Abstract: Methods and systems are disclosed for processing data used for hydrocarbon extraction from the earth. Symmetry transformation groups are identified from sampled earth structure data. A set of critical points is identified from the sampled data. Using the symmetry groups and the critical points, a plurality of subdivisions of shapes is generated, which together represent the original earth structures. The symmetry groups correspond to a plurality of shape families, each of which includes a set of predicted critical points. The subdivisions are preferably generated such that a shape family is selected according to a best fit between the critical points from the sampled data and the predicted critical points of the selected shape family.

Abstract: A system and method is disclosed for generating an oriented three-dimensional graphical representation of a borehole. A system is implemented for receiving oriented caliper and borehole trajectory data taken by a 4-arm (or more) caliper device relating to a borehole. This information is used to generate an oriented three-dimensional wire mesh model of the borehole and color map the generated three-dimensional wire mesh model using the caliper data and gamma ray (or other lithology indicator) to reflect one or both of the orientation of borehole ellipticity or the lithology of the borehole.