Fold–thrust structures – where have all the buckles gone?

ROBERT W. H. BUTLER*, CLARE E. BOND, MARK A. COOPER & HANNAH WATKINS Fold–thrust Research Group, School of Geosciences, University of Aberdeen, Aberdeen AB24 3UE, UK R.W.H.B., 0000-0002-7732-9686 *Correspondence: [email protected]

Abstract: The margins to evolving orogenic belts experience near layer-parallel contraction that can evolve into fold–thrust belts. Developing cross-section-scale understanding of these systems necessitates structural interpretation. However, over the past several decades a false distinction has arisen between some forms of so-called fault-related folding and buckle folding. We investigate the origins of this confusion and seek to develop unified approaches for interpreting fold–thrust belts that incorporate deformation arising both from the amplification of buckling instabilities and from localized shear failures (thrust faults). Discussions are illus- trated using short case studies from the Bolivian Subandean chain (Incahuasi anticline), the Canadian Cordillera (Livingstone anticlinorium) and Subalpine chains of France and Switzerland. Only fault–bend folding is purely fault-related and other forms, such as fault-propagation and detachment folds, all involve components of buck- ling. Better integration of understanding of buckling processes, the geometries and structural evolutions that they generate may help to understand how deformation is distributed within fold–thrust belts. It may also reduce the current biases engendered by adopting a narrow range of idealized geometries when constructing cross-sec- tions and evaluating structural evolution in these systems.

A key goal for many studies of continental tectonics the majority of existing approaches to folding and is to relate folds, faults and distributed strain to faulting in compressional regimes. We then examine create reliable geometric interpretations of three- the approaches through which current understand- dimensional structure. For many decades much of ing of buckle folds has developed in parallel to this work has been allied to the exploration of these fold–thrust models. We apply these concepts Earth resources, especially oil and gas. Since the to challenge the notion that detachment folds and early 1980s, descriptions of fold–thrust complexes buckle folds are somehow distinct. We then exam- (e.g. Suppe 1983; Jamison 1987), with application ine some case studies to show how buckling con- to subsurface interpretation (e.g. Shaw et al. 2005), cepts may better inform structural understanding. have led to mechanical approaches (e.g. Smart To unify these different approaches to better un- et al. 2012; Hughes & Shaw 2015) that rely on a derstand folding and its relationship to faulting, we very narrow range of deformation styles. Elsewhere examine structures in terms of their evolution of we argue that this emphasis has created significant deformation localization. This informs a reassess- bias in the ways larger-scale structural interpretations ment of both detachment folding and fault propaga- are built and their uncertainties assessed (Butler et al. tion folding that sit within the family of current fold– 2018). Here we discuss how the basic concepts of thrust models. Rather than interpret deformation in buckle folding, the principles of which are laid out terms of idealized geometries, and considering fold- by Ramsay (1967), may help to reduce an over- ing to be a consequence of faulting, we argue that it is reliance on a biased set of fold–thrust models. Buck- better to view structures as lying in a continuum of ling is the process by which layers fold when sub- possible geometries and localization behaviours jected to contraction along their lengths. Research (Butler 1992). on this folding mechanism has continued in parallel Much existing work examines structural evolu- with that on fold–thrust belts. Our aim here is to tion through cross-sections, seeking explanations draw these lines of research together, pooling knowl- for fold–thrust interactions in these single illustrative edge and, consequently to reunite interpreters of planes. We challenge this notion, developing con- fold–thrust systems with key components in the cepts of lateral fold growth inherent in buckling structural toolkit that is Folding and Fracturing of models, to argue that, even if illustrated by cross- Rocks (Ramsay 1967). sections, structural understanding is better served First, we briefly outline an evolution of ideas on through considering how deformation evolves in fold–thrust interpretations – as this history underpins three dimensions.

From:BOND,C.E.&LEBIT, H. D. (eds) 2020. Folding and Fracturing of Rocks: 50 Years of Research since the Seminal Text Book of J. G. Ramsay. Geological Society, London, Special Publications, 487,21–44. First published online February 20, 2019, https://doi.org/10.1144/SP487.7 © 2019 The Author(s). This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/). Published by The Geological Society of London. Publishing disclaimer: www.geolsoc.org.uk/pub_ethics

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Fold–thrust structures: an introduction the beds (‘bed-length balancing’) and the strata (the tyranny of concentric folding) must have been parallel-bedded before deformation (so-called ‘layer-cake stratigraphy’). These restric- The sedimentary rocks on the flanks of mountain tions require structures to approximate to concentric belts, ancient and modern, commonly show the folds. Subsequent development of section balancing effects of horizontal contraction, manifest as thrust concepts has lifted these restrictions. For example, faults and folds. These structures have been studied Woodward et al. (1986) and Geiser (1988) discuss for centuries – and current perspectives on the devel- the incorporation of explicit strain measurements opments of interpretations and concepts are provided into cross-section restoration and Butler (1992) by many authors (e.g. Frizon de Lamotte & Buil developed the method of formation area balancing, 2002; Groshong et al. 2012; Brandes & Tanner trading off strain-related thickness changes against 2014; Butler et al. 2018). These generally recognize pre-existing stratigraphic thickness variations. the importance of work, especially in the foothills of Thus, interpretations could be tested using structural the Canadian Cordillera, reported by Dahlstrom restoration even where pre-existing stratigraphy was (1969, 1970; but see also Fox 1959; and Bally et al. laterally variable and distortional strain was heterog- 1966). This was largely driven by the exploitation of enous through multilayers. oil and gas hosted in complex fold–thrust structures. Upscaling and downscaling Origins The success of adopting the foothills family of Subsurface interpretation in frontier fold–thrust structures, and the rigour of creating balanced belts, be that in the 1960s in the Canadian cordillera cross-sections, in forecasting subsurface structure of Alberta, or in the 2000s–present in the Papuan in Alberta was recognized and promoted by Elliott fold belt (e.g. Parish 2016), is an exercise in uncer- (Elliott & Johnson 1980; Boyer & Elliott 1982). In tainty management. It is generally driven by outcrop essence these approaches are about upscaling local geology and existing wells, which provide directly geology and so in turn led to widespread reinvestiga- measured dip and horizon data, but of great com- tion of the regional structure of thrust systems and plexity. This is allied with regional 2D seismic pro- their relationship to orogenic belts around the files that, for the Canadian cordillera in the 1960s, world. Some of these studies (e.g. Butler 1986) were of poor quality and thus only resolved simple explicitly simplify outcrop structure by adopting structural components. In effect the seismic data the foothills family to minimize the implicit values crudely imaged the top of the underlying basement of orogenic contraction experienced by thrust belts, to be gently dipping and apparently planar, and for example, to compare with volumes of continental therefore the complex structures in the sedimentary crust beneath mountain belts. As such they make no cover were detached from it. The deformation was claims of precision for the structure of the thrust ‘thin-skinned’. The challenge, as met by Dahlstrom belts themselves. (1969, 1970), was to elaborate a workflow for con- Decisions on how to simplify structures on cross- structing cross-sections through the volume of thin- sections vary depending on the scientific objective. skinned deformation that forecast subsurface struc- Arbitrary choices such as solutions with minimum ture before any further drilling. The first step lay in horizontal shortening may be appropriate for upscal- simplification. Dahlstrom defined a narrow range ing to deduce crustal-scale tectonic processes (e.g. of components that should be used in section con- Butler 2013), but not if the aim is to understand the struction, his so-called ‘foothills family’ of struc- relationships between individual folds and thrusts. tures. These are: concentric folding; décollement; Downscaling to forecast the location of specific thrusts (usually low-angle and often folded); tear stratigraphic units in the subsurface, or to relate strain faults; and late normal faults. The second part lies and fracture patterns to fold development, requires in testing cross-section-scale interpretations for different approaches. Consequently, Dahlstrom’s internal consistency. This was achieved by structural (1969, 1970) ‘foothills family’ of structures was de- restoration and thus the notion of balanced cross- veloped into quantitative geometric approaches for sections was formally defined (Dahlstrom 1969). In describing relationships between folds and thrusts such sections, the sinuous bed length for each strati- (e.g. Suppe 1983; Jamison 1987; Mitra 1990). In graphic horizon measured in the interpreted structure this way, folding is considered kinematically and has an equal length in the pre-deformation state. thus to be a consequence of the geometry, displace- Thus, restorable cross-sections are demonstrations ment and propagation of thrust faults. On this basis, of strain compatibility – all horizons display the Jamison (1987) formalized the types of fault-related same longitudinal strain in the section plane. When folds that can develop (Fig. 1). first developed by Dahlstrom (1969), this method If bed thickness is conserved during deformation, required that there be no distortional strain within a requirement for concentric folding, only a very

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(a) Buckle folding: an introductory review

