Abstract Detachment folds seem conceptually the simplest of all fault-related folds, yet they continue to offer substantial and rich challenges that are symptomatic of fault-related folding in general. The standard picture of detachment folds goes back at least to August Buxtorf's widely reproduced 1916 regional cross sections of the Swiss Jura in which he interpreted the Jura box folds to be regionally detached from the basement along a weak layer of Triassic evaporites. Most theoretical and conceptual models of detachment folding have followed Buxtorf's model with a twofold mechanical stratigraphy composed of a competent flexural lid conserving bed length overlying a weak basal detachment layer that conserves only volume. However, this standard model of detachment folding has a fundamental and classic problem from a balancing perspective, which is outlined in this chapter. Furthermore, the classic Jura box folds drawn by Buxtorf were in fact not at all constrained by subsurface data, except along the Grenchenberg railroad tunnel where a surprising and much more complex structure was encountered, involving a strongly folded thrust fault that was intersected three times in the 8.5-km (5.3-mi)-long tunnel. Hans Laubscher argued that such complexly folded thrust faults are in fact typical of many Jura box folds. Analogous structures have been observed in Canada, Mexico, and Spain. I argue here on the basis of mass-balance considerations that detachment folds with folded thrusts are one of several theoretically expected modes of detachment folding. More broadly, the classical models of detachment folding assume a closed-system behavior in which all shortening is locally consumed in the fold. These classical models include (1) local flow of a weak basal layer, for example, salt (Wiltschko and Chapple mechanism) and (2) pure-shear detachment folding (Groshong and Epard mechanism). Here we discuss several additional models of detachment folding, including open-system behavior with (3) far-field flow of the weak basal layer, (4) roof detachments above the basal layer, and (5) roof ramps above the basal layer such as the folded thrust fault of the Grenchenberg anticline. In this final mechanism, the flexural lid or other more competent stratigraphic intervals shorten by a combination of fault slip and flexure, whereas the less competent intervals, including the basal layer, shorten by flow. All of these mechanisms are end members capable of existing in combination within actual folds; several examples combine two or three of these mechanisms.

Abstract The thickness variations and shapes of strata deposited over actively growing folds provide a convolved record of the interaction of deformation and sedimentation. Here we show how key elements of the history of shortening can be extracted using area-of-relief measurements on many stratigraphic horizons in well-imaged structures. In pregrowth strata, the shortening is equal to the vertical gradient in the area of structural relief, S = d A /d z . In growth strata, this relationship must be modified because the observed gradient in the area of relief now includes the effects of both structural thickening and stratigraphic thinning caused by deposition over the growing structure, S = (d A /d z ) obs — (d A /d z ) strat . This stratigraphic thinning cannot be measured directly from thickness variations because of later structural thickening but can be determined through consideration of the ratio of the mean shortening rate to the sedimentation rate, , which is a key parameter. We apply these concepts to a set of actively growing detachment folds: Nankai Trough, Japan; Cascadia, offshore Oregon; Yaken anticline, western China; and Agbami anticline, Niger Delta. These examples show a considerable diversity and complexity, including the effects of excess area in weak basal detachment layers, multiple detachment levels, and large differences in . All show not only constant shortening as a function of height in pregrowth strata and approximately constant shortening rates, , over substantial stratigraphic thicknesses, but also abrupt and large increases in shortening rate by factors of 5-10 and significant hiatuses in fold growth. The typical shortening rates in these frontal structures are in the range of 0.1-3 