3D Modelling of Geological Surfaces using Generalized Interpolation with Radial Basis Functions.

@inproceedings{HillierGM2013,
 abstract = { A generalized interpolation framework using radial basis functions (RBF) is presented that implicitly models 3D continuous geological surfaces from scattered multivariate structural data. Generalized interpolants can use multiple types of independent geological constraints by deriving for each, linearly independent functionals. A particularly useful application of generalized interpolants is that they allow augmenting on-contact constraints with gradient constraints as defined by strike-dip data with assigned polarity. The general form of the mathematical framework presented herein allows us to further expand on solutions by including stratigraphic data from above and below the target surface as inequality constraints by minimizing the norm of the interpolant using quadratic programming techniques.
One case study is presented that demonstrates the advantages and general performance of the surface modelling method in a data environment where off-contact stratigraphic data is plentiful and the number of oncontact and gradient constraints is relatively small. },
 author = { Hillier, Michael AND Schetselaar, Ernst AND de Kemp, Eric AND Perron, Gervais },
 booktitle = { Proc. 33rd Gocad Meeting, Nancy },
 title = { 3D Modelling of Geological Surfaces using Generalized Interpolation with Radial Basis Functions. },
 year = { 2013 }
}