In geology, 3D fold evolution is the study of the full three dimensional structure of a fold as it changes in time. A fold is a common three-dimensional geological structure that is associated with strain deformation under stress. Fold evolution in three dimensions can be broadly divided into two stages, namely fold growth and fold linkage. The evolution depends on fold kinematics, Fold mechanism,Suppe, J., & Medwedeff, D. A. (1990). Geometry and kinematics of fault-propagation folding. Eclogae Geologicae Helvetiae, 83(3), 409–454.Cosgrove, J. W. (1999). Forced folds and fractures: An introduction. Geological Society, London, Special Publications, 169(1), 1–6. as well as a reporting of the history behind folds and relationships by which fold age is understood. There are several ways to reconstruct the evolution progress of folds, notably by using depositional evidence, geomorphological evidence and balanced restoration.Grasemann, B., & Schmalholz, S. M. (2012). Lateral fold growth and fold linkage. Geology, 40(11), 1039–1042.
3D fold growth
Under compressional stress, folds grow in all three dimensions, including vertical fold amplification and lateral fold propagation, both along fold crest and perpendicular to fold crests. Three-dimensional fold growth can be observed in areas like the Zagros Mountains in Iraq and Iran as well as Wheeler Ridge in California, United States.
Fold structure The vertical dimension of a fold can be described as an amplitude. The horizontal dimension of a fold can by described by wavelength and hinge line of a fold. As a fold grows in three-dimension, amplitude, wavelength and the length of the hinge line will increase.
Sheath fold
Sheath folds form in areas where rocks react differently to simple shear, due to variations in competence across layers. The hinge line is severely bent in sheath fold.
Fold kinematics Under force, rock strata buckle occurs by one of two kinematic processes, either by hinge migration or by limb rotation.Ahmadi, R., Ouali, J., Mercier, E., Mansy, J. L., Lanoë, B. V. V., Launeau, P., ... & Rafini, S. (2006). The geomorphologic responses to hinge migration in the fault-related folds in the Southern Tunisian Atlas. Journal of Structural Geology, 28(4), 721–728.
Hinge migration
A fold hinge can migrate when strata are folded by hinge migration but the hinge is fixed when strata are folded by limb rotation.Ortner, H., Kositz, A., Willingshofer, E., & Sokoutis, D. (2010, May). Geometry of growth strata in a transpressive fold belt in field and analogue model: Gosau Group at Muttekopf, Northern Calcareous Alps, Austria. In EGU General Assembly Conference Abstracts (Vol. 12, p. 6316). At least one of the fold hinges in the whole fold structure is mobile during three dimensional fold growth.Dahlstrom, C. D. (1990). Geometric Constraints Derived from the Law of Conservation of Volume and Applied to Evolutionary Models for Detachment Folding: Geologic Note:(1). AAPG Bulletin, 74(3), 336–344. For example, indicated by kinematic models, the structure of a fault-propagation folds should contain three anticlines/synclines with migrating hinges and 1 anticline with fixed hinge limb rotation.
Hinge migration can be distinguished from limb rotation by several structural and geomorphological features.
Growth strata, also known as syntectonic strata, are sedimentary layers that are deposited at the same time as folding. These layers are characterized by decreasing thickness of strata towards crest of an anticline(fig 1). They exist in various geometric patterns. The variation in geometric patterns can be attributed to fold kinematics, rate of uplift and sedimentation rate.Ahmadi, R., Mercier, E., & Ouali, J. (2013). Growth-strata geometry in fault-propagation folds: a case study from the Gafsa basin, southern Tunisian Atlas. Swiss Journal of Geosciences, 106(1), 91–107.
A knickpoint is a morphological term for a section of a present or abandoned river valley that shows an abrupt change in slope, and can be attributed to differential erosion or structural deformation. They are usually associated with waterfalls and lakes.
For the definition of wind gaps, please see subsection #streams deflected around the nose of fold. Hinge Migration VS Limb RotationStructural and geomorphological featuresHinge MigrationLimb RotationPattern of growth strataShoulder-shapedGradual taperingHinge deformationAt limb and hingeOnly near fixed hingeKnickpointShifting along direction of hinge migrationFixed positionWind gapsRamsey, L. A., Walker, R. T., & Jackson, J. (2008). Fold evolution and drainage development in the Zagros mountains of Fars province, SE Iran.Basin Research, 20(1), 23–48.Multiple wind gaps can be formed from a single riverUnlikely to form more than one wind gaps
Fold mechanism Folds that may experience prolonged 3D growth can be divided into two groups according to their causes, namely detachment fold and forced fold. They are mainly differentiated by the presence of major fault control on fold structure in forced folds, and the absence of it in detachment folds. Fold causes that do not contribute to significant fold growth in all three dimensions, such as en-echelon folds, drag folds and rollover anticline are not in these groups. Understanding the evolution of folds is important because it helps petroleum geologists to gain a better understanding on the distribution of structural traps of hydrocarbon.Watson, M. P., Hayward, A. B., Parkinson, D. N., & Zhang, Z. M. (1987). Plate tectonic history, basin development and petroleum source rock deposition onshore China. Marine and Petroleum Geology, 4(3), 205–225.Trudgill, B. D., Fiduk, J. C., Rowan, M. G., Weimer, P., Gale, P. E., Korn, B. E., ... & Henage, L. F. (1995). The Geological Evolution and Petroleum Potential of the Deep Water Perdido Fold Belt, Alaminos Canyon, Northwestern Deep Gulf of Mexico.Roure, F., & Sassi, W. (1995). Kinematics of deformation and petroleum system appraisal in Neogene foreland fold-and-thrust belts. Petroleum Geoscience, 1(3), 253–269.
