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_Journal of Structural Geology 32 (2010) 172–183_ _Cross-section restoration: A tool to simulate deformation. Application to a fault-propagation fold from the Cantabrian fold and thrust belt, NW Iberian Peninsula_ _Massimiliano Masini 1, Mayte Bulnes, Josep Poblet* _Departamento de Geolog??a, Universidad de Oviedo, C Jesu?s Arias de Velasco s n, 33005 Oviedo, Spain_ _Article info_ _Article history: Received 23 December 2008; Received in revised form 15 October 2009; Accepted 3 November 2009; Available online 18 November 2009_ _Keywords: Deformation Cross-section restoration Fault-propagation fold Layer-parallel shear Cantabrian fold and thrust belt Small-scale structures_ _Abstract_ _Simulation of deformation in sections across tectonic structures can provide important information about the present-day state of such structures. A technique for simulation of deformation, based on cross-section restoration, is presented. The deformation parameters are calculated through a model that provides information in numerical format and the results are illustrated overlapping gridded images and diagrams on top of the sections across the structures in order to visualize their geological significance. The validity of this method has been proved through its application to a structure formed in a contractional regime. The structure analyzed is located in the Cantabrian Mountains, NW Iberian Peninsula, and consists of a fault-propagation fold made up of Carboniferous limestones. The excellent outcrop of this structure allowed a complete geological cross-section reconstruction, and a detailed structural and kinematic analysis in order to obtain an accurate restoration. The results furnished by the restoration technique about the deformation values and patterns are in agreement with small-scale structures observed in the field as well as with the geometry and kinematics of the structure._ _? 2009 Elsevier Ltd. All rights reserved._ _1. Introduction_ _Knowing the deformation undergone by beds involved in tectonic structures is an important aim for structural geologists from the purely scientific point of view but also from the economic point of view since a large number of disciplines are interested in understanding the distribution and evolution of deformation in rocks (hydrocarbon, mining and ground water exploration, engineering geology, sub-surface storage of fluids, seismicity, etc.). Direct methods to measure deformation employ strain markers present in the rocks (fossils, fossil traces or different types of particles) such as those methods which construct strain ellipses using geometrical parameters measured from several lines on a plane (Ramsay, 1967; Ragan, 1985; Ramsay and Huber, 1987), the R4 method (Ramsay, 1967; Dunnet, 1969), the ‘‘all-object-separation’’ plot (Fry, 1979a,b) and analysis of fibrous mineral overgrowths (Durney and Ramsay, 1973; Hedlund et al., 1994) amongst others. Unfortunately, in many folded faulted regions it is not always possible to obtain deformation data since strain markers are absent._ _* Corresponding author. Tel.: ?34 98 5109548; fax: ?34 98 5103103. E-mail address: jpoblet@geol.uniovi.es (J. Poblet)._ _1 Now at YPF, Mendoza, Argentina._ _0191-8141 $ – see front matter ? 2009 Elsevier Ltd. All rights reserved. doi:10.1016 j.jsg.2009.11.002_ _One way to overcome this drawback consists of using techniques to simulate deformation which may be employed as predictive tools of deformation architecture in natural geological structures. These methods do not require collecting rock samples from the geological bodies analyzed because they deal with geological maps, cross-sections and 3D geological surfaces. Some of these techniques are curvature analysis of folded surfaces (e.g., Lisle, 1994; Samson and Mallet, 1997; Roberts, 2001), forward modelling (e.g., Thorbjornsen and Dunne, 1997; Bastida et al., 2003; Ormand and Hudleston, 2003; Allmendinger et al., 2004), restoration (e.g., Erickson et al., 2000; Hennings et al., 2000; Rouby et al., 2000; Dunbar and Cook, 2003; Moretti et al., 2007), restoration plus forward modelling (e.g., Allmendinger, 1998; Sanders et al., 2004; Poblet and Bulnes, 2007), etc._ _Here we present a method similar to that of Erickson et al. (2000), Hennings et al. (2000), Rouby et al. (2000), Dunbar and Cook (2003), and Moretti et al. (2007), since they employ restoration to quantify different parameters that characterise the deformation undergone by rocks in folded faulted regions. The strategy consists of introducing circular strain markers in a deformed cross-section, subsequently restoring the section together with the strain markers, and finally obtaining the strain ellipses (one for each strain marker) through application of_ _M. Masini et al. Journal of Structural Geology 32 (2010) 172–183_ _173_ _a mathematical model. The strain parameters are calculated in numerical format and the results are illustrated through graphical outputs displayed on top of the sections across the geological structures, which may be compared with the orientation and distribution of tectonic features such as minor-scale folds and fractures, structural fabrics, etc._ _The predictive capabilities of the method are shown through its application to a fault-propagation fold developed over a thrust fault in the Bodo?n Structural Unit (Cantabrian Zone, NW Iberian Peninsula) affecting Carboniferous limestones. This fault-related fold is an example of a contractional tectonic structure, where geological data quality, and the excellent outcrop and accessibility allowed us to carry out a complete structural analysis in order to verify the