Inversion of a Lagrangian time domain random walk (TDRW) approach to one-dimensional transport by derivation of the analytical sensitivities to parameters

Lagrangian approaches are well suited to transport in contrasted media but have been considered irrelevant when inversion is envisioned. The randomness of results for the same transport scenario adds to the rough evaluation by perturbation of the sensitivities, yielding an inaccurate search of parameters. It is shown here how a Time Domain Random Walk (TDRW) method can be inverted by deriving the sensitivities analytically. The calculations are very rapid and provide a precise evaluation of the descent directions followed by a Gauss–Newton optimizer. The method handles advection–dispersion + retention by matrix diffusion or sorption with first-order kinetics and proves its worth in all cases. Since analytical sensitivities are available, calculations are rigorous and allow discussing the inversion feasibility, the accuracy of the sought parameters, according to the predominant mechanism involved in the transport scenario.