Similar to fold–thrust structures, buckle folding has a history of research stretching back well over half a century. However, buckling research has been less concerned with forecasting poorly known subsur- fault-bend fold face structure. There are several excellent discussions (b) on buckle folding, building on the pioneering studies of Ramberg (1966) and Biot (1961). Ramsay (1967) provided an early overview of these works and this spawned extensive research, especially using ana- logue materials with measurable viscosities (chiefly plasticine and gelatin). Many of these results are fault-propagation fold reviewed by Price & Cosgrove (1990), who provide (c) a comprehensive account of buckling processes. Subsequently, with enhanced computing capability, numerical methods have been increasingly adopted to understand these processes (e.g. Abbassi & Man- cktelow 1992; Mancktelow & Abbassi 1992; Casey detachment fold & Butler 2004; Schmalholz 2008; Reber et al. 2010). Very little of this content is considered in Fig. 1. Idealized fold–thrust relationships, modified the thrust belt literature and so here we provide a after Jamison (1987).(a) fault-bend fold, formed solely (re)introduction, much of which may be familiar to as a consequence of displacement along a non-planar those currently engaged in buckle research. A compi- thrust. (b) fault-propagation folding, formed ahead of a lation of some buckling concepts is outlined in migrating fault tip on a thrust ramp. (c) detachment Figure 2. fl fold, formed above a thrust at. For a given imposed layer-parallel contraction, the geometry of folds in a single competent layer embedded in a lower viscosity matrix will depend on the thickness of the layer and its viscosity in narrow range of viable geometries also yield contrast to the matrix (Fig. 2a). Higher viscosity con- balanced cross-sections (e.g. Suppe 1983). This trasts favour concentric folding. Longer wavelengths restriction leads directly to explicit geometric ‘rules’ are developed in thicker layers. Ramberg (1966) and and these underpin algorithms in structural model- Biot (1961) independently established that there ling software (Groshong et al. 2012). In his trishear is a cube-root relationship between layer thickness model, Erslev (1991) relaxed the requirement for and wavelength so, as Price & Cosgrove (1990), bed-thickness conservation – but only in the fore- note, in multilayers of constant viscosity contrasts limb of fold–thrust structures. Shaw et al. (2005) (e.g. bedded turbidite sandstones and shales, or review all these models, with application to seismic thick limestones with interbedded shale formations), interpretation while Groshong et al. (2012) and it is the thicker beds that will dictate the wavelength Brandes & Tanner (2014) review their history. of the resultant fold belt. They term such beds ‘con- Just as Dahlstrom’s (1969, 1970) approaches trol units’. were driven by a need to reduce interpretation Single-layer buckles are encased in a deformed uncertainty when forecasting the subsurface struc- matrix. Based on reports of analogue experiments, ture in the pursuit of oil and gas, recent develop- Ramsay (1967) illustrates how this deformation var- ments have also had economic drivers. Many ies away from a competent buckled layer through a applications of fold–thrust models aim to forecast zone of contact strain (Fig. 2b). These patterns small-scale faults and fractures downscaling from have been reproduced numerically by Reber et al. larger fold–thrust structures. Consequently there (2010; Fig. 2c). As the buckled layer is created by have been various mechanical developments from layer-parallel shortening, the long axis of strain ellip- the kinematic models described above (e.g. Kamp- ses in the zone of homogeneous strain away from the fer & Leroy 2012; Smart et al. 2012; Hughes et al. buckled layer (represented by the long-dimension of 2014; Hughes & Shaw 2015). Note, however, the originally square elements in the rectilinear grids that these mechanical models generally assume a of Fig. 2b, c) is orthogonal to the original orientation specific kinematic evolution and are applied to a of the layer. In nature this attribute will be tracked by single fold–thrust structure, or a layer within it. axial-planar cleavage associated with the folds. The implications of adopting these approaches Based on approaches of Latham (1985; reviewed are discussed later. by Price & Cosgrove 1990), Casey & Butler (2004)

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4

3 30% (c) 5

2 (a)

homogeneous 60% strain (e) OETBUTLER ROBERT

zone of contact strain bending competent resistance buckled layer pin-joint limb rotation AL. ET failure of (b) hinge

fault slip strength and folding

(d) tightened hinge time (shortening) lock-up (interlimb angle)

Fig. 2. A compilation of buckle fold concepts and results of analogue experiments. (a) Single layer buckle folding, with layers of increasing competence (1–5), with the matrix competence equal to that in layer 1 (modified after Ramsay 1967). (b) The concept of contact strain, adjacent to a buckled single layer (modified after Ramsay 1967). (c) Numerical models of evolving buckled single layer (modified after Reber et al. 2010). (d) Result of an analogue multilayer model subjected to layer-parallel contraction that synchronously developed folds and faults (modified from a photograph by Price & Cosgrove 1990). (e) Evolution of stress–strain relationships during buckling, using the deformation history outlined by Casey & Butler (2004).

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argue for a complex evolving relationship between Fold trains strength and imposed shortening (Fig. 2d). Planar competent layers have a bending resistance that In contrast to the fold–thrust structures presented ear- must be overcome if folds are to amplify signifi- lier (Fig. 1), buckle folds are generally not considered cantly. This is particularly important for anisotropic in isolation, but rather as arrays. For example, ana- materials – such as well-bedded units. Once bending logue experiments by Dubey & Cobbold (1977) resistance is overcome, folding is efficiently achieved demonstrated that folds form in trains and that they through near-rigid limb rotation. Stress increases ini- propagate laterally as they amplify (Fig. 4a, b). The tially until the bending resistance of a layer is over- initial fold systems initiated in clusters on inherited come, at which point there can be a dramatic stress flaws in the plasticine multilayer. However, these drop throughout this deforming layer. Deformation clusters grew out laterally. Folds from different clus- can progress readily by limb rotation until limited ters can collide. Where folds are in phase they can by interlimb angle. Folds will then tend to lock up. combine to create long, fully connected hinge lines. Fold mergers like this, although long recognized, are similar to behaviours more recently deduced for Faulting and folding segment-linkage in the formation of large normal Rheological multilayers can deform by buckling and faults (e.g. Cartwright et al. 1995). However, other thrusting. Although these are distinct forms of folds may remain segmented, generating abrupt mechanical instability, extensive analogue modelling plunge terminations (see also Casey & Butler 2004; (reported by Price & Cosgrove 1990) demonstrates Fernandez & Kaus 2014). Progressive deformation that these can co-exist during the same deformation establishes a dominant wavelength of the fold train, (Fig. 2e). Continued deformation may result in faults overprinting the initial distribution of perturbations propagating into previously unfaulted, folded layers, that may have seeded the initial folds. or becoming shut down and folded if adjacent buck- les amplify appropriately. Multilayer fold trains Using well-exposed coastal outcrops along the flanks of Oslo Fiord, Morley (1994) describes arrays Dixon & Liu (1992) performed folding experiments of thrusts that apparently relate to over-tightening of in analogue materials that demonstrate the lateral fold hinges, rather than having formed as linked fault growth of buckle systems. The model illustrated networks. Morley’s interpretations are a rare pub- here (Fig. 5a, b) shows a series of three thick compe- lished example that folds can contain minor faults, tent layers (X, Y, Z) separated by low-viscosity mate- despite their description by Ramsay (1967, p. 421). rial within which is encased a highly competent Price & Cosgrove (1990) class these as accommoda- marker (contorted blue line in Fig. 5a, b). Compari- tion structures (Fig. 3a, b). They note that such struc- son of the two deformation states (Fig. 5a evolves tures tend to concentrate in the hinges of folds and into Fig. 5b) shows how the folds grow. Although are preferentially developed in competent layers the multilayer contains low viscosity levels, the adjacent to thicker beds (control units) that are dictat- folds in the competent units are broadly in harmony. ing the overall fold shape (Fig. 3c). The types of The experiment shows that, although folds may grow faults are characteristically rootless and pass onto across a model (Fig. 5a, b), once formed, they can segments of bedding planes. Examples include amplify together. The overall fold train geometry is ‘out-of-syncline’ thrusts (Dahlstrom 1970). controlled by the thicker units, confirming the reports There have been a few attempts to identify by Price & Cosgrove (1990). The models also illus- accommodation faults in thrust belts. Mitra (2003) trate how the structure of fold hinges in these control reports many examples, including within the Ven- units (X, Y, Z) can influence deformation. Consider tura Avenue Anticline of Southern California (Fig. fold III in Figure 5b. The upper layer (X) has ruptured 3d). Well data reveal multiple thrusts that accommo- by crestal faulting, allowing the fold limbs to rotate, date thickening of the Pico Formation (Pliocene), yet greatly decreasing the interlimb angle. This in turn these thrusts appear not to cut deeper horizons or influences the structure of the underlying thin layer. continue to crop out. Similar behaviour is interpreted In nature, these behaviours would probably be facil- by Boyer (1986) in his consideration of the Anschutz itated by erosion of the antiform crest. It is not just the Ranch East Field in the Wyoming Overthrust Belt upper layer (X) that develops tight folds. The middle (Fig. 3e). Here too, well penetrations identify com- control unit (layer Y) has tight interlimb angles (e.g. plex faulting along the hinge of a tight fold within folds IV and VI in Fig. 5b). These layers are locally the Preuss/Stump Formation (Jurassic). The fold faulted in their forelimbs. appears to be controlled by a competent layer at Multilayer folding has also been investigated depth defined by the Nugget Sandstone and Twin in 3D finite element models. The examples shown Creek Limestone. The accommodation fault passes here (von Tscharner et al. 2016; Fig. 5c, d) illu- into incompetent evaporites. strate the stratigraphic control on disharmonic

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W E

Tertiary

undifferentiated Cretaceous sea level

(a) (b)

rust ka Th red beds and Absaro 50 cm limestones (e) Preuss/Stump fine-grained clastics salt 3 km BUTLER ROBERT Twin Creek Limestone Nugget Sandstone

(c) SSE Ventura Avenue Anticline NNW TAL. ET

t ul 5 km Lion Fa Up Plioc-Quaternary Pico Fm Sisquoc Fm Mondelo and Monterey Fms Ricon Fm older units (d)

Fig. 3. Complex fold-fault patterns. (a and b) illustrates idealised patterns of ’accommodation faulting’ in antiform hinge zones, modified after (Price & Cosgrove 1990, fig. 12.23) while (c) shows a natural example developed in turbidite sandstones (modified from a photograph from Price & Cosgrove 1990, fig. 12.26). (d) shows the subsurface interpretation of the Ventura Avenue Anticline in California (modified after Mitra 2003, fig10).(e) is a subsurface interpretation of the Anschutz Ranch East oil field in the Utah- Wyoming thrust belt (modified after Boyer 1986, fig. 16).