mm/yr (0.003-0.12 in./yr) and represent only 1-10% of the regional plate tectonic rates of their larger tectonic settings (2-6 cm/yr [0.8-2.4 in./yr]), indicating that shortening is not currently concentrated in these frontal zones of these mountain belts and accretionary wedges. Abstract The thickness variations and shapes of strata deposited over actively growing folds provide a convolved record of the interaction of deformation and sedimentation. Here we show how key elements of the history of shortening can be extracted using area-of-relief measurements on many stratigraphic horizons in well-imaged structures. In pregrowth strata, the shortening is equal to the vertical gradient in the area of structural relief, S = d A /d z . In growth strata, this relationship must be modified because the observed gradient in the area of relief now includes the effects of both structural thickening and stratigraphic thinning caused by deposition over the growing structure, S = (d A /d z ) obs — (d A /d z ) strat . This stratigraphic thinning cannot be measured directly from thickness variations because of later structural thickening but can be determined through consideration of the ratio of the mean shortening rate to the sedimentation rate, , which is a key parameter. We apply these concepts to a set of actively growing detachment folds: Nankai Trough, Japan; Cascadia, offshore Oregon; Yaken anticline, western China; and Agbami anticline, Niger Delta. These examples show a considerable diversity and complexity, including the effects of excess area in weak basal detachment layers, multiple detachment levels, and large differences in . All show not only constant shortening as a function of height in pregrowth strata and approximately constant shortening rates, , over substantial stratigraphic thicknesses, but also abrupt and large increases in shortening rate by factors of 5-10 and significant hiatuses in fold growth. The typical shortening rates in these frontal structures are in the range of 0.1-3 mm/yr (0.003-0.12 in./yr) and represent only 1-10% of the regional plate tectonic rates of their larger tectonic settings (2-6 cm/yr [0.8-2.4 in./yr]), indicating that shortening is not currently concentrated in these frontal zones of these mountain belts and accretionary wedges. Abstract The thickness variations and shapes of strata deposited over actively growing folds provide a convolved record of the interaction of deformation and sedimentation. Here we show how key elements of the history of shortening can be extracted using area-of-relief measurements on many stratigraphic horizons in well-imaged structures. In pregrowth strata, the shortening is equal to the vertical gradient in the area of structural relief, S = d A /d z . In growth strata, this relationship must be modified because the observed gradient in the area of relief now includes the effects of both structural thickening and stratigraphic thinning caused by deposition over the growing structure, S = (d A /d z ) obs — (d A /d z ) strat . This stratigraphic thinning cannot be measured directly from thickness variations because of later structural thickening but can be determined through consideration of the ratio of the mean shortening rate to the sedimentation rate, , which is a key parameter. We apply these concepts to a set of actively growing detachment folds: Nankai Trough, Japan; Cascadia, offshore Oregon; Yaken anticline, western China; and Agbami anticline, Niger Delta. These examples show a considerable diversity and complexity, including the effects of excess area in weak basal detachment layers, multiple detachment levels, and large differences in . All show not only constant shortening as a function of height in pregrowth strata and approximately constant shortening rates, , over substantial stratigraphic thicknesses, but also abrupt and large increases in shortening rate by factors of 5-10 and significant hiatuses in fold growth. The typical shortening rates in these frontal structures are in the range of 0.1-3 mm/yr (0.003-0.12 in./yr) and represent only 1-10% of the regional plate tectonic rates of their larger tectonic settings (2-6 cm/yr [0.8-2.4 in./yr]), indicating that shortening is not currently concentrated in these frontal zones of these mountain belts and accretionary wedges.

