layer is strongly influenced by a compositional boundary, and that the evolution of the oceanic upper mantle is strongly influenced by a viscosity structure that is controlled by the extraction of water from olivine at mid-ocean ridges.

Strength of the lithosphere: Constraints imposed by laboratory experiments

The concept of strength envelopes, developed in the 1970s, allowed quantitative predictions of the strength of the lithosphere based on experimentally determined constitutive equations. Initial strength envelopes used an empirical relation for frictional sliding to describe deformation along brittle faults in the upper portion of the lithosphere and power law creep equations to estimate the plastic flow strength of rocks in the deeper part of the lithosphere. In the intervening decades, substantial progress has been made both in understanding the physical mechanisms involved in lithospheric deformation and in refining constitutive equations that describe these processes. The importance of a regime of semibrittle behavior is now recognized. Based on data from rocks without added pore fluids, the transition from brittle deformation to semibrittle flow can be estimated as the point at which the brittle fracture strength equals the peak stress to cause sliding. The transition from semibrittle deformation to plastic flow can be approximated as the stress at which the pressure exceeds the plastic flow strength. Current estimates of these stresses are on the order of a few hundred megapascals for relatively dry rocks. Knowledge of the stability of sliding along faults and of the onset of localization during brittle fracture has improved considerably. If the depth to the bottom of the seismogenic zone is determined by the transition to the stable frictional sliding regime, then that depth will be considerably more shallow than the depth of the transition to the plastic flow regime. Major questions concerning the strength of rocks remain. In particular, the effect of water on strength is critical to accurate predictions. Constitutive equations which include the effects of water fugacity and pore fluid pressure as well as temperature and strain rate are needed for both the brittle sliding and semibrittle flow regimes. Although the constitutive equations for dislocation creep and diffusional creep in single-phase aggregates are more robust, few data exist for plastic deformation in two-phase aggregates. Despite the fact that localization is ubiquitous in rocks deforming both in brittle and plastic regimes, only a limited amount of accurate experimental data are available to constrain predictions of this behavior. Accordingly, flow strengths now predicted from laboratory data probably overestimate the actual rock strength, perhaps by a significant amount. Still, the predictions are robust enough that uncertainties in geometry, mineralogy, loading conditions and thermodynamic state are probably the limiting factors in our understanding. Thus, experimentally determined rheologies can be applied to understand a broad range of topical problems in regional and global tectonics both on the Earth and on other planetary bodies.

Rheology of the Upper Mantle and the Mantle Wedge: A View from the Experimentalists

In this manuscript we review experimental constraints for the viscosity of the upper mantle. We first analyze experimental data to provide a critical review of flow law parameters for olivine aggregates and single crystals deformed in the diffusion creep and dislocation creep regimes under both wet and dry conditions. Using reasonable values for the physical state of the upper mantle, the viscosities predicted by extrapolation of the experimental flow laws compare well with independent estimates for the viscosity of the oceanic mantle, which is approximately 10 19 Pa s at a depth of ∼100 km. The viscosity of the mantle wedge of subduction zones could be even lower if the flux of water through it can result in olivine water contents greater than those estimated for the oceanic asthenosphere and promote the onset of melting. Calculations of the partitioning of water between hydrous melt and mantle peridotite suggest that the water content of the residue of arc melting is similar to that estimated for the asthenosphere. Thus, transport of water from the slab into the mantle wedge can continually replenish the water content of the upper mantle and facilitate the existence of a low viscosity asthenosphere.

Experimental constraints on the dynamics of the partially molten upper mantle: deformation in the diffusion creep regime

Experiments have been conducted to investigate the effect of melt on the creep behavior of water-free olivine aggregates deformed in the dislocation creep regime. The influence of the melt phase is modest at melt fractions less than ∼0.04. However, at melt fractions > 0.04, the creep rate of melt-added samples is enhanced by more than an order of magnitude relative to melt-free aggregates. This unexpectedly large influence of melt on strain rate arises because deformation occurs by grain boundary sliding (GBS) accommodated by a dislocation creep process. Four observations support this hypothesis. (1) The strain rate enhancement observed in the dislocation creep regime can be related to the stress concentration caused by the reduction in the solid-solid grain boundary area. (2) Both melt-free and melt-added samples exhibit strain rates indicating that deformation is limited by slip on (010)[100], the easiest slip system in olivine. (3) The GBS mechanism occurs near the transition between diffusion and dislocation creep. (4) Grains in specimens deformed in the GBS regime are not significantly flattened, even after ∼50% shortening. In melt-free aggregates, a transition from the GBS mechanism to dislocation creep limited by slip on (010)[001], the hardest slip system, is observed with an increase in grain size. A transition to (010)[001] limited creep was not observed for partially molten aggregates because grain growth was inhibited by the presence of melt. The results of this study indicate that the viscosity of the upper mantle may decrease by at least an order of magnitude if the retained melt fraction exceeds 0.04 or if the onset of melting results in a reduction in grain size and a concomitant transition from (010)[001] to (010)[100] limited creep.

