We have analyzed surface velocity data of the Mediterranean Sea as obtained from a primitive equation circulation model (Diecast model). We have computed the Finite Size Lyapunov Exponents (FSLEs) from this data set, which provide a measure of oceanic horizontal stirring, as well as reveal with their extreme values the barriers of transport. A particular property of the FSLE is that it is able to study spatial structures at scales under the resolution of the velocity data used in this computation. In this way, we can obtain information of submesoscales and mesoscales structures (1-100km). We investigate here how reliable are the results of a Lagrangian diagnosis at a similar and at a finer resolution than that of the velocity data. We address this work by the analysis of two properties: - Multifractal character of the spatial distribution of the FSLE, in order to study its scale invariance properties. - Relative error of the FSLE for three cases: a) by introducing a random perturbation in the velocity data, b) by decreasing the resolution of the velocity field, and finally, c) by adding white noise in the computation of the particle\'s trajectories.