Computing Curvilinear Distances in Tetrahedral Meshes

@inproceedings{CastagnacRM2008,
 abstract = { Tetrahedral meshes are probably the most accurate and flexible way of complicated geological structures on a computer. However, the modeling of petrophysical heterogeneites on such meshes raises a number of challenges. In this work, we investigate about an essential ingredient for geostatistical modeling on tetrahedral meshes : the computation of distances based on a local field anisotropy. More precisely given an a priori vector field, a new methodology for computing distances under orthotropic, locally varying anisotropy field is presented. This algorithm is based on a fourth order Runge Kutta distance approximation. First, curvilinear lines are built for materializing the main directions along which local variograms are computed. Second, the minor directions of the orthotropic variogram are computed. These then interpolate the petrophysical properties taking in account the anisotropy field, either using estimation or stochastic simulation. This algorithm could be used in various spatial data situations such as those encountered in petroleum and mining applications, especially in intrusive formation where 3D curvilinear mapping is impossible. },
 author = { Castagnac, Claire AND Caumon, Guillaume },
 booktitle = { 28th gOcad Meeting },
 month = { "june" },
 publisher = { ASGA },
 title = { Computing Curvilinear Distances in Tetrahedral Meshes },
 year = { 2008 }
}