CONVECTION METHODS AND FUNCTIONAL-EQUATIONS IN ORDER TO SOLVE INVERSETHERMOCHRONOLOGY PROBLEMS

Our aim is to give a complete account about convection methods which a llow: to get numerical simulations of both the simultaneous phenomena of population of nuclear tracks production and of thermal annealing of these tracks, giving rise, at the final state, to numerical histogram s, which are similar to the ones which can be got, nowadays, by etchin g techniques applied to a sample of apatite and track length measureme nts. to solve the corresponding inverse problem in which we have to go back from a given (computed or measured) histogram to a) the length a nd production time relation and b) to the thermal history, which is th e main unknown of this kind of inverse problems. We deal with densitie s of probabilities of presence of tracks lying in given length interva ls, which explain the use of models of functional equations both for t he direct and inverse problem. We consider an integral mass conservati on relation from which we derive two convection approaches. These appr oaches enable us to obtain functional equations in order to solve the inverse thermochronology problems for nearly all the main fading laws used in order to describe fission track annealing. These functional eq uations give rise to simple algebraic relation in the case of Bertagno lli's annealing law. This paper only concerns a mathematical modeling and the numerical aspects associated.