Geometrical modeling of the subsuface is now becoming a key issue in the oil exploration business. Modeling complex zone with heav tectonic deformations quires tools that should be able to handle correctly not obly the geometry of objets, such as faults and geological layers, but also to handle the relationships between these objects. In particular a fault is to be modeled as a surface, but also as a field of displacement vectors. Alternatively, a fault can be seen as a kind of hyperlink between its two sides, allowing for continuity of physical properties in layers that are geometrically displaced. Using the Discret Smooth Interpolation method, it is possible to design an interpolation constraint that takes into account both of these baheviours.