Effects of water on seismic attenuation

Fabio Cammarano and Barbara Romanowicz

Introduction

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 $\sim$0.1 $wt\%$ water. Assuming that MORB is the product of $\sim$10-20$\%$ melting of peridotite (Hirth and Kohlstedt, 1996), the primitive mantle rock should thus have $\sim$0.01 $wt\%$ $H_2O$, 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).

Methods and results

In general, it is reasonable to assume that $Q^{-1}\propto W^{\alpha r}$, where $Q^{-1}$ is attenuation (i.e. $1/Q_S$), $W$ is the water content, $\alpha$ is the frequency dependence, and $r$ is a constant which depends on the process. The value of this constant has been estimated to be between $\sim$1 for dislocation mechanisms and $\sim$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:

$$Q^{-1}=Q_{dry}^{-1}(P,T,d,\omega)+Q_{wet}^{-1}(P,T,W)$$ (2.9)

where $Q_{dry}^{-1}$ is here assumed to be the Faul and Jackson value and $Q_{wet}^{-1}$ is the water contribution. The reason for using such an expression is to preserve the knowledge of the T and grain-size dependence of the Faul and Jackson (2005) model for dry olivine and to include an empirical correction for water based on recent experimental results at high temperature (Aizawa et al., 2008). In spite of large uncertainties, we know that this correction is always positive (higher attenuation) (see Figure 2.31). The effects on pressure due to the addition of water must also be considered. Therefore,

$$Q_{wet}^{-1}(P,T,W)=A(T,P) W^{\alpha r}$$ (2.10)

where $\alpha$ is assumed to be the one from Faul and Jackson (i.e. 0.27). The estimated temperature dependence of $Q_{wet}^{-1}$ at low pressure (0.2 GPa) is based on the recent experiments by Aizawa et al (2008). We compared the T-dependent attenuation for two natural dunite samples which are characterized by different amounts of water (Figure 2.31a). The $\lq\lq$wet$''$ sample probably retains the entire inventory of water ($\sim$2 $wt\%$) during the high-T experiments, including 0.0187 wt% of molecular water. The $\lq\lq$dry$''$ sample, conversely, has lost most of the water and behaves similarly to anhydrous material (Figure 2.31). The effect of water on enhancing viscoelastic relaxation processes has been clearly observed for the first time with these experiments. However, a precise formalism describing the water dependence of solid-state viscoelastic relaxation is hampered because of the structural (and compositional) complexity of the natural samples; the marginal, but not negligible, role of partial melt; and, last but not least, the role of the fluid phase (Aizawa et al., 2008). Further studies on simpler material will better characterize the effects of water. At the moment, we can use the available indications to give a rough estimate of the possible effects of water on absolute $Q^{-1}$. The difference in observed attenuation between the $\lq\lq$dry$''$ and $\lq\lq$wet$''$ (saturated) samples increases exponentially with temperature, consistent with an enhanced activated process.

Pressure effects can be modeled by multiplying $A(T,P_0)$ with the exponential factor $\exp{(PV_W^*/RT)}$, where $V_W^*$ 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 $V_W^*$, we rely again on information from rheology. If $V_W^*=1.06\times10^{-5} m^3 mol^{-1}$, attenuation for a constant 0.01 $wt\%$ 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 $>0.13$ for surface wave observations. This is due to the very high values of attenuation around 100 km. When using a much larger activation volume ( $V^*=2.4\times10^{-5} m^3 mol^{-1}$), we find that interpretation in terms of average T does not change much (Cammarano and Romanowicz, 2008). However, only models with $GS<=1$ $mm$ and $<T>=1500$ $K$ are able to obtain a similar fit to the dry case. In this case, $Q^{-1}$ 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 $\lq\lq$water-contribution$''$ to $Q^{-1}$ 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 $<T>=1600$ $K$ is required for both the dry and the $0.01$ $wt\%$ wet case. However, values of $Q^{-1}$ 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 $\alpha$ with water content. In particular, the $\lq\lq$wet$''$ sample has a very similar frequency dependence ($\sim$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, $Q_S$ values due solely to a dry mechanism are already low enough compared to what is required seismically in the upper mantle.

Figure 2.31: Modeled effects of water on P-T dependent attenuation. a) T-dependent attenuation as function of water content at ambient P, period = 150 s and for a GS of 0.01 mm (solid lines). The $\lq\lq$wet$''$ and $\lq\lq$dry$''$ samples (dashed lines) are, respectively, the attenuation values for two natural dunite samples (1093 and 1066 of Aizawa et al., 2008). The original laboratory data have been interpreted with Burgers model (same formalism as Faul and Jackson, 2005), but in this case, without the (unconstrained) grain size dependence. Both samples have an average grain size around $0.02$ $mm$. b) Modeled T-dependent attenuation at different pressures for the dry case (solid) and with 0.01 wt% water, period = 150 s and grain size of 0.01 mm. Dashed lines are for $V_W^*=1.06\times10^5 m^3 mol{-1}$. Dotted lines are with $V_W^*=2.4\times10^5 m^3 mol{-1}$. For comparison, c) and d) show, respectively, variations of $Q^{-1}$ with grain size and effects of pressures for two given grain sizes (solid lines for 1mm and dashed for 0.01mm) computed with the Faul and Jackson model at a period of 150 s.

References

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.