Satellite image sequences visualize important patterns of the atmospheric and oceanographic circulation. Assessing motion from these data thus has a strong potential for improving the performances of the forecast models. Representing a vector field by a vector spline has been proven efficient for fluid motion assessment: the vector spline formulation makes it possible to initially select the locations where the conservation equation has to be taken into account; it efficiently implements the 2nd order div-curl regularity, advocated for turbulent fluids. The scientific contribution of this article is to formulate vector splines in a multiscale scheme, with the double objective of assessing motion even in the case of large displacements and capturing the spectrum of spatial scales associated to turbulent flows. The proposed method only requires the inversion of a band matrix, which is performed by an efficient numerical scheme making the method tractable for large satellite image sequences.