The friction coefficient and the base topography of a stationary and a dynamic ice sheet are perturbed in two models for the ice: the full Stokes equations and the shallow shelf approximation. The sensitivity to the perturbations of the velocity and the height at the surface is quantified by solving the adjoint equations of the stress and the height equations providing weights for the perturbed data. The adjoint equations are solved numerically and the sensitivity is computed in several examples in two dimensions. A transfer matrix couples the perturbations at the base with the perturbations at the top. Comparisons are made with analytical solutions to simplified problems. The sensitivity to perturbations depends on their wavelengths and the distance to the grounding line. A perturbation in the topography has a direct effect at the ice surface above it, while a change in the friction coefficient is less visible there.