In order to highlight the characteristics of the trade-off between grain size and temperature, we show in figure 2.57 (top panel), the misfit values for isothermal structure from 100 to 400km for various constant grain sizes. We found that Q observations are much more sensitive to T than grain size, as shown by the contour lines in figure 2.57. Note that the cold structure of the lithospheric part does not affect measurements significantly. Indeed, we test that a negligible variation of the misfit pattern is obtained when using a standard 60My old oceanic geotherm for all thermal structures in the first 80km, plus a linear gradient in the 20km below to join the isotherms. The average temperature () of the upper mantle is very well constrained by seismic observations for a given grain size. For example, we found that a 1 mm grain size requires 1500K, while a higher temperature (1600K) is required around 1cm and slightly increases with coarser grain sizes. Subsequently, by giving a reference temperature at 100km of 1600K, more or less consistent with the temperature expected from a 60my old oceanic geotherm at that depth, we tested linear temperature gradients down to 400km, from -1.5 to 1.5 , for various grain sizes (middle panel of figure 2.57). Again, we found that observations are able to discriminate between different thermal gradients with depth at given grain sizes. In general, positive gradients are required at grain sizes cm, while negative ones are preferred for millimeter grain-sizes. There is an obvious trade-off, here not shown, between the Tref(100km) and the gradients below. A reference temperature of 1700K at 100km will be more compatible with positive thermal gradients. In particular, we found that an adiabatic 1300 temperature is compatible with observations at 1cm constant grain size.
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