On the Straining of Cross-Bed Populations

The orientation of a strained cross-bed plane relative to regional bedding is a function of its initial orientation, the orientation of regional bedding, and the cumulative strain. If the maximum original dihedral angle between cross-bedding and bedding is known (in our studies it ranged from 25-40°) and is approximately constant regardless of orientation, the homogeneous deformation of cross-bed populations can be modelled. The model uses this dihedral angle ($\alpha$), and the intersection lineation of bedding and cross-bedding (Â). In the absence of ductility contrasts between layers, with strain the dihedral angle opens, closes, or remains the same, and the line rotates toward the direction of extension (if not parallel to an axis of strain). A number of different deformation models are discussed, generated by changing the type and magnitude of strain and the orientation of regional bedding with respect to the principal planes of strain. Two field studies of cross-bed distributions from both strained and unstrained quartzites in the Precambrian of Michigan and Paleozoic of Nevada were made. Strains calculated from deformed cross-bed populations (using maximum dihedral angle of the unstrained population) match (Michigan) or do not match (Nevada) those of interbedded deformed pebbles. Mismatch between model and observed strain is most likely a result of heterogeneous cumulative strain. Although the deformed cross-bed distribution can be of some use in establishing the cumulative strain, the original paleocurrent directions cannot be reconstructed because the rigid rotation history is not known and non-trivial in general. Furthermore, for large strains it is highly likely that an entire portion of the original population of cross-beds was flattened in the plane of bedding such that their dihedral angles are now less than 10° (that is, the cross-beds approach parallel laminations). Such flattened cross-beds are not measurable or perhaps even visible, and therefore the original cross-bed or paleocurrent distribution cannot be restored.