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(a)(b)

9% shortening PLAN VIEWS fully connected hinge line fold hinge 36% shortening termination

single merged fold cluster

fold clusters segmented hinge-line

Fig. 4. Plan views showing the linkage of folds by lateral hinge-line propagation. (a, b) Redrawn from an analogue experiment using a plasticene multilayer by Dubey & Cobbold (1977).

deformation. Here bucking is developed in compe- (e.g. Ramsay 1967; Price & Cosgrove 1990). How- tent units against a step that mimics a basement ever, these strain states are restricted to within, or fault. If the incompetent matrix (green in Fig. 5c, are immediately adjacent to, competent layers. d) is thick above the basement then the two com- More generally, single-layer buckles are shown to petent layers can fold harmonically. A thinner pass out into homogeneous strain that accommo- low-viscosity layer immediately above the basement dates shortening (Fig. 2b, c). As noted earlier, this promotes disharmonic deformation. predicts axial planar cleavage in antiforms and syn- forms alike. If Groshong’s (2015) assertions are correct, in regions of horizontal subcontraction, Detachment folding and buckle folding: a cleavage would be axial planar in the antiforms false distinction? (near upright) but subperpendicular to synform axial surfaces (near horizontal). These relationships are Groshong (2015) makes an explicit distinction certainly not generally observed in regions of dis- between detachment folds and buckles, although tributed folding, such as slate belts (e.g. Coward & both systems can develop above fixed décollement Siddans 1979; Woodward et al. 1986). levels. For his definition of detachment folding, the Perhaps the confusion of buckling has arisen antiforms rise away from the décollement, creating because of the way in which results of analogue an ‘excess area’ beneath a specific horizon that is experiments have been reported. This is illustrated equal to the amount of horizontal shortening multi- in Figure 6c, using an experiment of progressive plied by the height of the horizon above the detach- deformation described by Cobbold (1975, fig. 5) on ment away from the fold (Fig. 6a). In contrast, he buckling in heterogeneous paraffin wax. His images conceptualizes buckling with uplift of the anticline are redrafted here in colour with added labelling crest but with net subsidence beneath synclines for reference. The original model was set up with a (Fig. 6b). Likewise, Mitra (2003 see also Ghana- single competent layer (X on Fig. 6c), embedded dian et al. 2017) illustrates buckling of the above within a matrix of lower viscosity upon which were décollement surfaces where ductile material is evac- printed reference lines, parallel to the competent uated beneath synclines and flows into anticline layer and the lower edge of the deformation appara- hinges. tus. One of these reference lines is labelled here Note that the basic conceptualization of buckle (Y on Fig. 6c). The aim of Cobbold’s study was to folding (Fig. 2b, c), developed both from analogue chart the amplification of folds and so his illustrations experiments and from numerical modelling, does focus on the buckled competent layer itself (X on not show evacuation beneath synclines. Consider Fig. 6c), centred through the middle of the growing the state of finite strain around single-layer buckle fold. Consider the low strain state with the left-hand folds. Some classical buckling models (e.g. Fig. 2b) high-strain image (Fig. 6c) – the frame of reference depict outer-arc stretching tangential to fold hinges of the initial location of the competent layer relative

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I II III IV V VI VII VIII

X Y Z

(a)

I II III IV V VI VII VIII

X

Y

Z

(b)

(c)(d)

Fig. 5. The development of fold trains in analogue (a, b) and numerical (c, d) experiments. a–b is the evolution of a single experiment using a plasticine and silicone putty multilayer with increasing contraction, reported by (Dixon & Liu 1992, fig. 3). Antiforms and layers are labelled for reference in text. The numerical experiments are after (von Tscharner et al. 2016, fig. 4) and show contraction of a rheological multilayer against a ‘basement step’ analogous to deformation of a thick basin fill (c) and a thin basin fill (d).

to the deformation apparatus is lost. Cobbold’s short-hand for ‘regional orientation and elevation’ images are cropped, as evidenced by the trimming of that horizon at a scale significantly greater than of the printed pre-deformation reference lines of a particular deformation structure. It is easiest to between successive deformation states. If the images apply in sedimentary basins, where the ‘regional’ are rehung relative to the pre-deformation reference describes the very long wavelength of a particular lines (e.g. Y on Fig. 6c), the control layer X is horizon. The behaviour of the horizon relative to its shown to have moved upwards (right-hand high- ‘regional’ is diagnostic of tectonic regimes. Exten- strain state in Fig. 6c). There is no subsidence of sional faulting drops rocks below their regional. the synforms and the surrounding deformation is Contractional faulting brings rocks above their broadly as described by Ramsay (1967, Fig. 2a) and ‘regional’. These are net behaviours and are espe- others since. cially useful for analysing reactivation of faults (see The key for analysing fold development is to Williams et al. 1989). As implied by the strain state relate the deformation of a layer to its ‘regional’. shown by Ramsay (1967, p. 417), the folded compe- The term ‘regional’, as applied to a deformed hori- tent layer is raised above its ‘regional’ throughout. zon and formalized by Williams et al. (1989),is It is differential but still upward movement of the

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buckled layer that creates antiforms and synforms. folding mechanism, as proposed by Groshong Nowhere in the model is there subsidence. (2015), but the ductility of the deeper parts of a The ‘regional’ concept can be applied to the ana- deforming stratigraphic section. The distinction logue model experiments in Figure 6c. Here it is the between detachment folding and buckling on these mis-identification of the ‘regional’ for the base of the grounds is false. competent layer (X) in the left-hand illustration that leads to the false deduction of synform subsidence. When the higher strain state is rehung using the The Incahuasi anticline as a buckle fold deeper marker horizon (Y, the right hand illustra- tion), the ‘regional’ for the base of the control layer In the oil and gas industry, the effectiveness of struc- moves down. This is a minimum illustration for the tural interpretations on the scale of cross-sections is location of the ‘regional’, because if the levels in repeatedly tested by drilling. However, being com- the model beneath the marker horizon are involved mercially sensitive, interpretation failures are rarely (as they were, when considering the low-strain state), reported. An honourable exception is Total’s devel- the original location of the control layer (X) would opment history of the Incahuasi structure in the Sub- move further down still. This example is consistent Andean fold belt of Bolivia (Heidmann et al. 2017; with the illustrations of Ramsay (1967; Fig. 2a). Fig. 7). In areas of no imposed longitudinal strain, rocks The target for exploration drilling has been the can still move relative to their ‘regionals’ as a conse- porous sandstones of the Huamampampa Formation quence of redistribution of material at depth, for (Devonian) that host major gas reserves. These example owing to salt flow. In this case, subsidence underlie the Los Monos Formation (Devonian), a beneath salt-withdrawal basins (a pre-kinematic stra- shale-prone unit that forms a top seal. It also acts tum goes below its ‘regional’) is compensated for by as a ductile unit across which deformation changes uplift of a salt pillow (the same pre-kinematic stra- (e.g. Rocha & Cristallini 2015, and references tum goes above its ‘regional’). It appears to be char- therein). The overlying Carboniferous to late Creta- acteristic of systems that have a thick layer of ceous units appear to deform as a single competent exceptionally low-viscosity material at depth. Subsi- beam. At outcrop these strata form a fold-belt with dence of synclines is driven by deposition of synki- remarkable lateral continuity of anticline hinges nematic strata – so-called ‘down-building’. (>200 km) separated by synclines that host Tertiary Simpson (2009) provides results from numerical synkinematic foredeep sediments (Fig. 7a). The modelling that explores the geometry of fold–thrust Huamampampa Formation lies at the top of a Silu- structures that form above low-viscosity layers in rian–Devonian package that is generally assumed décollement zones (Fig. 6d, e). These models use to deform as a single unit, detached from the under- exceptionally low viscosities, perhaps appropriate lying basement along the Upper Silurian Kirusillas to salt or over-pressured mud. Deformation of the shales. Prior to Total’s drilling campaign there had competent beam above this material generates arrays been various attempts to forecast subsurface struc- of buckle folds together with localized shears, equiv- ture of the fold-belt using analogue models (e.g. alent to thrusts. Where the low-viscosity zone is thin, Leturmy et al. 2000; Driehaus et al. 2014; Darnault the synclines in overlying competent units remain et al. 2016), generally preconditioned to create a above their ‘regional’ (Fig. 6e). In contrast, where two-tier thrust system decoupled along the Los the low-viscosity zone is thick, the synclines subside Monos Formation. below their ‘regional’ (Fig. 6d) While these behav- Two-tier deformation formed the initial subsur- iours may be appropriate to some submarine thrust face model for Total’s drilling (Fig. 7b). The target systems at the toes of gravitationally spreading sedi- was the crest of a proposed hanging wall anticline mentary prisms, it is not obvious that these models in the underlying thrust system. However, this first are applicable to foreland fold–thrust belts. Excep- well penetrated a faulted anticline and was termi- tions may include those fold belts that include nated in Cretaceous strata on the western limb of thick evaporite sequences at depth, such as the Pro- the fold. In the light of this result, the structural inter- vencal sector of the French Alps (Graham et al. pretation was modified (Fig. 7c) and a side-track 2012) and the Fars sector of the Zagros (e.g. Mouth- well proposed to target the deeper structure. As this ereau et al. 2007). Note that syncline subsidence dur- side-track was drilled, rather than encounter the Hua- ing folding generates growth stratal patterns that are mampampa Formation in the crest of a simple anti- distinct from normal buckling (contrast Fig. 6d, e), as cline, these sandstones were found to be faulted identified by Oveisi et al. (2007) in their modelling and locally over-turned. Consequently, the structural of deformed marine terraces along the frontal folds interpretation was modified again (Fig. 7d). of the central Zagros. The history of iterative subsurface interpretation In summary, the vertical motion of synclines and drilling on the Incahuasi structure is interesting. relative to their ‘regional’ is not controlled by the As knowledge was gained, the role of the Los Monos

