This paper investigates the use of a numerical model of firn diffusion and bubble trapping in the reconstruction of atmospheric records from firn measurements. We describe the concept of mean age and effective age of tracers in firn air and how the growth rate of a tracer in the atmosphere can alter the effective age. We discuss an iterative method to assign effective ages to firn measurements for tracers with fairly simple atmospheric histories, taking into account atmospheric growth rate variations. We then develop a Bayesian synthesis inversion calculation for inverting firn concentration measurements. This calculation gives estimates of the atmospheric concentration record with uncertainties. The dating and inversion techniques are demonstrated here with carbon tetrachloride measurements from a long firn record from Law Dome, Antarctica. The techniques are then applied to measurements of a range of halocarbons in a companion paper by Sturrock et al. <2002>.