<jats:title>Abstract</jats:title><jats:p>The suitability of a kinematic approach for finding the velocity field from dated internal-layer architecture in firn is investigated. 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. Different combinations of constraints on horizontal and 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. Solutions of the inverse problem are evaluated by comparing the velocity-field solutions with synthetic input velocity data. Unlike conventional accumulation estimates, the new approach takes lateral advection into account, enabling improved separation of spatial and temporal variations in accumulation. Two glaciological applications are presented: the determination of the migration velocity of a spatially non-stationary accumulation pattern and reconstruction of past accumulation and its stationarity over time.</jats:p>