Description of folded geological structures using differential geometry

Abstract

Traditionally,  in  structural  geology  the  description  of  folds  has  been  made  by  means of  the cylindrical model. Consequently, the fundamental geometric information is reduced to 2D because in the cylindrical model, all sections perpendicular to the fold axis are identical. On the other hand, the progressive use of 3D data such as GPS, remote sensing, 3D seismic reflection etc. has promoted the application of differential geometry in the description of folded structures. Therefore, differential geometry has become a new and powerful tool to rigorously quantify both, the modeled and measured geometry of geologic structures. In this work, the concept of geologic curvature is applied for the description of folded structures by using differential geometry. Additionally, the use of this method is strongly suggested, because it provides a reliable framework for the quantitative description of either, plane and curved surfaces. For such, a sample application is presented here for the analysis and quantification of geologic folds through graphic representations and compiled MATLAB® codes. An illustrated comparison between the traditional method and the differential geometry for the description of geological structures is presented here, by taking into account the versatility, efficiency, and benefits of each. Finally, a worked example is presented to illustrate the use of differential geometry in the modeling of folded structures; bearing in mind that modeling is a fundamental component of modern Structural Geology and critical for the actual exploration techniques, e.g. oil, mining, etc.