Geology

doi: 10.1130/0091-7613(1996)024<0175:UAIATF>2.3.CO;2 1996;24;175-178Geology

 Jaume Vergés, Douglas W. Burbank and Andrew Meigs Unfolding: An inverse approach to fold kinematics  

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Unfolding: An inverse approach to fold kinematicsJaume Verges Departament de Geologia Dinamica, Geofısica i Paleontologia, Universidad de Barcelona,

08071 Barcelona, SpainDouglas W. Burbank

Department of Geological Sciences, University of Southern California, Los Angeles, California 90089Andrew Meigs

ABSTRACTPreserved fold shapes usually reveal little about their kinematic evolution. Syntectonic

strata preserved in growth synclines in contact with a fold, however, can permit ‘‘unfold-ing’’: a sequential reconstruction of fold growth backward through time from a geometryobserved at present to an initial undeformed state. Such reconstructions can define thekinematics of fold growth. Growth strata associated with anticlinal forelimbs in the Ebrobasin exhibit depositional tapering of beds on fold flanks and progressive limb rotation.Unfolding a well-dated detachment fold defines its kinematic evolution and coevally varyingrates of shortening, forelimb uplift, and forelimb rotation. Interplay of these rates withsedimentation rates controls onlap and offlap relations.

INTRODUCTIONFolds are a fundamental structure of con-

tractional orogens, and yet deciphering theirkinematic history continues to be controver-sial. Given a present-day cross section of afold, we are usually unable to determine un-ambiguously the history of fold growth. Foldgeometries from some thrust belts are con-sistent with geometrically based kinematicmodels, often with self-similar growth pat-terns (Medwedeff, 1992; Shaw and Suppe,1994). Other studies suggest that preservedfold shapes represent only the end productof a geometrically variable growth history(e.g., Ramsay, 1974). The crux of the prob-lem rests in the motion of rocks with respectto fold hinges and the angles of fold limbswith time. Two different data sets can po-tentially resolve fold evolution: distributionof strain throughout the fold (Fischer et al.,1992) and growth strata (Suppe et al., 1992).Growth strata deposited above the limb of adeforming fold can place clear geometricconstraints on fold growth through time.Herein we describe a methodology for astep-by-step restoration of growth stratabackward through time (termed ‘‘unfold-ing’’) to determine fold kinematics. Al-though our examples formed above detach-ment folds, the methodology is independentof fold history and should be applicable toother folding styles.

DETACHMENT FOLDS AND RELATEDGROWTH STRATAAlong the margins of the Ebro foreland

basin (Fig. 1), well-preserved growth strataare associated with numerous folds (Riba,1976), some of which can be defined as de-tachment folds (Fig. 2). In our usage, a de-tachment fold is one that forms by bucklingabove a detachment which is subparallel tooriginal layering and in which the majorityof shortening is accommodated by folding,rather than faulting (Jamison, 1987). The

Spanish examples display four salient char-acteristics when seen in profile (Fig. 1): (1)the full succession of growth strata displaysa wedge-shaped geometry; (2) single beds orgroups of beds within the wedge-shaped do-main thicken across the forelimb from theanticlinal crest to a maximum thickness nearthe synclinal axis; (3) angular unconformi-ties may occur between groups of beds in thewedge-shaped domain; and (4) growthstrata above the forelimb show an increasein dip from stratigraphically higher to lowerstrata. Whereas the relations described be-low apply equally well to backlimbs andforelimbs, our discussion is restricted toforelimbs, where angular stratal geometriestend to be more pronounced.A well-exposed example of the interrela-

tions between syntectonic deposition andevolving structures occurs at Oliana alongthe eastern oblique margin of the SouthCentral Unit (Fig. 1, A and B). Here, be-tween ;37.2 and 34.0 Ma, an imbricate sys-tem of southeast-directed thrusts developedon the backlimb of the Oliana anticline co-evally with deposition of growth strata(Verges and Munoz, 1990; Burbank et al.,1992). The fold and thrust system is de-tached above a decollement in Upper Trias-sic evaporites (Verges, 1993). Folds in bothpregrowth and growth strata show kink-shaped geometries with rounded hinges andinterlimb angles ranging from 408 to 708. Wefocus on strata preserved in a growth syn-cline attached to the Can Juncas anticline,which has an overturned forelimb and awavelength of ;0.5 km (Figs. 1B and 3).Given the typical structural styles of thefolds and faults above evaporites in thesouthern Pyrenees and the absence of sur-face faults at Can Juncas, we interpret thisfold as a detachment anticline.A pronounced unconformity marks the

