3D balanced unfolding : the tetrahedral approach

@inproceedings{MuronRM2003,
 abstract = { Structural models are based on incomplete data, it remains a possible interpretation that needs to be validated. A widely used technique is structural restoration and involves unfolding of geological structures to go backwards through geological time. This paper sums up the current gOcad approach developed these past few years. It is particularly focused on a new 3D kernel based on tetrahedral meshes that allows to handle complexly folded and faulted volumes. 3D balanced unfolding problem consists in the computation of the restoration vectors (inverse of displacement vectors) overall a topological model. This vector field has to honor the sollowing conditions: 1. two simple constraints derived from a continuum mechanics analogy (mass preservation and a strain minimization constraints) 2. a set of boundary conditions (e.g. reference horizon has to be flat after unfolding). It is shown that these different conditions can be turned into a linear system and solved in a least squared sense. Results can be easily analyzed using either the final restored geometry or the generated strain. },
 author = { Muron, Pierre AND Mallet, Jean-Laurent },
 booktitle = { 23th gOcad Meeting },
 month = { "june" },
 publisher = { ASGA },
 title = { 3D balanced unfolding : the tetrahedral approach },
 year = { 2003 }
}