Abstract Two adjacent active thrust ramps in western Taiwan show contrasting hanging-wall structural geometries that suggest different kinematics, although they involve the same stratigraphic section and basal detachment. The Chelungpu thrust shows a classic fault-bend folding geometry, which predicts folding by kink-band migration without limb rotation, whereas the hanging wall of the Changhua thrust shows the characteristic geometry of a shear fault-bend folding, which predicts a progressive limb rotation with minor kink-band migration. We test the kinematic predictions of classical and shear fault-bend folding theories by analyzing deformed flights of terraces and co-seismic displacements in the 7.6 moment magnitude scale Chi-Chi earthquake. In particular, differences in terrace uplift across active axial surfaces are used to show that the assumptions of classical fault-bend folding are closely approximated, including constant fault-parallel displacement, implying conservation of bed length, and hanging-wall uplift rates that are proportional to the sine of the fault dip. This provides a basis for precise determination of total fault slip because the formation of each terrace, combined with terrace dating, gives long-term fault-slip rates for the Chelungpu thrust system. Even the coseismic displacements of 3 to 9 m (10 to 29 ft) in the Chi-Chi earthquake are approximately fault parallel but have additional transient components that are averaged out over the time scale of terrace deformation, which represents 10–100 large earthquakes. In contrast, terrace deformation in the hanging wall of the Changhua thrust ramp shows progressive limb rotation, as predicted from its shear fault-bend folding geometry, which combined with terrace dating allows an estimation of the long-term fault-slip rate of 21 mm/yr (0.83 in./yr) over the last 31 ka. A combined shortening rate of 37 mm/yr (1.46 in./yr) is obtained for this part of the western Taiwan thrust belt, which is about 45% of the total plate-tectonic shortening rate across Taiwan. The Changhua shear fault-bend fold ramp is in the early stages of its development with only 1.7 km (1.06 mi) total displacement, whereas the Chelungpu classical fault-bend fold ramp in the same stratigraphy has nearly an order of magnitude more displacement (∼14 km [8.7 mi]). We suggest that shear fault-bend folding may be favored mechanically at low displacement, whereas classical fault-bend folding would be favored at large displacement.

Abstract The east–west-trending late Cenozoic Kuqa fold belt is a part of the compressive southern margin of the Tianshan Mountains in western China. Approximately 20,000 km (12,000 mi) of two-dimensional seismic reflection profiles are integrated with surface geology and well data to examine the deformation style and structural evolution of the Kuqa fold belt. Mesozoic through Holocene strata in the northern Tarim Basin have been deformed in a thrust system that roots northward into the Paleozoic basement of the southern Tianshan. The south-vergent deformation is characterized by a series of forward-breaking thrust faults, fault-related folds, and detachment folds. Two major decollement levels exist: an upper detachment in salt-gypsum lithologies in the Paleogene–Miocene Kumgeliem, Suweiyi, and Jidike formations, and the lower detachment mostly within Jurassic coal and mudstone strata. Fault-propagation folds developed above both detachments and have been refolded in some cases by displacement on the lower thrust faults. Imbricate thrust faults and duplex structures linking the two detachments developed with salt that apparently flowed into the cores of the duplex structure. Near the high Tianshan mountain front, Mesozoic and Cenozoic strata are involved in deformation that began at approximately 25–26 Ma as documented by growth strata north of Kuqa. Toward the southward limit of the fold belt, Miocene through Holocene strata are folded in the Quilitage and Yaken anticlines, which began growing above a thrust system that propagated at about 5.5 Ma. The Yaken anticline at the south edge of the eastern Kuqa fold belt has only emerged as a topographic anticline in the last 0.2–0.3 Ma associated with an acceleration of the Quilitage-Yaken thrust system. Structural restoration suggests a shortening of 15–20 km (9–12 mi) across the eastern Kuqa fold belt. Considering that this shortening began about 25 Ma, the average shortening rate was about 0.7 mm/yr (0.03 in./yr). Because the frontal thrust system underlying the Quilitage and Yaken anticlines has a shortening of 6 km (3.7 mi) that began approximately 5.5 Ma, their average shortening rate is about 1.1 mm/yr (0.04 in./yr). However, the shortening rate on this frontal system from about 5.5 Ma to about 0.2–0.3 Ma is approximately 0.6 mm/yr (0.02 in./yr) followed by an acceleration to about 4–5 mm/yr (0.16–0.19 in./yr) at approximately 0.2–0.3 Ma, causing the topographic emergence of these structures. These results indicate that shortening rates in the Kuqa fold belt have increased in the late Pleistocene, which is consistent with more regional present-day geodetic shortening rates of about 9 mm/yr (0.35 in./yr) across the southern Tianshan, which also indicate a substantial acceleration relative to Neogene shortening rates.