contact between the base of the growthstrata and the overturned pregrowth strata

in the fold’s forelimb. The oldest growthstrata prominently onlap paleotopographythat existed prior to fold growth. Clear onlapof the forelimb persisted as folding initiated.From the synclinal axial surface to the crestof the anticline, growth strata show a gen-eral thinning defined by marked changes indip of both individual beds and stratal units(Fig. 4A). These strata comprise 170 m offluvial deposits characterized by siltstoneand sandstone interbedded with conglomer-ate beds up to 25 m thick. Paleocurrent in-dicators define flow parallel to the fold crestand synclinal axis.Few successions of growth strata have

been dated with precision sufficient to defineshort-term variability in rates of sedimenta-tion, uplift, shortening, or forelimb rotation.Paleomagnetic dates on the growth strata ofthe Can Juncas anticline (Burbank andVerges, 1994), however, provide ages forthree horizons from which rates of sedimentaccumulation and fold growth can becalculated.

UNFOLDING: REVERSE STEP-BY-STEPFOLD RESTORATIONThe methodology relies on a step-by-step

unfolding of stratal units backward throughtime. For each time step, younger growthstrata are removed, the uppermost deposi-tional surface or bounding unconformity isrestored to its original prefolding orienta-tion, and underlying growth and pregrowthstrata are concurrently back rotated. Inthese fluvial strata, where paleoflow is par-allel to the anticlinal trend, a horizontal dep-ositional surface in cross section can be as-sumed. Transverse rivers or alluvial fansmay have slopes of a few degrees. If known,such slopes can be integrated into therestoration.A deformed-state cross section, parallel

to the tectonic transport, at Can Juncas (Oli-ana) has been built using dip data, map dis-tribution, measured stratigraphic sections,and lengths of tapered and untapered syn-tectonic strata across the anticline-growthsyncline pair (Fig. 4A). Restorations for twostages (35.37 and 34.96Ma) have beenmadeby pinning the unthinned growth strata inthe distal part of the growth syncline wellbeyond the folded domain, preservingstratal areas, and minimizing changes intaper in order to minimize bed-lengthchanges during folding (Fig. 4, B and C).

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The deformation path of the forelimb hasbeen broken into horizontal and verticalcomponents by tracking the motion of ma-terial points near the top of the forelimb(Fig. 4).Overall, during 0.7 m.y., growth strata ac-

cumulated at a mean rate of ;0.16 mm/yr,as the forelimb rotated at a mean rate of;1.38/104 yr. In contrast to long-term rates,short-term rates (at the scale of single mag-netic chrons) provide more insight on theinterplay among variables that control the

fold shape and patterns of growth strata. Al-though sedimentation rates were slow priorto 35.37 Ma (Fig. 4), they remained fasterthan the rate of forelimb uplift and resultedin onlap during early fold growth. Between

35.37 and 34.96 Ma, accumulation acceler-ated to;0.16 mm/yr. However, because thisrate is less than the vertical uplift rate (0.22mm/yr), growth strata show offlap geome-tries and gentle thinning toward the crest of

Figure 1. A: Geologic map of Ebro basin with locations of field examples. B: Growth fold at Can Juncas showing prominent thinning towardanticlinal crest in pregrowth strata (top right). C: Internal geometry of evaporite-cored La Garriga fold is dominated by clear onlap of overturnedfold forelimb (arrows). D: Growth syncline near Horta de Sant Joan (Barranco dels Estrets) in Catalan Coastal Ranges showing overturned basalconglomerates (at right) deposited on deformed carbonate and siltstone. Note prominent internal unconformity that younger growth strataprogressively onlaps (arrows).

Figure 2. Detachment fold geometry andthickness variations in growth syncline as re-lated to its forelimb and backlimb.

Figure 3. Regional cross section showing imbricate system of thrusts and folds above backlimbof Oliana anticline. Growth strata are linked to Can Juncas detachment anticline. Shaded unitsin pregrowth stratigraphy are competent layers.

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the anticline. Coevally, the forelimb steep-ened at a rate of ;0.88/104 yr, and the foldachieved ;85% of its maximum height(Fig. 4B). Subsequently, from 34.96 to 34.67Ma, accumulation rates dropped to ;0.13mm/yr, whereas forelimb rotation increasedalmost 2.5 fold to ;2.08/104 yr (Fig. 4B).

