  We define a compactification of symmetric spaces of noncompact type, seen as
spaces of isometry classes of marked lattices, analogous to the Thurston
compactification of the Teichm\"uller space, and we show that it is
equivariantly isomorphic to a Satake compactification. We then use it to define
a new compactification of the Torelli space of a hyperbolic surface with marked
points, and we show that it is equivariantly isomorphic to the Satake
compactification of the image of the period mapping. Finally, we describe the
natural stratification of a subset of the boundary.
