What Do Kinematic Models Imply About the Constitutive Properties of Rocks Deformed in Flat-Ramp-Flat Folds?

Kinematic theories of flat-ramp-flat folds relate fault angles to stratal dips in a way that allows prediction of structural geometries in areas of economic or scientific interest. However, these geometric descriptions imply constitutive properties of rocks that might be discordant with field and laboratory measurements. In this study, we compare deformation resulting from kinematic and mechanical models of flat-ramp-flat folds with identical geometries to determine the conditions over which kinematic models may be reasonably applied to folded rocks. Results show that most mechanical models do not conform to the geometries predicted by the kinematic models, and only low basal friction (0.1) and shallow ramps (ramp angle 10 degrees) produce geometries consistent with kinematic predictions. This implies that the kinematic models might be appropriate for a narrow set of geometric and basal fault friction parameters. Plain Language Summary Flat-ramp-flat folds kinematic models are widely used to infer subsurface fault geometry based on surface expressions of folded rock, investigate the thermal history of rocks now exposed at the surface, and assess the seismic hazard potential of faults producing flat-ramp-flat folds. While such models have the appeal of simplicity in their construction and application, they require loaded rocks to deform in specific ways to produce the required particle paths. In this sense, kinematic models require the rocks to possess certain, but poorly specified, constitutive properties that may or may not conform to laboratory-measured rock properties. We present a comprehensive kinematic-mechanical model comparison, accounting for both fault friction and elastoplastic deformation, to place bounds on the conditions over which the most common kinematic models may be reasonably applied to flat-ramp-flat geometries. We found that kinematic model particle paths were rarely reproduced by the finite element models. Only models implementing shallow (10 degrees) ramp angles and frictionless faults reproduced the particle motions required by the kinematic models. Our study suggests that kinematic models are best applied to flat-ramp-flat models of shallow dip and require virtually no frictional resistance along the basal fault ramp, or where high fluid pressure is present.