Fault-propagation, ductile strain, and displacement-distance relationships

Displacement-distance analysis of fault-related fold structures can reveal important information about the distribution of fault displacement, and, in some cases, the history of fault propagation. This method is commonly used to: (1) determine the ratio of displacement rate to propagation rate (sp ratio), (2) predict the location of unconstrained fault tips, (3) determine the location of fault nucleation points, and (4) evaluate structural interpretations. Although the displacement-distance approach represents a potentially useful method for gaining information about displacement-parallel fault propagation histories of natural fault-related fold structures, the theoretical relationship between sp and relative stretch (εr) that forms the basis of this method remains essentially untested. Because displacement rates and propagation rates are generally unknown for natural structures, these relationships can only be objectively tested by analysing model structures with known geometries, strain distributions, and fault propagation histories. Displacement-distance analysis of different fault-related fold models reveals that: (1) displacement-distance relationships are highly dependent on the nature of the hanging wall strain, (2) relative stretch is not related to sp in any general way, (3) fault tip locations cannot always be predicted by linear extrapolation of displacement-distance trajectories, (4) displacement maxima are not necessarily indicative of fault nucleation points in all cases, and (5) although calculation of sp ratios from observed relative stretch magnitudes may not be appropriate, the use of displacement-distance relationships can nonetheless be useful in comparing structures and improving structural interpretations.