During this stage, the uplift rate of the ma-terial points in growth strata at 34.96 Maexceeded both the accumulation rate andthe uplift rate of the material point in pre-growth strata. When combined with a rapidrate of horizontal shortening (;0.46 mm/yr), pronounced offlap developed. Although

the extent to which layer-parallel slip con-tributes to the total shortening is difficult toquantify from field relations, some such slipis implied by our restorations, specifically inthe lower stratal units (Fig. 4B).

DISCUSSIONBecause both kinematics and structural

geometry should be used to assess the va-lidity of a cross section (Geiser, 1988), un-folding provides a useful constraint on thegeometrical evolution of a fold and a checkon the viability of an interpretation. Unfold-ing of dated growth strata reveals a detailedhistory of fold kinematics and changes in var-iables (rates of uplift, horizontal displace-ment, and limb rotation), which, along withrates of sediment accumulation and periodsof erosion, affect the internal organizationof the growth strata. The resultant geomet-ric restorations can be compared with pre-dicted geometries of published folding mod-els. Our restorations at Can Juncas yieldthree critical fold-evolution observations(Fig. 4). First, the syncline axial surfacechanges its orientation through time, result-ing in a broad hinge region. Axial surfaces ofthe present-day section are localized in thishinge region. Second, the forelimb rotatesto a steeper dip toward the syncline withtime. Third, the fold exhibits variable ratesof crestal uplift and limb rotation duringgrowth.Delineation of the axial surfaces at each

step helps define the growth and amplifica-tion of the fold. The fold grows and the fore-limb rotates because the horizontal separa-tion of the axial surfaces decreases withtime, the axial surfaces concurrently rotatefrom a steeper to a shallower inclination,and the length of the forelimb does notchange during folding (Fig. 4). Throughtime, the resultant deformational path ofmaterial points in the forelimb is forwardand upward with respect to the syncline, un-til the forelimb is vertical. Subsequently, thepath of these material points is forward andslightly downward (overturned limb).Although the Can Juncas fold shows a su-

perposition of axial surfaces within thehinge regions of the fold, other detachmentfolds in the Ebro region show pregrowth andgrowth strata passing forward through theanticlinal axial surface, such that crestalsegments become incorporated into alengthening forelimb (Millan et al., 1994).Whether axial surfaces have been fixed oractive is often not easily discerned from apreserved fold geometry. Past changes in theorientation and position of such surfaces,however, can be defined through sequentialunfolding of growth strata.Given the time and geometric control at

the Can Juncas anticline, rates of limb ro-

Figure 4. A: Detailed cross section of growth syncline at Can Juncas showing position ofmagnetostratigraphy (Burbank and Verges, 1994). Prior to 36.4 Ma, growth strata filled paleo-valley, and are not involved in unfolding. B: Unfolded geometry with strata younger than 34.96Ma removed. For this and subsequent stages, total forelimb rotation and incremental move-ment of material points are shown. Positions of both synclinal and anticlinal axial surfaces aredepicted. C: Unfolded geometry at 35.37 Ma. D: Mean chron-length rates of horizontal andvertical translation, limb rotation, and sediment accumulation during fold growth. Instanta-neous rate changes at chron boundaries are not geologically meaningful. Ratios of verticaluplift to accumulation define intervals of onlap and offlap.

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tation, horizontal and vertical displace-ment, and sediment accumulation can bedecoupled and independently compared(Fig. 4). Throughout growth, rates of limbrotation increase due to changes in theratio of horizontal to vertical displace-ment. Whereas the rate of uplift is greaterthan horizontal shortening during the initialphases of folding (until the forelimb has at-tained 508 dip), horizontal displacementrates equal and subsequently exceed upliftafter 34.96 Ma, resulting in shearing of theforelimb of the anticline. The growth-stratageometry is not completely defined, how-ever, simply by comparison of rates of upliftand accumulation. Increased rates of limbrotation, driven by an acceleration of hori-zontal displacement and coupled with offlap,result in a strong angular discordance withinthe youngest growth strata (Fig. 4, A and B).Although the limb rotation rates we havedocumented are chron-length averages, pro-nounced tapering of several individual bedssuggests that limb rotation rates vary onshorter time scales.The evolving shape and related deforma-