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(a) W

Monteagudo Irenda -XI Los Yanguilo-Huacareta wells Caipipendi Inau INCAHUASI well Huesos E Charagua

Upper beam Sil-Dev

10 km (b) West East Tertiary synkinematic planned well trajectory Carboniferous- Cretaceous Upper beam

Los Monos Huamampampa

Silurian- Devonian

(c) planned side track trajectory

completed well 5 km

(d)

completed wells

Icla Formation detachment level

Fig. 7. The interpretation of the Incahuasi anticline in the Bolivian foothills, after Heidmann et al. (2017). (a) Simplified long cross-section through the thrust belt provided for context (simplified from fig. 8 of Heidmann et al. 2017). Total’s evolving interpretation of the Incahuasi anticline with the acquisition of well data is shown in the remaining parts of the diagram (b–d); modified from fig. 15 of Heidmann et al. (2017).(b) The pre-drill interpretation; (c) shows a modified interpretation after the first well-bore; (d) shows a final interpretation that incorporates information from the first well-bore and its side-track.

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Formation as a significant zone of structural decou- with the upper units, with localized accommodation pling reduced. At the start of the drilling campaign faulting in the anticline hinge. It is these faults that the Carboniferous–Cretaceous upper stratigraphic were encountered as the side-track well entered the beam was interpreted to be entirely decoupled from Huamampampa Formation. The fold may also con- the Silurian–Devonian beam below and each had tinue below this unit too, so that the whole strati- its own structural style. By the end of the campaign, graphic pile deforms as a single entity. the Huamampampa Formation was interpreted as Our model differs from that of Heidmann et al. folded, broadly in harmony with the upper beam. (2017). We suggest that the older Silurian rocks are A further detachment horizon, located within the not involved in the Incahuasi structure and there is Icla Formation, was incorporated by Heidmann a décollement surface within the lower Devonian et al. (2017) so that the older Devonian and Silurian rocks (Icla Formation) beneath the Huamampampa strata could shorten by simple fault-bend folds. reservoir unit. This version conserves the cross- However, does the structural style need to vary sectional areas of different formations between with depth, from buckle folding at shallow levels deformed and undeformed states (which achieves and fault-bend folding at depth? formational area balance). It is possible that the The Incahuasi anticline is re-assessed here using deeper Silurian strata are involved – especially if some buckling concepts (Fig. 8). This new interpre- deformation in these deep levels was largely homo- tation has been balanced, so that all formations show geneous layer-parallel shortening. Testing this inter- the same horizontal contraction. The upper units of pretation requires knowledge of the ‘regional’ for the Carboniferous to Cretaceous age are illustrated as various stratigraphic units in the Incahuasi structure. acting as the control unit (in the sense of Price & The long section in Figure 7a provides some insight. Cosgrove 1990). Rather than interpret the Los The base of the synclines in the upper beam of Cre- Monos Formation as a mechanical detachment (cf. taceous and younger strata, the lower enveloping Heidmann et al. 2017), we suggest that it represents surface of the folds, inclines gently west. However, a transitional strain zone across which there is broad if there has been deformation in the underlying structural continuity. The underlying Devonian and Silurian and Devonian strata, this enveloping sur- Silurian strata are also shown to fold harmonically face does not constitute a ‘regional’. Information is

axial surface continues to depth eroded crest of anticline

pin-joint Tertiary limb rotation synkinematic Y’ Carboniferous- X’ Cretaceous Upper beam Los Monos Huamampampa Icla Formation Silurian- Devonian

5 km Y X accommodation faults

control layer distributed strain in incompetent formations basal decollement or homogeneous strain below?

Fig. 8. A reinterpretation of the Incahuasi structure as a buckle-folded multilayer – with continuity of the axial surface to depth. Contrast with the pre-drill interpretation and its evolution (Fig. 7b–d).

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needed for deeper basement trends and the position fractures in prospective subsurface reservoirs relative of horizons in the foreland – information that lies to the timing of hydrocarbon charge. It could also beyond the scope of even the long section repro- compromise the integrity of seals. duced in Figure 7a. If the Subandean fold–thrust belt of Bolivia, incorporating the Incahuasi anticline, is best consid- 3D folding: the nucleation problem ered as a train of buckle folds, we can apply the con- cepts of fold amplification of Casey & Butler (2004, Early work on analogue materials demonstrated that Fig. 2e). Erosion of the anticline fold crests could buckle fold trains can initiate on pre-existing hetero- have a critical influence on the amplification and geneities (Dubey & Cobbold 1977). This notion can tightening of folds, allowing deformation to progress be explored using the folds of the Subalpine chains beyond the expected lock-up interlimb angle (as and Helvetics of the NW Alps. Structures are devel- shown in the analogue experiments of Dixon & oped in the multilayer of thick Mesozoic platform Liu 1992; Fig. 5b). In contrast, sedimentation in carbonates interbedded with shale-prone formations the synclines could inhibit the growth of further anti- (Fig. 10). The youngest carbonate platform, termed clines between the existing folds, enhancing those the Urgonian limestone (Hauterivian–Barremian), structures that had already formed. forms regional folds with hinge lines that can be traced over tens of kilometres (e.g. Ramsay 1989). Folding in the Urgonian is apparently out-of-phase Cyclic folding and faulting: the Livingstone with structures in the underlying units, for example anticlinorium the competent Tithonian limestones (Fig. 10). In the Subalpine fold belt, two formations are separated Kink-band folding, accommodated by flexural slip, is by thick lower Cretaceous shales. Jurassic strata the generally accepted mechanism for the formation below the Tithonian limestone are also shale-prone of structures in the foothills of the Canadian cordil- and thick. These stratigraphic successions are inher- lera (Dahlstrom 1970). Tight kink anticlines in the ited from a Mesozoic basin section. In contrast, to the hanging walls to thrusts are conventionally inter- west the fold–thrust belt involves an interbedded preted as fault-propagation folds that have evolved succession of thick platform carbonates and thin and been carried by the thrust. Cooley et al.’s shales. Consequently in this western area the stratig- (2011) interpretation of the Livingstone anticlino- raphy deforms harmonically and the role of major rium of the foothills of the Canadian cordillera buckling appears to be less important (Fig. 10; see (Fig. 9) challenges this notion. The anticlinorium is Butler et al. 2018, for further discussion). a composite array of folds associated with the Living- Within the Subalpine system, anticlines in the stone Thrust. The strata are dominated by well- Urgonian limestone at several locations coincide with bedded Mississippian carbonates typical of this part pre-existing normal faults. Two examples are shown of the Alberta foothills. Cooley et al. (2011) mapped here, from either end of the system. In the Vercors, a the folds and, supported by detailed fracture studies single east-dipping normal fault can be reconstructed and diagenetic histories of vein fills, deduced the from the folded Urgonian (Fig. 11a; Butler 1987). deformation history. The Central Peak anticline initi- At the Col de Sanetsch in the Helvetic Alps of Swit- ated at depth, in parallel to the growth of the Living- zerland, the Urgonian limestone is folded into a stone Thrust. In this sense, it is a thrust-propagation NW-facing fold pair. It contains arrays of SE-dip- fold. However, the anticline tightened after the thrust ping normal faults that are onlapped by Tertiary had accumulated its displacement. The structure has strata deposited before folding (Fig. 11b). In both a two-stage history. of these cases the normal faults have throws that The history of the Livingstone anticlinorium are less than the thickness of the Urgonian limestone. contrasts with the idealized evolution of fault- Nevertheless, it is tempting to suggest that these pre- propagation folds. The results of Cooley et al. (2011) existing faults were sufficient to nucleate folding. indicate that deformation need not evolve as a sim- Presumably the folds propagated laterally from ple passage from distributed folding to localized these inherited flaws in the Urgonian beam to create thrusting but rather it can cycle between these dif- the connected fold trains of the Subalps, as modelled ferent localization behaviours. Similar patterns by von Tscharner et al. (2016). have been deduced for fold–thrust complexes in the Figure 12 is a hypothetical illustration of fold French Subalpine chains (e.g. Butler & Bowler nucleation and growth. Isolated arrays of small 1995). Interacting folds and thrusts are also modelled normal faults, equivalent to those illustrated in Fig- numerically by Jaquet et al. (2014). Cycling between ure 11, were developed before folding. They act as localized thrusting and distributed folding has impor- perturbations, in the sense of Dubey & Cobbold tant implications for some hydrocarbon systems as (1977), to nucleate early fold growth (Fig. 12b). As it could change the timing of the development of layer-parallel shortening continues, some of the

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Fig. 9. Evolution of fold–thrust structures in the Central Peak anticline in the Livingstone Range, Canadian Rocky Mountains foothills; modified after Cooley et al. (2011, fig. 16).

