Abstract. Quantifying time-responses of the ocean to tracer input is important to the interpretation of paleodata from sediment cores – because surface-injected tracers do not instantaneously spread throughout the ocean. To obtain insights into the time response, a computationally efficient state-transition matrix method is demonstrated and used to compute successive states of passive tracer concentrations in the global ocean. Times to equilibrium exceed a thousand years for regions of the global ocean outside of the injection and convective areas and concentration gradients give time-lags from hundreds to thousands of years between the Atlantic and Pacific abyss, depending on the injection region and the nature of the boundary conditions employed. Equilibrium times can be much longer than radiocarbon ages – both because the latter are strongly biased towards the youngest fraction of fluid captured in a sample, and because they represent distinct physical properties. Use of different boundary conditions – concentration, or flux – produces varying response times, with the latter depending directly upon pulse duration. With pulses, the sometimes very different transient approach to equilibrium in various parts of the ocean generates event identification problems.