Age-depth distributions of cold firn present amemory of spatio-temporal variations in accumulationat the surface and the velocity field.The surface deposited at a given time submergesand deforms depending on accumulation characteristics,flow velocities, firn densification and rheologicalproperties. The structure of older surfaces in acold ice body can be mapped by ice-penetrating radarsurveys through reflections from isochronuous internalhorizons, which can be dated by ice-core analysis.Of special interest to firn- and ice-core relatedstudies are the trajectory fields of probed locations.This requires knowledge about the complete velocity field.However, as the constitutive relations for solid icecannot easily be transferred and applied to firn,simple conventional flow modeling is not feasible.To circumvent rheological difficulties, a kinematicinverse model is presented to extract information onhorizontal and vertical velocities from the age distribution.The model is solely based on advection and conservationof mass equations, which together with the known agedistribution form a linear system of equations.The system is solved using singular value decomposition,thus yielding more insights into the structure of theproblem and the solution compared to other inversion schemes.Model perfomence is tested with synthetic steady-state agedistribution, calculated by a finite-difference model withprescribed advection velocities, density and accumulationprofiles. Various kinds and different numbers of boundaryconditions are used for inversion. Results indicate thatthe problem is well-posed and that the solutions arerelatively stable. This encourages extended application ofthis kinematic approach, e.g. combination with differentflow laws to determine rheological properties by inversion.