We present a method to extract the atmospheric signal of trace gas mixing ratios from firn and bubbly ice measurements. This method, validated using data from Antarctic sites (Vostok and DE08), includes a numerical model that simulates air transport in the firn, and inverse theory. We focus here on atmospheric CH4 reconstruction, but the method can be used to reconstruct recent changes in any trace gas elemental or isotopic composition measured in firn and ice, that has no chemical interaction with solid H2O. This study also provides useful information on the effective diffusity-porosity relationship and quantifies the smoothing effect due to gas diffusion in firn and at pore closure, showing the typical time periods of events that are filtered by the firn and therefore not observed in the gas record of ice cores. ¿ 1997 American Geophysical Union