Relief and shortening in detachment folds

We present new thickness-relief methods for determining shortening S(z  ), mean shortening S¯(z) and curvimetric shortening Sc(z) as a function of height in well-imaged structures. Thickness-relief measurements allow us to constrain the fractions of the deformation that are layer-parallel pure shear, simple shear, and flexural, and to measure the excess area Ae of fold cores caused, for example, by flow of evaporites. The key measurements are made in the thickness domain, which allows for more certain determination of regional stratigraphic gradients, which is required for reliable separation of structural relief from primary stratigraphic thickness variations. We apply these methods to a diverse set of active detachment folds from the fronts of the Nankai trough Japan, Cascadia accretionary wedge Oregon, southern Tianshan China and Agbami anticline deep-water Niger delta. Three of these folds can be approximated by pure-shear detachment fold models because more than 95% of the shortening is by layer-parallel heterogeneous pure shear plus horizontal compaction. For this reason curvimetric shortening is one to two orders of magnitude less than total shortening. In contrast, Agbami anticline shows layer-parallel stretching above the excess area of the fold core. In all examples the layer-parallel simple-shear component is negligible or absent.