The Mohr circle for curvature and its application to fold description

Abstract

Most conventional methods for the analysis of fold structures are founded on the assumption of cylindricity. It has been repeatedly shown that these methods can be useful for dealing with a wide range of structural geometries, even those for which the assumption is only approximately valid, e.g. structures produced by the interference of superimposed fold sets. In some instances though, such as in the analysis of oil-field structures, it is the presence and type of non-cylindricity in a structure which is of primary interest. The description of such folded surfaces requires more general methods of analyzing surface curvature based on the principles of differential geometry. The Mohr circle construction, already familiar to structural geologists in the context of stress and strain, is shown to be useful for the analysis of surface curvature and torsion. A practical method of mapping principal curvatures and their trajectories, involving the application of the Mohr circle, is described and applied, by way of example, for the survey of the Goose Egg Dome in Wyoming and a small-scale fold from Laksefjord, Norway.