With people constantly migrating to different urban areas, our mobility needs for work, services and leisure are transforming rapidly. The changing urban demographics pose several challenges for the efficient management of transit services. To forecast transit demand, planners often resort to sociological investigations or modelling that are either difficult to obtain, inaccurate or outdated. How can we then estimate the variegated demand for mobility? We propose a simple method to identify the spatiotemporal demand for public transit in a city. Using a Gaussian mixture model, we decompose empirical ridership data into a set of temporal demand profiles representative of ridership over any given day. A case of approximately 4.6 million daily transit traces from the Greater London region reveals distinct demand profiles. We find that a weighted mixture of these profiles can generate any station traffic remarkably well, uncovering spatially concentric clusters of mobility needs. Our method of analysing the spatiotemporal geography of a city can be extended to other urban regions with different modes of public transit.