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2 : prendre en compte le melange dans l’echantillonnage
Calibrer l’echantillonnage avec les modeles de convection
Dans les modèles geodynamiques : simuler correctement les flux – phénomènes de fractionnement
Faire la difference entre essayer une hypothese et realiser des predictions
Xenon has radiogenic and fissiogenic isotopes. It is possible to measure the individual contribution of these nuclear reactions to the xenon budget as you see here for MORBs. 129Xe comes from the decay of 129I, whereas 136Xe comes from the fission of 244Pu and 238U. Each one of these decays has a specific half-life and the combination of the 3 gives an excellent view of the degassing processes that were dominating at the 10, 100 and 1Gy scales. the difference between the atmosphere and mantle rocks shows that the atmosphere has been extracted before the complete decay of 129I and 244Pu.
We can estimate the ratios between the radiogenic and fissiogenic xenon isotopes for a closed-system (a mantle that would have not degassed nor differentiated). That is what you see on a log scale (taking 136Xe coming from the fission of 238U as the reference). We can measure these ratios in present-day mantle rocks and we observe that 129Xe and 136Xe coming from 244Pu fission have been lost from the mantle more efficiently than 136Xe coming from 238U decay. Since 238U decay is long term, that means that degassing was much more efficient early in earh history. this has been already pointed out in several studies in the 80’s and more recently by yokochi and marty.
The goal of this work is to give a quantitative framework to interpret these data and first we have to know how Xe is degassed from the mantle throughout the history of the planet. Degassing happened in three main stages. The first is accretion: degassing occured through shock degassing and melting. The second, that can be more or less contemporary to the first is magma ocean formation and cooling: highly vigorous convection and gas release at the surface of the earth. when the magma ocean cooled sufficiently that solid-state convection could start, degassing occured through sub-surface magmatism. today degassing of the mantle is located in places where melts reach the surface like ridges, arcs and hotspots. In the first two stages, one can consider that degassing is complete and happens at a very short time scale. On the last stage, degassing of the mantle is partial since it occurs only in places where melts are generated, and at a slow rate.
To model degassing in the solid-state convection stage we can use a simple box model approach where the parent element (U, Pu or I) is simply decaying or extracted to crustal components, and where Xe is degassed. the flux of degassing D(t) is parameterized by the flux of mantle rock that melts, assuming that Xe is very incompatible so that all the Xenon in the zone that melts is transfered to the melt and hence to the atmosphere. the volume of mantle that melts depends on the surface area where melting occurs and the depth at which the solidus is reached. it is the intercept of the solidus curved given by petrology studies and the mantla adiabat that depends on the temperature of the mantle.
We then need to know the temperature evolution to compute the evolution of the degassing flux. However we don’t have precise informations on the cooling history of the mantle during the solid-state convection stage. we know that it started when the temperature of the mantle was sufficiently low that less than 40% of it was melted and it has been proposed that the average temperature is around 2700K. and we know that today the average temperature is probably 2220K from the eruption temperature of MORBs. between those two we have little information. The worst thing is that the physics of mantle cooling is still debated and there is no consensus on how to model from first principle mantle cooling (see the work of Labrosse and Jaupart for instance). So we decided not to assume any physics and to test several ad hoc temperature evolution that could be consistent at first order. we then tried smooth functions in which the power $a$ and time of solid-state convection $t_i$ would be the important parameters to vary. The given temperature histories can simulate early or late cooling.
As for temperature, the rate of metling area has to be imposed. and it is probably even more difficult to provide a physical and predictive framework for that. so we also tested smooth power law functions that would depend on the depth of melting, assuming this would be the major factor determining the rate of melting area. the depth of melting is computed from the thermal history. hence, the parameter to vary here is the power $b$. $b$ is the sensitivity of the melting area flux to the depth of the solidus basically.
a simpler view of the theraml and melting area histories are depicted here. in gray are plotted the range of acceptable histories from our models. the time of solid-state convection onset here was also tested and ranges from 30 to 120my. the main feature is the change of cooling and melting rates at about 500my depending on the models. the present-day cooling rate of the mantle is here relatively constant afterwards and close to 50K per By. In the early period of several hundreedmy, the mantle would have cooled by 200 to 300K. during this stage, the heat released my magmas at the surface is comparable to the present-day surface heat flow. this suggests that cooling by melt extraction could be the dominated mode of mantle cooling whereas it changes afterwards toward conductive cooling through a boudary layer. a change of style of convection is then expected and it could be the onset of plate-tectonics here.
a probably more robust prediction of our model is the melting/processing history. in gray is the range of acceptable histories. to reproduce the values of the xenon ratios, the mantle has to be processed between 4 and 9 times. during the early cooling stage that corresponds more or less to the hadean, 75% of the processing occured. Hence most of the melting history of the Earth happened in the fisrt By of the planet. nothing is happening anymore in the present-day mantle.
Cours M2 - Nancy / partie 2
Peut-on faire mieux ?
Modélisation de la Dynamique
du Manteau terrestre
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