tion rates of the Can Juncas fold can becompared with simple geometrical foldingmodels which allow for increasing limb dipsduring growth. Models of symmetric chev-ron (Ramsay, 1974), sinusoidal (Rockwell etal., 1988), and detachment folds (Hardy andPoblet, 1994) predict that with a constantrate of horizontal shortening, high initialrates of uplift decay rapidly. In contrast, therate of uplift at Can Juncas does not de-crease with time because the rate of hori-zontal shortening accelerates. Similar to themodel predictions, however, constant ratesof uplift at Can Juncas can only be sustainedby increasing rates of shortening throughtime. In the face of steady accumulation,these fold models each predict stratigraphicofflap, followed by onlap. Onlap geometriesdominate the early folding at Can Juncas,and thus we interpret lower rates of verticaluplift for this time interval.Rates of forelimb rotation are dependent

on the geometry of folding, rates of short-ening, and the wavelength of the growingfold. Fold wavelength is largely a function ofthe thickness of pregrowth strata. Compa-rable limb rotation rates would be expectedonly if the rates of shortening were scaled tovariations in the pregrowth strata thicknessand fold wavelength.The hinge of the detachment fold at Can

Juncas separates pregrowth strata of normalthickness from contiguous strata that hadbeen thinned by erosion prior to the foldingdescribed here (Fig. 4). It might thus appearthat this is not a particularly representativeexample of detachment folding, due to atyp-ical initial conditions. It is likely, however,

that the axes of folds are commonly posi-tioned by differential thicknesses of pre-growth strata, because heterogeneities maylocalize strain.

CONCLUSIONSGeometric models for fold development

(Suppe, 1983; Suppe and Medwedeff, 1990)have served to focus attention on and to pro-vide testable hypotheses for the kinematicsand sequential growth of folds. Similarly, ge-ometries of growth strata are predicted torecord sensitively the evolving shape of theforelimb and backlimb of a fold. Given thisprediction, interpretations of seismicallyimaged growth strata have been used to il-lustrate some folding models (Suppe et al.,1992). Neither the steep forelimb dips atCan Juncas anticline nor a fold of its scale,however, would be clearly imaged by typicalseismic data. Yet, despite its small scale, thehigh-quality exposure and precise dating ofthe growth strata at Can Juncas providepowerful tools for examination of fold de-velopment through time. Whereas forwardmodels predict fold evolution, unfolding ofgrowth strata reconstructs incremental foldevolution. Furthermore, unfolding permitscalculation of rates of deformation which,when combined with rates of deposition,emphasize the interactions among variablerates that determine the geometry of anevolving fold and related growth strata. Ap-plication of this methodology to other foldswith associated growth strata should resultin a more complete description and under-standing of natural folding paths.

ACKNOWLEDGMENTSSupported by the Subprograma Perfecciona-

miento de Doctores and Direccion General deInvestigacion Cientıfica y Tecnica (grants PB91-0252 and PB91-0805 to Verges), the NationalScience Foundation (grants EAR-9018951 andEAR-9304863 to Burbank), the Petroleum Re-search Fund of the American Chemical Society(grants PRF-17625 and PRF-23881 to Burbank),and the American Association of Petroleum Ge-ologists, the Geological Society of America, andSigma Xi (grants to Meigs). We thank M. Lopez-Blanco for field assistance, and R. Allmendinger,J. Suppe, G. Axen, and two anonymous reviewersfor constructive reviews.

REFERENCES CITEDBurbank, D. W., and Verges, J., 1994, Recon-

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Burbank, D. W., Verges, J., Munoz, J. A., andBentham, P. A., 1992, Coeval hindward- andforward-imbricating thrusting in the centralsouthern Pyrenees: Timing and rates ofshortening and deposition: Geological Soci-ety of America Bulletin, v. 104, p. 1–18.

Fischer, M. P., Woodward, N. B., and Mitchell,M. M., 1992, The kinematics of break-thrustfolds: Journal of Structural Geology, v. 14,p. 451–460.

Geiser, P. A., 1988, The role of kinematics in theconstruction and analysis of geological crosssections in deformed terranes, in Mitra, G.,and Wojtal, S., eds., Geometries and mech-anisms of thrusting with special reference tothe Appalachians: Geological Society ofAmerica Special Paper 222, p. 47–76.

Hardy, S., and Poblet, J., 1994, Geometric andnumerical model of progressive limb rota-tion in detachment folds: Geology, v. 22,p. 371–374.

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Millan, H., Aurell, M., and Melendez, A., 1994,Synchronous detachment folds and coevalsedimentation in the Prepyrenean ExternalSierras (Spain): A case study for a tectonicorigin of sequences and system tracts: Sedi-mentology, v. 41, p. 1001–1024.

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Manuscript received April 21, 1995Revised manuscript received October 12, 1995Manuscript accepted October 23, 1995

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