A trace amount of water may be present in the upper mantle and would strongly affect the rheological properties of mantle rocks. Theoretically, this can be explained by the role of hydrogen in enhancing the kinetics of defect motion (for more details, see Karato, 2006 and Kohlstedt, 2008), thus significantly weakening olivine and olivine-rich rocks. A similar behaviour has been predicted for viscoelastic relaxation at seismic frequencies. Geochemical estimates on mid-ocean ridge basalts (MORB) indicate about 0.1 water. Assuming that MORB is the product of 10-20 melting of peridotite (Hirth and Kohlstedt, 1996), the primitive mantle rock should thus have 0.01 , which is distributed between the individual mineralogical phases according to the partitioning coefficient of each mineral (Hirth and Kohlstedt, 1996). In complex tectonic areas and mantle wedges, the amount of water should increase potentially. For the first time, recent laboratory experiments (Aizawa et al., 2008) allow the estimation of the effects of water on seismic attenuation. These data, together with previous data on dry olivine (Faul and Jackson, 2005), provide values for seismic attenuation to be expected in the upper mantle and can be used to build radial profiles of seismic attenuation based on temperature, grain size and water content, which are able to fit seismic observations (Cammarano and Romanowicz, 2008).
In general, it is reasonable to assume that
, where is attenuation (i.e. ), is the water content, is the frequency dependence, and is a constant which depends on the process. The value of this constant has been estimated to be between 1 for dislocation mechanisms and 2 in case of grain boundary mechanisms (Karato, 2006).
To model effects of water, we consider a positive contribution added to the dry attenuation. We define the total attenuation as:
Pressure effects can be modeled by multiplying with the exponential factor , where is the contribution to activation volume due to water content. Note that P dependence of the dry case is already included in attenuation predicted with Faul and Jackson's model (2005). In the absence of direct constraints on , we rely again on information from rheology. If , attenuation for a constant 0.01 water is much larger than for the dry case, both at low and high pressure (Figure 2.31b). With this constant amount of water and the described P-T dependent model, we do not find any attenuation profile that is able to satisfactorily fit the data for any reasonable T and GS profile. For example, assuming isothermal structures for given grain sizes, we found that the best-fit model always has a value for surface wave observations. This is due to the very high values of attenuation around 100 km. When using a much larger activation volume ( ), we find that interpretation in terms of average T does not change much (Cammarano and Romanowicz, 2008). However, only models with and are able to obtain a similar fit to the dry case. In this case, values at 100 km (3 GPa) are sensibly lower than before and values at higher P are very similar to the dry case (see Figure 2.31b). We point out that our water-contribution to is independent of grain size, but it does become larger as temperature increases. For example, at a GS of 1 cm and assuming isothermal structure, a is required for both the dry and the wet case. However, values of for the wet case are significantly higher, especially at shallow depths, and the misfit is not as low as in the dry case. On the other hand, for a given 1 mm GS, seismic observations are best explained with a 1500 K isotherm. In this case, the dry and wet profiles are more similar, as the effect of water on absolute attenuation is less important at lower temperatures.
Finally, we note that when modeling water effects, we should consider the feedback with all the other parameters and not only P and T. We decided to neglect the effect of water on frequency dependence. The Aizawa experiments seem to support such an assumption, not showing any systematic variation of with water content. In particular, the wet sample has a very similar frequency dependence (0.26) to the Faul and Jackson (2005) value. We also assume that there is no feedback between the grain-size dependence and water dependence. In conclusion, water enhances attenuation and trade-offs with temperature. Based on the available constraints, it is likely, however, that water will have a secondary effect on global attenuation measurements. Indeed, values due solely to a dry mechanism are already low enough compared to what is required seismically in the upper mantle.
Aizawa Y., A. Barnhoorn, U. Faul, J.F. Gerald and I. Jackson, The influence of water on seismic wave attenuation in dunite: an exploratory study, J. Petrol., 49, 841-855, 2008.
Cammarano F. and B. Romanowicz, Radial profiles of seismic attenuation in the upper mantle based on physical models.GJI, in press, 2008.
Faul, U.H., and I. Jackson, The seismological signature of temperature and grain size variations in the upper mantle, Earth Planet. Sci. Lett., 234, 119-134, 2005.
Hirth, G. and D. Kohlstedt, Water in the oceanic upper mantle: implications for rheology, melt extraction and evolution of the lithosphere, Earth Planet. Sci. Lett., 144, 93-108, 1996.
Karato, S., Influence of hydrogen-related defects on the electrical conductivity and plastic deformation of mantle minerals: A critical review, in Earth's Deep Water Cycle, pp. 113-130, AGU, Washington DC, 2006.
Kohlstedt, D., Constitutive equations, rheological behavior, and viscosity of rocks, Treatise on Geophysics, Elsevier, 2008.
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