A Field-Based Theory for Time Geography

Classic time geography is powerful but rigid, admitting only uniform travel velocities. Computational time geographic methods that resolve the uniform velocity assumption through transportation networks or isochrones only partially address this weakness and do not have a rigorous theoretical foundation. This article develops an analytical time geographic theory for the case where travel velocities vary continuously across space. Using the continuous transportation or urban fields tradition in quantitative geography and regional science, this article formulates analytical definitions of the space-time path and prism for the case where unobserved components are characterized by minimum cost curves through an inverse velocity field rather than straight line segments through a uniform velocity plane. This provides a geometrically and visually oriented approach to capturing complex velocities that complements existing methods. Time geographic fields also generalize time geography as the classic and isochrone versions are special cases; these now have a rigorous analytical foundation. It also can extend the network approach by treating links as regions with continuously varying velocities. Time geographic fields are also useful for nonnetwork-constrained phenomena such as movement through terrain, water, and air. This article illustrates the approach using a computational implementation based on a lattice approximation.