High‐temperature deformation of dry diabase with application to tectonics on Venus

We have performed an experimental study to quantify the high-temperature creep behavior of natural diabase rocks under dry deformation conditions. Samples of both Maryland diabase and Columbia diabase were investigated to measure the effects of temperature, oxygen fugacity, and plagioclase-to-pyroxene ratio on creep strength. Flow laws determined for creep of these diabases were characterized by an activation energy of Q = 485±30 kJ/mol and a stress exponent of n = 4.7±0.6, indicative of deformation dominated by dislocation creep processes. Although n and Q are the same for the two rocks within experimental error, the Maryland diabase, which has the lower plagioclase content, is significantly stronger than the Columbia diabase. Thus the modal abundance of the various minerals plays an important role in defining rock strength. Within the sample-to-sample variation, no clear influence of oxygen fugacity on creep strength could be discerned for either rock. The dry creep strengths of both rocks are significantly greater than values previously measured on diabase under “as-received” or wet conditions [Shelton and Tullis, 1981; Caristan, 1982]. Application of these results to the present conditions in the lithosphere on Venus predicts a high viscosity crust with strong dynamic coupling between mantle convection and crustal deformation, consistent with measurements of topography and gravity for that planet.

Superplastic deformation of ice: Experimental observations

Creep experiments on fine-grained ice reveal the existence of three creep regimes: (1) a dislocation creep regime, (2) a superplastic flow regime in which grain boundary sliding is an important deformation process, and (3) a basal slip creep regime in which the strain rate is limited by basal slip. Dislocation creep in ice is likely climb-limited, is characterized by a stress exponent of 4.0, and is independent of grain size. Superplastic flow is characterized by a stress exponent of 1.8 and depends inversely on grain size to the 1.4 power. Basal slip limited creep is characterized by a stress exponent of 2.4 and is independent of grain size. A fourth creep mechanism, diffusional flow, which usually occurs at very low stresses, is inaccessible at practical laboratory strain rates even for our finest grain sizes of ∼3 μm. A constitutive equation based on these experimental results that includes flow laws for these four creep mechanisms is described. This equation is in excellent agreement with published laboratory creep data for coarse-grained samples at high temperatures. Superplastic flow of ice is the rate-limiting creep mechanism over a wide range of temperatures and grain sizes at stresses ≲0.1 MPa, conditions which overlap those occurring in glaciers, ice sheets, and icy planetary interiors.

High‐temperature creep of olivine single crystals 1. Mechanical results for buffered samples

To investigate the rheological behavior of the Earths upper mantle, over 100 high-temperature deformation experiments have been performed on single crystals of San Carlos olivine in controlled chemical environments at a total pressure of 0.1 MPa. Constitutive equations have been determined which describe the dependence of creep rate on applied stress, temperature and oxygen fugacity in terms of power law relations. In addition, the effects of orthopyroxene activity and loading orientation on the creep behavior have been investigated. For samples of each of three compression directions, [101]c, [011]c and [110]c, buffered by orthopyroxene or magnesiowustite, either two or three power law equations are required to describe the dependence of strain rate at fixed stress on temperature and oxygen fugacity over the full range of experimental conditions. It is proposed that in each power law regime a different creep mechanism controls the creep rate. For all of the experimental conditions, the activation energy for creep is independent of the stress level and the stress exponent is constant at 3.5±0.1. Activation energies for the various creep mechanisms varied from 230 to 1000 kJ/mol; and oxygen fugacity exponents lie in the range −0.03 to 0.4. From the constitutive equations determined based on the power law equations for all of the creep mechanisms, e˙-T-fo2 deformation maps were constructed at a stress of 1 MPa for olivine.