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Fig. 10. Interpreted cross-section through the front of the Bornes sector of the Subalpine fold–thrust belt of the French Alps (modified after Butler et al. 2018, fig 17b).

Fig. 11. The nucleation of anticlines on pre-existing heterogeneities. These two examples come from the western Alps and show the Urgonian limestone (Hauterivian–Barremian), which is generally assumed to form a competent formation within an alternating series of limestones and shales (control bed in the sense of Price & Cosgrove 1990). (a) Interpreted cross-section from the Col de la Bataille, Vercors, France. (b) Annotated photograph from the Col de Sanetsch, Switzerland (visible cliff-height c 700 m, to the summit of Spitzhorn).

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Fig. 12. Conceptual fold nucleation on pre-existing structures and the lateral propagation of fold hinge lines – shown here in plan view of the top of a control unit. (a) The initial distribution of minor normal faults that will serve to nucleate the initial fold clusters (b). (c) The lateral propagation of these hinge lines into previously unfaulted parts of the horizon. Considerations of cross-sections in these unfaulted areas would fail to identify the full causes of fold development.

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folds amplify and propagate their hinges laterally – common feature of decoupling of the cover rocks eventually to connect into a continuous fold train from the underlying basement. In this regard, his (Fig. 12c). This raises an important issue when con- cross-section is similar to those considered by Dahl- sidering an individual cross-section through a fold- strom (1970) in the Canadian foothills. Both view belt. Explanations of the spatial distribution of spe- the deformation as thin-skinned. Buxtorf’s interpre- cific folds or structural styles may lie outside tation of the structure beneath the Grenchenberg tun- the cross-section or structure of interest. A holistic nel (Fig. 13) is amongst the most widely reproduced consideration of the fold–thrust belt may be more in structural geology. This section and its subsequent informative. reworking was much-cited as an example of buckle folding above a basal decoupling surface (e.g. Ram- Implications for modelling strategies say 1967). Subsequently it has become a much-cited example of detachment folding, featuring in text There have been various attempts to mimic the fold books such as Fossen (2016). Likewise, the various patterns of the Subalpine and Helvetic Alps (e.g. other fold–thrust models illustrated in Figure 1 all von Tscharner et al. 2016). These represent a con- have long heritage. Fault-bend folds (Fig. 1a) were siderable advance on approaches that impose a kine- famously interpreted in the Appalachians by Rich matic model to a multilayer to reproduce deformation (1934). The notion that thrusts grow as strain local- within the Urgonian limestone (e.g. Smart et al. izes in folded strata, the feature of fault-propagation 2012) in that they are three-dimensional. They do, folding (Fig. 1b; Williams & Chapman 1983), goes however, use flawless rheological beams. Yet if the back at least to Willis (1894) and Heim (1878). results from analogue models of Dubey & Cobbold However, since the early 1980s, although these (1977) are generally applicable, buckle fold clusters historical roots are often cited, the descriptions of nucleate on perturbations, thus the initial fold pattern structural geology surrounding them, have become will develop from the amplification of these pre- blurred. Thus, the now prevalent terminology of existing heterogeneities. It is only at rather significant fault-related folding, outlined on Figure 1, has bulk contraction (>35%) that the fold system self- been increasingly used to develop structural inter- organizes with dominant wavelengths controlled by pretations, without addressing underlying issues, layer thicknesses. If taken into the natural world, especially concerning buckling instabilities and dis- this implies that almost all foothills systems are still tributed strain. under the influence of their heterogeneities. Perhaps the deformation of sedimentary multilayers is compa- Evolving literature and confirmation bias rable with mineral physics – it is the existence of lattice defects that allows crystals to deform plasti- Figure 14 charts the increase in the application of cally (e.g. Nicolas & Poirier 1976, p. 52). Folds and idealized fold thrust geometries as depicted on thrusts may preferentially nucleate on pre-existing Figure 1, from the early 1980s to the present. It imperfections in stratigraphic units such as faults or also shows the publication of research on buckle facies heterogeneities. folds, sourced from the online tool Scopus – Elsev- ier’s abstract and citation database, for the same Comparing approaches period. Cursory inspection may suggest that, if the literature reflects geological reality, the dominant The folded Mesozoic strata of the Jura mountains of style of deformation is detachment folding and Switzerland were interpreted by Buxtorf (1916), there are relatively few buckle folds. What are the largely using outcrop, well data and then new rail- implications of this? Are detachment folds distinct way tunnels. His cross-section (Fig. 13) shows vari- from buckle folds? Are true buckle folds rather ations in deformation localization, while retaining a rare? Can cross-sections across mountain belts like

Fig. 13. Buxtorf’s (1916) oft-reproduced cross-section through the Jura mountains of Switzerland, based on wells and railway tunnel.

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Fig. 14. A comparison of publication history of papers that cite the terms ‘fault-bend folding’, ‘detachment-folding’ and buckling/buckle folding. The sample was created by searching Scopus and filtering on papers classified as Earth and environmental science. Vertical scales refer to number of papers per three-year bin, coded to the type of fold.

the Jura be reliably constructed using simple meth- students, brought up on a diet of post 1990 text- ods and folding concepts (e.g. Poblet & McClay books and subsurface interpretation manuals, will 1996; Mitra 2003; Shaw et al. 2005)? invariably interpret structures such as those on Bux- We argue below that the distinction between torf’s cross-sections through the Jura (Fig. 13)as detachment folding and buckle folding above a detachment folds and name them as such, rather décollement is false. Hence, much of the literature than consider them to be buckle folds. It is perhaps represented in Figure 14 simply follows the newer unsurprising therefore that examples of natural struc- categorization of detachment folds, as part of the tures or their interpretations illustrated on cross- fold–thrust belt model suite, rather than buckle fold- sections that conform to the specific styles illustrated ing. The effect is to polarize structural geologists and in Figure 1 are widely documented. Alternative ap- risks detaching those engaged in subsurface inter- proaches and observed structural geometries may pretation from a rich vein of knowledge. be under-reported or poorly cited in published litera- The use of categorization of concepts and associ- ture. Such bias is increased by reliance on modelling ated nomenclature can be useful standard scientific software that only allows for a narrow range of de- practice to aid communication and to share ana- formation modes for cross-section construction logues. Applications include fossils (e.g. Woodward (Groshong et al. 2012). Perhaps the reliance on sim- 1885), plants (e.g. Jones & Luchsinger 1979) and ple kinematic descriptions of fold–thrust complexes minerals (e.g. Morimoto 1988; Leake et al. 1997). charts the increasing use of seismic reflection data to Grouping in this way generally implies associa- construct cross-sections through the subsurface. In tions within categories and is appropriate when this context, conventional structural interpretation these objects are similar. However, the approach strategies emphasize beds, the continuity of stratal can promote studies that seek to confirm existing reflectors and their offsets across faults. Deforma- understanding at the expense of those that seek to tion fabrics and patterns of distortional strain, the challenge conventional wisdom. This is termed ‘con- necessary companions of non-concentric folding, firmation’ bias, unwitting selectivity in the acquisi- are difficult to detect by seismic reflection methods tion and use of evidence (Nickerson 1998), which (but see Iacopini & Butler 2011), and so are gener- is compounded by the availability of models –‘avail- ally ignored. ability bias’. These types of bias are widely recog- So consider this rationale: fault displacement and nized in scientific investigations (e.g. Mynatt et al. bed length can be measured and sections constructed 1977) and can restrict the range of concepts or mod- and restored accordingly; deformation by distributed els chosen to explain natural phenomena. Alcalde strain cannot be readily detected or quantified; et al. (2017) show the impact of a limited range therefore the possibility of strain is ignored; so bed of training examples on interpretations of a fault in deformation is assumed to have occurred by concen- a seismic image. If the findings of this paper are tric folding alone. The resultant cross-section is generically applicable, today’s structural geology restorable and thus is assessed as carrying a low

