Chemical structure and evolution of the mantle and continents determined by inversion of Nd and Sr isotopic data,I. Theoretical methods

While the chemical structure of the earth's mantle is probably rather complex, multi-box models have been used as a first approximation to evaluate this structure. Most commonly, a three-box model is used, involving the continental crust, the upper mantle and the lower mantle. The depleted upper mantle and the continental crust are assumed to represe1nt complementary reservoirs, related by crust formation processes occurring during geologic history.Here we investigate the Rb/Sr and Sm/Nd isotopic systematics of several three-box models, using mass balance equations and the definition of the mean age of the reservoirs. The geochemical uniqueness of the models, chosen from a large family of possible models, is evaluated from elementary graph theory, and these models are then solved using a total inversion approach. This paper (Part I) describes the methodology of the procedure; the companion paper (Part II) discusses the application of this approach to multi-box mantle models.