What can we infer about the spatial distribution of some tracer into the Earth's mantle from the sampled basalt collections? Among the whole mass of the involved mantle, some goes into basaltic source regions, a part of which contributes to basalt genesis. Then, some of these basalts erupt on the Earth's surface and finally become emplaced in outcrops. Finally, some outcrops are more or less extensively visited and sampled, and these samples are processed for geochemical analysis and measurements for instance of tracer concentrations and isotopic compositions. In the following, the considered geochemical quantities will be the classical trace element concentrations and isotopic ratios of long-period radiogenic elements.
The reconstruction of the quantitative tracer distribution for the all the erupted basalts from the measurements on samples can be theoretically resolved. The proposed solution accounts for the measurement uncertainty and for the relative eruption rates or emplaced volumes. To go further back in the geodynamical processes, one can use the petrogenetic models which related the distribution of tracer concentrations and isotopic compositions in the produced basalts to those of the source. An important result of this treatment is the evaluation of the true degree of isotopic heterogeneity in the source of oceanic basalts.
A first step is to try to infer how valid these characteristics evaluated for a sample mantle are for the whole mantle. This asks the question of the efficiency of convective mixing in the mantle.
Finally, we develop a simple first-order model of evolution of the isotopic and chemical heterogeneity for the Earth's upper mantle. We express a simple relationship between the mantle isochron ages and the stirring time of the mantle, which is a measure of the characteristic time of erasure of the geochemical heterogeneity by convective mixing.