We first analytically determine the relationship between velocity field and isochrone geometry along a steady flowline of an ice sheet. The method is based upon the stream function and its vertically normalized form, the normalized stream function (NSF). We show that the slope of the isochrones is the slope of the iso-NSF lines, plus a path term which is the cumulative result of the past trajectory of the ice particles. Secondly, we show how this property can be used to infer the internal velocity field from isochrones along a flowline with known mass balance conditions. We illustrate the method on two different situations: varying basal sliding and varying velocity profile around a divide. Third and finally, we show how internal layers can be inverted to infer the surface accumulation rate and we apply this method on a flowline downstream of the EPICA Dronning Maud Land drilling site.