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risk of being wrong, certainly compared with unre- Localization: forced folds v. buckle folds stored interpretations. However, this risk assessment would rely on arbitrarily negating the significance Here we develop a broader basis for understanding of distributed deformation and focusing exclusively relationships between folds and thrusts, linking the on interpretations that are restorable using purely idealized fold–thrust models (Fig. 1) to buckle fold concentric folding and fault slip. As such it is concepts (Fig. 2). Our aim is to provide a more holis- unreliable. tic view of deformation, and deformation localiza- The above scenario is an example of the McNa- tion in compressional settings that better considers mara Fallacy, a form of cognitive bias that engenders the true structural evolution of folds, faults and over-confidence in a particular deduction (e.g. Bass their interplay in multilayered stratigraphy. Notwith- 1995). It is a widely recognized syndrome resulting standing the issues raised above, we restrict discus- from over-reliance on a narrow range of data, gener- sions here to cross-sections, but recognize the ally the most readily quantitative, at the expense of importance of adopting 3D approaches for under- factors that are less amenable to quantification (e.g. standing structural evolution (but see Butler 1992). Martin 1997; O’Mahony 2017). In our scenario, Consider layer-parallel contractional deforma- the bias lies in retaining only a narrow range of pos- tion acting upon a sequence of parallel-bedded strata sible structural geometries and relegating others as (Fig. 15). We can chart the distribution of deforma- being irrelevant complexities – only adopting model- tion within an individual layer with respect to the ling solutions that follow a few numerical approxi- aggregation of shortening. For ideal fault-bend fold- mations while ignoring interpretation possibilities ing, a fault nucleates instantly so deformation is that cannot be so simply modelled. The challenge localized onto an infinitesimally small part of this then is to increase the availability of models and ap- layer. As shortening increases displacement remains proaches, rather than rely on a narrow, over-defined entirely localized (Fig. 15). Note that in the hanging set of possible solutions. wall to the fault, the layer is deformed, simply as a

Fig. 15. Conceptual model for the different styles of fold–thrust structure outlined in Figure 1, examining the pattern of distributed deformation (represented by the length of buckled bed), using the approach of Butler (1992).It illustrates the differences between ‘forced folding’ (where deformation is solely localized on the thrust surface) and buckling. Only fault-bend folds are purely ‘forced’ and thus only these folds are entirely fault-related. All other forms involve a component of buckling.

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consequence of displacement. Fischer & Coward that layer buckling is a rare process in fold–thrust (1982) quantify these flexural flows. As Cosgrove belts. We have argued here that this is wrong – and & Ameen (1999; following Stearns 1978) note, this that there is a spectrum of folding and faulting styles is an example of forced folding – a consequence of that can co-exist in stratigraphic multilayers. To displacements in the surrounding rocks. They draw answer our titular question, the buckles are still distinction between folds formed as a consequence there. In many studies over the past 25 years, struc- of compression acting parallel to layering – buckles. tures which have involved components of layer buck- In these systems a single horizon never localizes a ling have simply been renamed as fault-propagation thrust ramp, but simply, the strata above the detach- or detachment folds. Yet through renaming, swathes ment, décollement or thrust flat continues to accom- of relevant knowledge on buckling systems have modate deformation by folding. If the layer retains been largely neglected, not only by communities constant thickness during deformation, folding in striving to interpret and forecast the subsurface, but that layer must be accommodated by rotation and, also by those attempting to downscale to forecast pat- as noted previously (Butler 1992), if there is a terns of fracture and strain within folds. fixed décollement surface, there must be hinge The use of restricted structural styles in cross- migration. Consequently, the amount of rotated bed section construction was strongly criticized by must increase as shortening is accommodated (Fig. Ramsay & Huber (1987, p. 557), although wrongly 15). Williams & Chapman (1983) developed a gene- conflated with the concept of section balancing. Sim- ral strain case so that layer thickness can change plification is an inherent process in most scientific during deformation. investigation – its appropriateness depends on the We can consider the two behaviours discussed specific problem under investigation. So the reasons above to represent end-members (Fig. 15) – either: for adopting particular geometric solutions depend (1) instantaneous displacement localization or (2) on the purpose of a particular cross-section or mod- distributed folding continuing through the entire elling campaign. deformation history. However, fault-propagation Ramsay (1967), in developing mathematical folding envisages deformation evolving so that a approaches to quantify the geometry of deformed layer first deforms by folding but then localizes dis- rocks, focused on spatially continuous strain. Upscal- placement as a thrust grows into it (see Mitra 2003 ing emphasizes strain compatibility so that heteroge- and many others). This chronology may be an neous strains change gradually through a deformed expression of strain hardening. However, the univer- rock volume. In contrast, the development of thrust sal relevance of this model is challenged by studies concepts has emphasized discontinuous deformation such as that of Cooley et al. (2011) discussed and characterizes these discontinuities – the thrust above (Fig. 9). Folding happened both before and faults. Upscaling and the consideration of strain com- after movement on the Livingstone Thrust. patibility underpins the notion of section balancing. The concept of mechanical stratigraphy is used However, by emphasizing displacement and the by some to assess strain development (especially associated forced folds, the roles of distributed strain fracture patterns) assuming larger-scale structural and buckling have been neglected. Buckle folds and geometries and evolutions that build upon concepts forced folds have different mechanics and yield dif- of fault-related folds (e.g. Smart et al. 2012; Hughes ferent forecasts of fracture and other strain patterns et al. 2014). Using the terminology of Cosgrove & (Cosgrove & Ameen 1999). There was once exten- Ameen (1999), these are effectively viewed as forced sive research on strain patterns in thrust sheets (e.- folds as distinct from buckles. This view is rein- g. Coward & Kim 1981; Morley 1986; Woodward forced by contributions from Groshong (2015). et al. 1986; Geiser 1988; Mitra 1994) that sought The implication is that buckling is a rare process in to quantify distributed deformation alongside thrust fold–thrust belts. Yet buckle folds and forced folds displacements. However, there are few such studies have different mechanics and yield different fore- today. casts of fracture and other strain patterns (discussed The problem of over-confidence in structural by Cosgrove & Ameen 1999). Failure to consider interpretation is compounded by publications, as buckling processes will make inappropriate fracture illustrated in Figure 14. As a structural geology forecasts of structurally controlled fractures. community we should consciously challenge our interpretations that conform to ‘classic’ rules and geometries. In this way we may limit further bias in Discussion: where have all the our interpretations of fold–thrust structures and buckles gone? cease contributing further to availability bias (Bond et al. 2007; Alcalde et al. 2017). For decades, most studies of fold–thrust belts have Interpretations biased from adopting Dahlstrom’s considered folding to be a consequence of thrust ‘foothills family’, and the derivative range of fold– geometry and faulting processes. The implication is thrust models (e.g. Shaw et al. 2005; Fig. 1), can

