Foliation fields and 3D cartography in geology: Principles of a method based on potential interpolation

A modeling method that takes into account known points on a geological interface and plane orientation data such as stratification or foliation planes is described and tested. The orientations data do not necessarily belong to one of the interfaces but are assumed to sample the main anisotropy of a geological formation as in current geological situations. The problem is to determine the surfaces which pass through the known points on interfaces and which are compatible with the orientation data. The method is based on the interpolation of a scalar field defined in the space the gradient in which is orthogonal to the orientations, given that some points have the same but unknown scalar value (points of the same interface), and that scalar gradient is known on the other points (foliations). The modeled interfaces are represented as isovalues of the interpolated field. Preliminary two-dimensional tests carried-out with different covariance models demonstrate the validity of the method, which is easily transposable in three dimensions.