We present a kinematic approach to find the velocity field from dated internal-layer architecture in firn.Internal layers are isochrones and the depositional age of a layer particle is treated as a tracer.The forward problem uses two-dimensional steady-state advection of age, and conservation of mass to predict layer architecture.It thus only considers the kinematic equations and does not use any dynamic equations, an advantage for the application in firn, where rheological properties vary spatially.Different combinations of constraints on horizontal or vertical velocity properties are added.The inverse problem can be formulated as the solution of underdetermined and overdetermined systems of equations.The systems are solved using singular-value decomposition, allowing analysis of the singular-value spectrum, model resolution, and data resolution.For synthetic scenarios, the solutions of the inverse problem are evaluated by comparing the velocity-field solutions with synthetic input velocity data.Compared to conventional accumulation estimates, the new approach takes lateral advection into account, enabling improved separation of spatial and temporal variations in accumulation (deduced from the vertical velocity components). We present two glaciological applications: the determination of the migration velocity of a spatially non-stationary and highly variable accumulation pattern in a dune field, and reconstruction of past accumulation with a focus on its stationarity over time.