Spatial Connectivity: From Variograms to Multiple-Point Measures

Anisotropy and curvilinearity are common characteristics of geological structures. Traditional measures of connectivity such as the variogram are rectilinear in that they do not take into account the curvilinearity of these structures. Recent developments in geostatistics have demonstrated and simulated the effect of curvilinearity and multiple-point (mp) connectivity on the output of transfer functions such as flow simulators. A set of curvilinear channels and set of elliptical lenses may share the same variogram and rectilinear connectivity but would yield different flow responses because of their different curvilinearity. A measure of curvilinearity generalizing the variogram measure is therefore proposed. The proposed measure is directional with a tolerance cone and depends on distance with a tolerance, as with an experimental variogram.