We study the influence of deep vortices on the ocean surface in terms of sea-surface elevation, a quantity related to a fluid stream function. We use several mathematical and numerical models, from the most idealized configurations (point vortices) to realistic ones (finite volume vortices). We determine analytically the surface influence of vortices at rest (steady signature) and in motion (dynamical signature). Then, using a nonlinear, numerical hydrodynamicmodel for oceanic vortices, we determine the growth with time of a dynamical signature for drifting vortices without steady signature. We conclude on the possibility to detect several types of oceanic vortices with surface measurements, using the results from our theory and experiments.