The temporal and spatial variations of accumulation are key questions for studies on the determination and prediction of future changes of the ice sheets.Age-depth distributions of cold firn present a memory of spatio-temporal variations in accumulation at the surface and the velocity field.The surface deposited at a given time submerges and deforms depending on accumulation characteristics, flow velocities, firn densification and rheologicalproperties. The structure of older surfaces in a cold ice body can be mapped by ice-penetrating radar surveys through reflections from isochronuous internalhorizons, which can be dated by ice-core analysis.Standard methods for calculating accumulation from the layer architecture usually neglect horizontal advection, and thus introduce some errors.A particular problem occurs in regions of strong advection and for spatially migrating variations in accumulation, as observed in megadune fields.A kinematic inverse model is presented to extract information on horizontal and vertical velocities, and thus corrected accumulation, from the age distribution.The model is solely based on advection and conservation of mass equations, thus avoiding a constitutive relation for firn.The system is solved using singular value decomposition, yielding more insights into the structure of the problem and the solution compared to other inversion schemes.Advantages of this approach are presented and combinations of boundary conditions for several applications discussed to yield an improved reconstruction of accumulation rates for studies related to climate reconstruction.