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be managed if the purpose is to upscale from BOYER, S.E. 1986. Styles of folding within thrust sheets: structural interpretations. This might be to evaluate examples from the Appalachian and Rocky Mountains tectonic processes through obtaining estimates of of the USA and Canada. Journal of Structural Geology, – shortening of rocks in the upper crust, if quoted 8, 325 339. as minima, or a range of likely values rather than sin- BOYER, S.E. & ELLIOTT, D. 1982. Thrust systems. Bulletin of the American Association of Petroleum Geologists, 66, gle determinations (e.g. Elliott & Johnson 1980; 1196–1230. reviewed by Butler 2013). Or it could be to develop BRANDES,C.&TANNER, D.C. 2014. Fault-related folding: a predictions of the large-scale thermal evolution of review of kinematic models and their application. Earth thrust belts (e.g. Deville & Sassi 2005; McQuarrie Science Reviews, 138, 352–370. & Ehlers 2017). However, understanding the evolu- BUTLER, R.W.H. 1986. Thrust tectonics, deep structure and tion of folds, predicting smaller-scale structures crustal subduction in the Alps and Himalayas. Journal within specific layers and forecasting their geometry of the Geological Society, London, 143, 857–873, // / / in the subsurface are hindered by considering only a https: doi.org 10.1144 gsjgs.143.6.0857. narrow range of deformation modes. The history of BUTLER, R.W.H. 1987. Thrust system evolution within pre- viously rifted areas: an example from the Vercors, exploration drilling for hydrocarbons in thrust sys- French subalpine chains. Memorie della Società Geo- tems bears testimony to these inherent uncertainties logica Italiana, 38,5–18. (Butler et al. 2018), as typified by our discussion BUTLER, R.W.H. 1992. Evolution of Alpine fold–thrust of the Incahuasi structure (Fig. 7). Understanding complexes: a linked kinematic approach. In:MITRA, the risks of interpretation failure and the construction S. & FISHER, G. (eds) Structural Geology of Fold and of cross-sections that improve predictions of subsur- Thrust Belts. Johns Hopkins University Press, Balti- face structure may be enhanced by better integration more, MD, 29–44. BUTLER, R.W.H. 2013. Area balancing as a test of models both of information on the heterogenous localization fi of strain within layered sequences and of buckle for the deep structure of mountain belts, with speci c – reference to the Alps. Journal of Structural Geology, folding concepts into fold thrust models. 52,2–16. BUTLER, R.W.H. & BOWLER, S. 1995. Local displacement rate cycles in the life of a fold–thrust belt. Terra Acknowledgements We dedicate the paper to the Nova, 7, 408–416. memory of Martin Casey (1948–2008), who did much BUTLER, R.W.H., BOND, C.E., COOPER, M.A. & WATKINS, through good-humoured argument to ensure that buckling H.M. 2018. Interpreting structural geometry in fold– ideas were not lost to what he called ‘the Ramping Club’ thrust belts: why style matters. Journal of Structural (the thrust belt community). The Fold–Thrust Research Geology, 114, 251–273. Group has been funded by InterOil, OilSearch and Santos. BUXTORF, A. 1916. Prognosen und Befunde beim Hauen- We thank Paul Griffiths and an anonymous referee for com- steinbasis- und Grenchenbergtunnel und die Bedeutung ments together with Hermann Lebit for scientific editing. der letzteren für die Geologie des Juragebirges Ver- The views expressed here of course remain those of handlungen der Naturforschenden Gesellschaft, 27, the authors. 185–254. CARTWRIGHT, J.A., TRUDGILL, B.D. & MANSFIELD, C.S. 1995. Fault growth by segment linkage: an explanation for References scatter in maximum displacement and trace length data from the Canyonlands Grabens of SE Utah. Jour- ABBASSI, M.R. & MANCKTELOW, N.S. 1992. Single layer nal of Structural Geology, 17, 1319–1326. buckle folding in non-linear materials – I. Experimental CASEY,M.&BUTLER, R.W.H. 2004. Modelling approaches study of fold development from an isolated initial per- to understanding fold development: implications for turbation. Journal of Structural Geology, 14,85–104. hydrocarbon reservoirs. Marine and Petroleum Geol- ALCALDE, J., BOND, C.E., JOHNSON, G., BUTLER, R.W.H., ogy, 21, 933–946. COOPER, M.A. & ELLIS, J.F. 2017. The importance of COBBOLD, P.R. 1975. Fold propagation in single embedded model availability on seismic interpretation. Journal layers. Tectonophysics, 27, 333–351. of Structural Geology, 97, 161–171. COOLEY, M.A., PRICE, R.A., DIXON, J.M. & KYSER, T.K. BALLY, A.W., GORDY, P.L. & STEWART, G.A. 1966. Struc- 2011. Along-strike variations and internal details of ture, seismic data and orogenic evolution of southern chevron-style, flexural-slip thrust-propagation folds Canadian Rocky Mountains. Bull. Can. Pet. Geol., within the southern Livingstone Range anticlinorium, 14, 337–381. a paleohydrocarbon reservoir in southern Alberta Foot- BASS, B.M. 1995. Comment: transformational leadership. hills, Canada. Bulletin of the American Association of Looking at other possible antecedents and conse- Petroleum Geologists, 95, 1821–1849. quences. Journal of Management Enquiry, 4, 293–297. COSGROVE, J.W. & AMEEN, M.S. 1999. A comparison of the BIOT, M.A. 1961. Theory of folding of stratified viscoelastic geometry, spatial organization and fracture patterns media and its implications in tectonics and orogenesis. associated with forced folds and buckle folds. In:COS- Geological Society of America Bulletin, 72, 1595–1620. GROVE, J.W. & AMEEN, M.S. (eds) Forced Folds and BOND, C.E., GIBBS, A.D., SHIPTON, Z.K. & JONES, S. 2007. Fractures. Geological Society, London, Special Publi- What do you think this is? ‘Conceptual uncertainty’ cations, 169,7–21, https://doi.org/10.1144/GSL.SP. in geoscience interpretation. GSA Today, 17,4. 2000.169.01.02.

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COWARD, M.P. & KIM, J.H. 1981. Strain within thrust deformed terranes. Geological Society of America Spe- sheets. In:MCCLAY, K.R. & PRICE, N.J. (eds) Thrust cial Paper, 222,47–76. and Nappe Tectonics. Geological Society, London, GHANADIAN, M., FAGHIH, A., FARD, I.A., KUSKY,T.&MAL- Special Publications, 9, 275–292, https://doi.org/10. EKI, M. 2017. On the role of incompetent strata in the 1144/GSL.SP.1981.009.01.25. structural evolution of the Zagros Fold–thrust Belt, COWARD, M.P. & SIDDANS, A.W.B. 1979. The tectonic evo- Dezful Embayment, Iran. Marine and Petroleum Geol- lution of the Welsh Caledonides. In:HARRIS, A.L., HOL- ogy, 81, 320–333. LAND, C.H. & LEAKE, B.E. (eds) The Caledonides of the GRAHAM, R.H., JACKSON, M., PILCHER,R.&KILSDONK,B. British Isles – Reviewed. Geological Society, London, 2012. Allochthonous salt in the sub-Alpine fold–thrust Special Publications, 8, 187–198, https://doi.org/10. belt of Haure Provence, France. In:ALSOP, G.I., 1144/GSL.SP.1979.008.01.18. ARCHER, S.G., HARTLEY, A.J., GRANT, N.T. & HODGEKIN- DAHLSTROM, C.D.A. 1969. Balanced cross-sections. Cana- SON, R. (eds) Salt Tectonics, Sediments and Prospectiv- dian Journal of Earth Sciences, 6, 743–757. ity. Geological Society, London, Special Publications, DAHLSTROM, C.D.A. 1970. Structural geology in the eastern 363, 595–615, https://doi.org/10.1144/SP363.30. margin of the Canadian Rocky Mountains. Bulletin of GROSHONG, R.H. 2015. Quality control and risk assessment Canadian Petroleum Geology, 18, 332–406. of seismic profiles using area–depth–strain analysis. DARNAULT, R., CALLOT, J.-P., BALLARD, J.-F., FRAISSE, G., Interpretation, 3, SAA1–SAA15. MENGUS, J.-M. & RINGENBACH, J.-C. 2016. Control of GROSHONG, R.H., BOND, C.E., GIBBS, A., RATLIFF,R.& syntectonic erosion and sedimentation on kinematic WILTSCHKO, D.V. 2012. Preface: structural balancing evolution of a multidecollement fold and thrust zone: at the start of the 21st century: 100 years since Cham- analogue modeling of folding in the southern suban- berlin. Journal of Structural Geology, 41,1–5. dean of Bolivia. Journal of Structural Geology, 89, HEIDMANN, J.-C., DURAND, J., MALLARD, P., BALLARD, J.-F. 30–43. &MORON, J.-M. 2017. Discovery of a Bolivian Foot- DEVILLE,E.&SASSI, W. 2005. Contrasting thermal evolu- hills giant gas field: Incahausi. Memoir of the American tion of thrust systems: an analytical and modeling Association of Petroleum Geologists, 113, 153–164. approach in the front of the western Alps. American HEIM, A. 1878. Untersuchungen über den Mechanismusder Association of Petroleum Geologists Bulletin, 90, Gebirgsbildung. Benno Schwabe, Basel. 887–907. HUGHES, A.N. & SHAW, J.H. 2015. Insights into the mechan- DIXON, J.M. & LIU, S. 1992. Centrifuge modelling of the ics of fault-propagation folding styles. Bulletin of the propagation of thrust faults. In:MCCLAY, K.R. (ed.) Geological Society of America, 127, 1752–1765. Thrust Tectonics. Springer, Dordrecht, 53–69. HUGHES, A.N., BENESH, N.P. & SHAW, J.H. 2014. Factors DRIEHAUS, L., NALPAS,T.&BALLARD, J.F. 2014. Interaction that control the development of fault-bend v. fault-prop- between deformation and sedimentation in a multide- agation folds: insights from mechanical models based collement thrust zone: analogue modelling and applica- on the discrete element method (DEM). Journal of tion to the Sub-Andean thrust belt of Bolivia. Journal of Structural Geology, 68, 121–141. Structural Geology, 65,59–68. IACOPINI,D.&BUTLER, R.W.H. 2011. Imaging deformation DUBEY, A.K. & COBBOLD, P.R. 1977. Noncylindrical flex- in submarine thrust belts using seismic attributes. Earth ural slip folds in nature and experiment. Tectonophy- and Planetary Science Letters, 302, 414–422. sics, 38, 223–239. JAMISON, W.R. 1987. Geometric analysis of fold develop- ELLIOTT,D.&JOHNSON, M.R.W. 1980. Structural evolution ment in overthrust terranes. Journal of Structural Geol- in the northern part of the Moine Thrust Zone, NW ogy, 9, 207–219. Scotland. Transactions of the Royal Society, Edin- JAQUET, Y., BAUVILLE,A.&SCHMALHOLZ, S.M. 2014. Vis- burgh: Earth Sciences, 71,69–96. cous overthrusting v. folding: 2-D quantitative modeling ERSLEV, E. 1991. Trishear fault-propagation folding. Geol- and its application to the Helvetic and Jura fold and thrust ogy, 19, 617–620. belts. Journal of Structural Geology, 62,25–37. FERNANDEZ,N.&KAUS, B.J.P. 2014. Fold interaction and JONES, S.B., JR &LUCHSINGER, A.E. 1979. Plant System- wavelength selection in 3D models of multilayer atics. McGraw-Hill, New York. detachment folding. Tectonophysics, 632, 199–217. KAMPFER,G.&LEROY, Y.M. 2012. The competition FISCHER, M.W. & COWARD, M.P. 1982. Strains and folds between folding and faulting in the upper crust based within thrust sheets: the Heilam sheet, NW Scotland. on the maximum strength theorem. Proceedings of the Tectonophysics, 88, 291–312. Royal Society, A468, 1280–1303. FOSSEN, H. 2016. Structural Geology, 2nd edn. Cambridge LATHAM, J.-P. 1985. The influence of non-linear pro- University Press, Cambridge. perties and resistance to bending on the development FOX, F.G. 1959. Structure and accumulation of hydrocar- of internal structure. Journal of Structural Geology, 7, bons in southern foothills, Alberta, Canada. Bulletin 225–236. of the American Association of Petroleum Geologists, LEAKE, B.E., WOOLLEY, A.R. ET AL. 1997. Report. Nomen- 43, 992–1025. clature of amphiboles: report of the subcommittee on FRIZON DE LAMOTTE,D.&BUIL, D. 2002. La question des amphiboles of the international mineralogical associa- relations entre failles et plis dans les zones externes tion commission on new minerals and mineral names. des chaînesde montagnes. Ebauche d’une histoire des Mineralogical Magazine, 61, 295–321. e idées au cours du XX siècle. Comité français d’His- LETURMY, P., MUGNIER, J.L., VINOUR, P., BABY, P., COLETTA, toire de la Géologie 3ème série, 16,47–62. B. & CHABRON, E. 2000. Piggyback basin development GEISER, P.A. 1988. The role of kinematics in the construc- above a thin-skinned thrust belt with two detachments tion and analysis of geological cross-sections in levels as a function of interactions between tectonic

Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/4914379/9781786204721_c004.pdf by guest on 29 September 2021 WHERE HAVE ALL THE BUCKLES GONE? 43

and superficial mass transfer: the case of the Subandean POBLET,J.&MCCLAY, K. 1996. Geometry and kinematics of Zone (Bolivia). Tectonophysics, 320,45–67. single-layer detachment folds. Bulletin of the American MANCKTELOW, N.S. & ABBASSI, M.R. 1992. Single layer Association of Petroleum Geologists, 80, 1085–1109. buckle folding in non-linear materials – II. Comparison PRICE, N.J. & COSGROVE, J.W. 1990. Analysis of Geological between theory and experiment. Journal of Structural Structures. Cambridge University Press, Cambridge. Geology, 14, 105–120. RAMBERG, H. 1966. Experimental models of fold moun- MARTIN, S. 1997. Two models of educational assessment: a tains. Geologiska Föreningen i Stockholm Förhandlin- response from initial teacher education: if the cap fits…. gar, 87, 484–491. Assessment and Evaluation in Higher Education, 22, RAMSAY, J.G. 1967. Folding and Fracturing of Rocks. 337–343. McGraw-Hill, New York. MCQUARRIE,N.&EHLERS, T.A. 2017. Techniques for RAMSAY, J.G. 1989. Fold and fault geometry in the western understanding fold-and-thrust belt kinematics and ther- Helvetic nappes of Switzerland and France and its mal evolution. In:LAW, R.D., THIGPEN, J.R., MERSCHAT, implication for the evolution of the arc of the western A., STOWELL,H.&BAILEY, C. (eds) Linkages and Feed- Alps. In:COWARD, M.P., DIETRICH,D.&PARK, R.G. backs in Orogenic Process: A volume in Honor of Rob- (eds) Alpine Tectonics. Geological Society, London, ert D Hatcher Jr. Geological Society of America, Special Publications, 45,33–45, https://doi.org/10. Boulder, CO, USA, Memoirs, 213,25–54. 1144/GSL.SP.1989.045.01.02. MITRA, G. 1994. Strain variations in thrust sheets across the RAMSAY, J.G. & HUBER, M.I. 1987. The Techniques of Mod- Sevier fold-and-thrust belt (Idaho, Utah-Wyoming): ern Structural Geology. Volume 2: Folds and Frac- implications for section restoration and wedge taper tures. Academic Press, London. evolution. Journal of Structural Geology, 16, 585–602. REBER, J.E., SCHMALHOLZ, S.M. & BURG, J.-P. 2010. Stress MITRA, S. 1990. Fault-propagation folds: geometry, kine- orientation and fracturing during three-dimensional matic evolution, and hydrocarbon traps. American Asso- buckling: numerical simulation and application to ciation of Petroleum Geologists Bulletin, 74, 921–945. chocolate-tablet structures in folded turbidites, SW Por- MITRA, S. 2003. A unified kinematic model for the evolu- tugal. Tectonophysics, 493, 187–195. tion of detachment folds. Journal of Structural Geol- RICH, J.L. 1934. Mechanics of low-angle overthrust faulting ogy, 25, 1659–1673. as illustrated by Cumberland thrust block, Virginia, MORIMOTO, N. 1988. Nomenclature of pyroxenes. Mineral- Kentucky and Tennessee. American Association of ogy and Petrology, 39,55–76. Petroleum Geologists Bulletin, 18, 1584–1596. MORLEY, C.K. 1986. Vertical strain variations in the Ose– ROCHA,E.&CRISTALLINI, E.O. 2015. Controls on structural Røa thrust sheet, North-western Oslo Fjord, Norway. styles along the deformation front of the Subandean Journal of Structural Geology, 8, 621–632. zone of southern Bolivia. Journal of Structural Geol- MORLEY, C.K. 1994. Fold-generated imbricates: examples ogy, 73,83–96. from the Caledonides of Southern Norway. Journal of SCHMALHOLZ, S.M. 2008. 3D numerical modeling of for- Structural Geology, 16, 619–631. ward folding and reverse unfolding of a viscous single- MOUTHEREAU, F., LACOMBE, O., TENSI, J., BELLAHSEN, N., layer: implications for the formation of folds and fold KARGAR,S.&AMROUCH, K. 2007. Mechanical con- patterns. Tectonophysics, 446,31–41. straints on the development of the Zagros folded belt SHAW, J., CONNORS,C.&SUPPE, J. (eds) 2005. Seismic inter- (Fars). In:LACOMBE, O., LAVÉ, J., ROURE,F.&VERGES, pretation of contractional fault-related folds. American J. (eds) Thrust Belts and Foreland Basins: From Fold Association of Petroleum Geologists Studies in Geol- Kinematics to Hydrocarbon Systems. Springer, Berlin, ogy, 53, 156. 247–266. SIMPSON, G.D.H. 2009. Mechanical modelling of folding MYNATT, C.R., DOHERTY, M.E. & TWEENEY, R.D. 1977. v. faulting in brittle–ductile wedges. Journal of Struc- Confirmation bias in a simulated research environment: tural Geology, 31, 369–381. an experimental study of scientific inference. Quarterly SMART, K.J., FERRILL, D.A., MORRIS, A.P. & MCGINNIS, R.N. Journal of Experimental Psychology, 29,85–95. 2012. Geomechanical modeling of stress and strain evo- NICKERSON, R.S. 1998. Confirmation bias: a ubiquitous phe- lution in contractional fault-related folding. Tectono- nomenon in many guises. Review of General Psychol- physics, 576–577, 171–196. ogy, 2, 175–220. STEARNS, D.W. 1978. Faulting and forced folding in the NICOLAS,A.&POIRIER, J.P. 1976. Crystalline Plasticity and Rocky Mountain foreland. Geological Society of Amer- Solid State Flow in Metamorphic Rocks. Wiley, London. ica Memoirs, 151,1–38. O’MAHONY, S. 2017. Medecine and the McNamara fallacy. SUPPE, J. 1983. Geometry and kinematics of fault bend fold- Journal of the Royal College of Physicians of Edin- ing. American Journal of Science, 283, 648–721. burgh, 47, 281–287. VON TSCHARNER, M., SCHMALHOLZ, S.M. & EPARD, J.-L. OVEISI, B., LAVÉ,J.&VAN DER BEEK, P. 2007. Rates and pro- 2016. 3-D numerical models of viscous flow applied cesses of active folding evidenced by Pleistocene ter- to fold nappes and the Rawil depression in the Helvetic races at the central Zagros front (Itan). In:LACOMBE, nappe system (western Switzerland). Journal of Struc- O., LAVÉ, J., ROURE,F.&VERGES, J. (eds) Thrust tural Geology, 86,32–46. Belts and Foreland Basins: From Fold Kinematics to WILLIAMS, G.D. & CHAPMAN, T.J. 1983. Strains developed Hydrocarbon Systems. Springer, Berlin, 267–287. in the hangingwalls of thrusts due to their slip/propaga- PARISH, M. 2016. Changes in structural style along the fron- tion rate: a dislocation model. Journal of Structural tal Papuan fold belt from seismic imaging. American Geology, 5, 563–571. Association of Petroleum Geologists Data Pages, WILLIAMS, G.D., POWELL,C.M.&COOPER, M.A. 1989. Geom- Search and Discovery, 30448, 25. etry and kinematics of inversion tectonics. In:COOPER,

Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/4914379/9781786204721_c004.pdf by guest on 29 September 2021 44 ROBERT BUTLER ET AL.

M.A. & WILLIAMS,G.D.(eds)Inversion Tectonics. Geo- WOODWARD, A.S. 1885. IV. On the literature and nomencla- logical Society, London, Special Publications, 44,3–15, ture of British Fossil Crocodilia. Geological Magazine, https://doi.org/10.1144/GSL.SP.1989.044.01.02. 2, 496–510. WILLIS, B. 1894. The Mechanics of Appalachian Structure. WOODWARD, N.B., GRAY, D.R. & SPEARS, D.B. 1986. Department of the Interior, US Geological Survey, Including strain data in balanced cross-sections. Jour- Washington, DC, USA. nal of Structural Geology, 8, 313–324.

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