Geometrical modeling of fault-related folds: a pseudo-three-dimensional approach

Area-balanced cross-sections of ramp anticlines and tip-line folds in thin-skinned fold-thrust belts can be quantitatively constructed using plane-strain fault-bend and fault-propagation fold models. Cross-sections alone, however, are somewhat inadequate for interpreting along-strike changes in thrust-related fold geometry. Complex interplay between along-strike changes in fault slip and fault shape determines a range of geometric configurations which are difficult to visualize without the aid of quantitative three-dimensional models. We extend conventional two-dimensional folding theories into the third dimension by allowing for continuous variations in fault slip and fault shape along strike. Geometric equations relating map-view angles between fold axial-surface traces are derived for a case assuming a uniform fault geometry and an along-strike displacement gradient. The resulting folds possess no unique fold axis, but rather are characterized by multiple fold hingelines each corresponding to bends in the fault. For typical displacement gradients observed in the field, analysis of the models suggests that discernible differences exist between map patterns of fault-bend folds and fault-propagation folds, whereas little difference exists between map patterns of similar and parallel fault-bend folds. Map-view angles between axial-surface traces for parallel fault-bend folds and fault-propagation folds are a function of both ramp cutoff angle and fault slip, whereas these same angles for similar fault-bend folds are solely a manifestation of fault slip. Examples assuming uniform shortening and continuously varying fault geometry along strike are also presented. Fault geometry is varied along strike to simulate oblique and lateral ramps. Depending upon model type and fault shape parameter modified, resulting folds exhibit either cylindrical or non-cylindrical fold geometries. Closure is generated by a decrease in fold amplitude where there is a decrease in ramp cutoff angle along strike or where a fault laterally cuts up section. In either instance, closure develops without varying shortening along strike. Model map patterns resemble actual thrust-related fold geometries and can be compared to maps of real structures to help predict subsurface geology.