Detachment fold
As shown in the visual analogy for detachment folds in fig 4, folds are found in rock strata above the decollement (paper: incompetent) while rock strata below it (table: competent, if it deforms it will fracture) remains undeformed, as shortening strain is concentrated at the rock strata above decollement.Ramsay, J. G., & Huber, M. I. (1987). The techniques of modern structural geology: Folds and fractures(Vol. 2). Academic press.Homza, T. X., & Wallace, W. K. (1995). Geometric and kinematic models for detachment folds with fixed and variable detachment depths. Journal of Structural Geology, 17(4), 575–588. In a setting in which overlapping strata acquires contrasting competency, a decollement (interface between paper and table) is usually found along strata in competent rock unit (such as sandstone) or along the interface of competent and incompetent rock unit (such as an evaporite). A fold acquires higher amplitude, longer wavelength and broader width when rock strata above the decollement are subjected to shortening stress parallel to, or at a low angle to the strata. Apart from stress parameters, contrast of competency across strata and variation of displacement along the decollement are the main factors contributing to fold geometry and three dimensional growth pattern.Jamison, W. R. (1987). Geometric analysis of fold development in overthrust terranes. Journal of Structural Geology, 9(2), 207–219.Mitra, S. (2002). Structural models of faulted detachment folds. AAPG bulletin, 86(9), 1673–1694.
Forced fold Two common types of forced folds are, namely, fault-bend fold and fault-propagation fold. Folding occurs above the hanging wall of a fold ramp in a fault-bend fold, while folding occurs above the truncation of a thrust fault(fault tip) in a fault-propagation fold. They are usually highly asymmetric with one side of the limb much steeper than the other side. Shortening stress is usually at a high angle to the strata and is concentrated along the slipping plane and in the hanging wall of the thrust fault. The fold acquires higher amplitude, longer wavelength and broader width as rock slips along the fault plane of the underlying coeval thrust fault, casting major influence on the three dimensional growth of the fold. Therefore, forced folds are controlled by the fault structure in the basement rocks along planar or listric fault surfaces.Johnson, K. M., & Johnson, A. M. (2002). Mechanical analysis of the geometry of forced-folds. Journal of Structural Geology, 24(3), 401–410. The amount of fault displacement would control the amplitude of a fold, the lateral growth of fault would implies lateral growth of fold and fault linkage implies fold linkage on the surface. When compared to detachment folds, contrasting competency across strata is not as pronounced and the tectonic environments that they are found in are often more diverse.
A detachment fold can evolve into a forced fold when shortening stress exceeds the maximum strength of rock, and as a result the decollement may propagate upwards towards the anticlinal core and fault the detachment fold. The resultant structure poses characteristics of both detachment fold and fault propagation fold.Mitra, S. (2003). A unified kinematic model for the evolution of detachment folds. Journal of Structural Geology, 25(10), 1659–1673. An exemplar structure of this kind can be found in Mississippi Fan fold belt in Gulf of Mexico.Rowan, M. G. (1997). Three-dimensional geometry and evolution of a segmented detachment fold, Mississippi Fan foldbelt, Gulf of Mexico. Journal of Structural Geology, 19(3), 463–480.
Identification of 3D fold growth
Fold growth in cross-sectional, across fold-axis dimension Modelling of the kinematic evolution of folds in cross-sectional view is usually based on one of the following schemes: balanced restoration, forward kinematic modelling or a combination of the two.Suppe, J., Sàbat, F., Munoz, J. A., Poblet, J., Roca, E., & Vergés, J. (1997). Bed-by-bed fold growth by kink-band migration: Sant Llorenç de Morunys, eastern Pyrenees. Journal of Structural Geology, 19(3), 443–461.Vergés, J., Burbank, D. W., & Meigs, A. (1996). Unfolding: An inverse approach to fold kinematics. Geology, 24(2), 175–178.Mount, V. S., Suppe, J., & Hook, S. C. (1990). A Forward Modeling Strategy for Balancing Cross Sections (1). AAPG Bulletin, 74(5), 521–531.Nunns, A. G. (1991). Structural Restoration of Seismic and Geologic Sections in Extensional Regimes (1). AAPG Bulletin, 75(2), 278–297.
Fold growth in lateral dimension Section restoration in all three dimension can only be done by highly specialized software and is mainly used for studies in hydrocarbon.Clarke, S. M., Burley, S. D., Williams, G. D., Richards, A. J., Meredith, D. J., & Egan, S. S. (2006). Integrated four-dimensional modelling of sedimentary basin architecture and hydrocarbon migration. Geological Society, London, Special Publications, 253(1), 185–211.