Effects of chemical environment on the solubility and incorporation mechanism for hydrogen in olivine

To investigate the solubility and the sites of incorporation of hydrogen in olivine as a function of point defect concentration, two-stage high-temperature annealing experiments have been carried out. The first annealing stage (the dry preannealing stage) was conducted at a total pressure of 0.1 MPa, a temperature of 1300° C and various oxygen fugacities in the range 10−11–10−4 MPa for times > 12 h. In these heat treatments, the samples were buffered against either orthopyroxene or magnesiowustite, or they remained unbuffered. The second annealing stage (the hydrothermal annealing stage) was performed at 300 MPa and 900–1050 ° C under a hydrogen fugacity of ∼ 158 MPa for 1–5 h. Infrared spectra from the annealed samples revealed two distinct groups of bands. Group I bands occurred at wavenumbers in the range 3450–3650 cm−1, while Group II bands occurred in the range 3200–3450 cm−1. The hydrogen solubility associated with Group I bands is proportional to fO2 to the 1/6 power for samples preannealed in contact with orthopyroxene, to the 1/3 power for samples preannealed in contact with magnesiowustite, and to the 1/13 power for samples preannealed in the absence of a solid-state buffer. The hydrogen concentration for Group II bands varies with fo2 to the 1/3 power for opxbuffered samples, to the 1/2 power for mw-buffered samples, and to the 1/3 power for unbuffered samples. The dependence of hydrogen solubility on oxygen fugacity and orthopyroxene activity suggests that hydrogen is incorporated into the olivine structure via association with point defects. The presence of two distinct groups of absorption bands indicates that hydrogen is associated with two distinct lattice defects. The following point defect model for the mechanism of incorporation of hydrogen in olivine is consistent with these results: Hydrogen ions responsible for the Group I bands are associated with doubly charged oxygen interstitials, while hydrogen ions responsible for the Group II bands are associated with singly charged oxygen interstitials. Furthermore, the infrared bands observed in naturally derived olivines are present in spectra from our hydrothermally annealed crystals. Thus, the mechanisms of incorporation of hydrogen in olivine under geological conditions are the same as those operative under laboratory conditions. The maximum solubility reached in these experiments was ∼ 360H/106Si, which corresponds to ∼ 0.002 wt% of H2O. This value is a lower bound for the solubility of hydrogen in olivine under upper mantle conditions.

Solution-precipitation enhanced diffusional creep of partially molten olivine-basalt aggregates during hot-pressing

Hot-pressing experiments have been used to study the effect of a chemically and texturally equilibrated liquid phase on the diffusional creep properties of polycrystalline olivine. Densification (creep) rate data on polycrystalline olivine both with and without the liquid basalt were collected as functions of applied stress/pressure (5–30 MPa), temperature (1300°–1400°C) and grain size (3–13 μm). Olivine-liquid basalt aggregates creep at rates which are persistently a factor of 2–5 greater than similar, melt-free specimens. Microstructural observations of dense olivine-basalt specimens indicate that the creep rate is enhanced by a solution-precipitation (pressure solution) mechanism during the densification of these specimens. Yet, the stress exponent (n = 1), grain-size exponent (m = 3) and average thermal activation energy (Q ≅ 380 kJ/mole) determined for the densification experiments are the same for olivine and olivine-basalt specimens. These observations suggest that because melt does not wet grain boundaries the kinetics of deformation of partially molten olivine-basalt aggregates are rate-limited by diffusive matter transport through melt-free olivine grain boundaries. The creep rate enhancement measured for olivine-basalt specimens occurs because the diffusive path length is effectively reduced by the presence of melt at triple junctions.

Influence of melt on the creep behavior of olivine–basalt aggregates under hydrous conditions

The influence of melt on the creep behavior of olivine–basalt aggregates under hydrous conditions has been investigated by performing a series of high-temperature triaxial compression experiments. Samples with melt fractions of 0.02≤φ≤0.12 were deformed under water-saturated conditions at temperatures between 1373 and 1473 K and a confining pressure of 300 MPa in a gas-medium apparatus. At constant differential stress and temperature, the rate of deformation increased rapidly but systematically with increasing melt fraction. In the diffusion creep regime, at a given differential stress, samples with melt fractions of 0.02 and 0.12 deformed a factor of ∼2 and ∼20, respectively, faster than a melt-free sample. In the dislocation creep regime, a sample with a melt fraction of 0.12 deformed a factor of ∼40 faster than a melt-free sample. For partially molten olivine–basalt aggregates deformed under hydrous conditions, the dependence of creep rate on melt fraction can be expressed in the form ϵ(φ)=ϵ(0) exp(αφ), where α≈26 for diffusion creep and α≈31 for dislocation creep. The results of this study, combined with reasonable estimates for the spatial variation in the concentrations of water and melt (as well as for the geotherm and the activation volume for creep), provide constraints on the viscosity structure of Earth’s upper mantle. As an example, we present a viscosity profile for the mantle wedge above a subducting plate, demonstrating that the viscosity in that region can vary by ∼3 orders of magnitude over a depth of ∼60 km due to the combined effects of water and melt weakening.