The two thermoelastic models for the same pyrolitic composition gave similar results in terms of thermal structure in the first 400km (Figure 2.55, second panel from the right) when coupled to the same P-T dependent Q model and assuming a given constant grain size and reference period (see Figure 2.55). Some differences between the two models appear in the first 150km. The two models differ in the transition zone as well, because of the large uncertainties on the shear properties of wadsleyite and ringwoodite. Here, we do not discuss further those features. Instead, we focus on the interpretation of the dV$_S$/dz gradient between 250 and 350km. Both pyrolite models (PEPI03 and LARS07) imply a negative thermal gradient to explain the $V_S$ model required by seismic data (Figure 2.55). However, the consistent average Q structure predicted by those models attains very high values around 350km (Figure 2.55, third panel from the right) and we tested that the resulting $<$Q$>$ model is not consistent with the seismically observed global attenuation. Reducing the grain size, as expected, has the overall effect of reducing the temperatures to explain the same $V_S$ structure, but the thermal gradients stay almost the same. We tested that even for a constant grain-size of 1mm, the resulting Q is still too high ($Q_S \sim 450$) for both thermoelastic models at 350 km. The average density and $V_P$ structures that are consistently determined by the mineral physics models are also plotted in Figure 2.55. The observed discrepancies are due to the different relative variations of $V_S$ compared to density and $V_P$ (heterogeneity ratios) between the two mineral physics models. Note, however, that variations in density are extremely small compared to the variations expected when interpreting the same $<$$V_S$$>$ model with variations in composition (compare density panels in Figure 2.55 and 2.56). We do not plot the similar indirect effects on $V_P$ and density for a thermal interpretation when using different grain sizes. Alternatively to the discussed negative thermal gradient, an increase in grain size has been invoked to explain the isotropic features below 250km (Faul and Jackson, 2005). In our case, we found that such explanations would get a $<$$Q_S$$>$ structure that does not fit the seismic observations. The largest variations in thermal interpretation are obtained when varying the pressure dependence of the Q model, i.e. the activation volume V* (see also previous report). For example, by using a $V*=0.6\times 10^{-5}$, we found that a thermal explanation characterized by an overall cold upper mantle ( $<T> \sim 1500K$) and a negative thermal gradient below 250km is now feasible. In spite of the low average T, the low V* keeps the $Q_S$ values small enough in hot areas to get a $<$$Q_S$$>$ consistent with observed seismic attenuations (Figure 2.55). Note, however, that $Q_S$ values may be too low at some depths ($\sim20$) compared to what is inferred seismically. In Figure 2.56, we show the different thermal interpretation using the LARS07 model for 4 compositions. If we assume an adiabatic $1300^oC$ geotherm, it is possible to explain the $V_S$ gradient with a compositional variation with depth. The required compositional gradient may be estimated visually by looking at what depth the thermal profiles for different compositions cross the mantle adiabat (Figure 2.56). We observe an increase from 17% of MORB component mixed with harzburgite (that is the value of an average pyrolite) at 250km until 35% at $\sim$ 350km.

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