method presented here. The fact that the stratigraphic sequence is well-known and that the structure is tilted, so that almost the whole structure is exposed and only a small amount of data extrapolation is needed to complete the geometry of the structure, makes it an excellent candidate to be studied in detail. In addition, the analysis of this natural example furnished information on the deformation undergone by different portions of fault-propagation folds related to thrusts._ _The main goals pursued here are (a) show a practical application of the method using 2D sections across geological structures and (b) provide additional insight about deformation in fault-related folds developed over thrust faults._ _2. Methodology_ _The methodology presented in this paper is based on the following procedure:_ _(a) construction of a retro-deformable geological cross-section parallel to the tectonic transport direction using all the available surface and sub-surface data;_ _(b) introduction of strain markers along the geological section, so that the size, density and distribution of the markers are a function of the features of the structure or region to be analyzed, the precision of the results one would like to obtain and the occurrence of specific areas in which high deformation amounts are suspected or have a particular geological significance;_ _(c) partial or total restoration of the geological section including strain markers;_ _(d) application of a mathematical transformation to the restored strain markers in order to calculate the orientation of the semi-axes and lines of no finite deformation of the deformation ellipses, and the magnitudes of ellipse ellipticity and layer-parallel strain derived from each strain marker;_ _(e) data contouring in order to interpolate deformation parameters in between strain markers;_ _(f) results display (contour colour images of amount of ellipticity, diagrams showing orientations of ellipse semi-axes, etc.) onto the present-day, deformed geological cross-section;_ _(g) comparison of the cross-section including the deformation simulation with the deformed, geological cross-section including second-order structures to check whether the deformation parameters and patterns simulated are in accordance with the type, orientation and motion along the small-scale structures, and therefore, the deformation simulation is geologically reasonable; and_ _(h) use of the geological cross-section including the deformation simulation as a predictive tool for those regions in which not enough data are available, e.g., hidden portions of the structures in the sub-surface or offshore, poor seismic imaging or bad quality outcrops of some parts of the structure._ _If the deformation simulation does not agree with the second-order structures present in the region and/or some anomalies or artefacts are detected in the deformation simulation, the following parameters must be checked and the procedure must be totally or partially repeated depending on the error encountered (Bulnes and Poblet, 1999): quality of the (a) geological data collected in the outcrop, sub-surface and/or offshore; (b) structural interpretation and (c) cross-section construction; (d) orientation of the section line; (e) position and dip of the pin and loose lines; (f) restoration algorithm(s) employed; (g) plane strain assumption; (h) size, density or position of the strain markers; (i) data interpolation algorithm(s) used; and/or (j) influence of parameters not considered such as vertical horizontal compaction amongst others._ _The method described above may be applied to different types of structures developed in contractional, extensional, inversion tectonics, etc., settings in which the distribution of strain along the folded faulted layers may occur through different mechanisms such as layer-parallel shear, vertical inclined shear, etc. In the natural example analyzed here, layer-parallel shear was the main mechanism, a common mode of distribution of deformation in sedimentary sequences involved in different types of structures formed under contractional conditions in upper crustal domains._ _This is the reason why the mat'_ Ключевые слова: excellent outcrop, foliation, tectonophysics, method presented, footwall ramp, folding, hennings, region, geological map, parallel, los fuejos structure, geometry, tectonic, shear, data, bed, young researchers, shear vein, rez-estau, parameter, layer-parallel shear, geometric modication, strain ellipse, sub-surface portion, cantabrian zone, cross, fuejos structure, detachment surface, regional-scale anticline, masini journal, anticline forelimb, strain, curvature analysis, nite deformation, geological, surface, iberian, cantabrian, cross-section restoration, input parameter, predictive tool, strain marker, lvarez-marro, tectonics, cantabrian fold, footwall block, sua rez-rodrguez, aapg, intersection lineation, red colour, tectonic transport, ?nite, foliation surface, type, imbricate thrust, conjugate band, structure, major anticline, local coordinate, geological signicance, high deformation, complex algorithm, band dened, geolog?, maximum elongation, thrust, structural, simulation, poblet, stratigraphic sequence, developed, propagation, mcclay, trabajos geolog?, tension gash, main mechanism, deformation parameter, fault propagation, geologically reasonable, structure formed, algorithm, cross-section, elongation, geology, maximum, bedding, alba, mechanism, method, present-day cross-section, hangingwall, fault plane, forelimb, ramp, structural geology, anticline, geologa alonso, outcrop, spanish ministry, deformation, portion, nw, minimum elongation, displacement, kinematic indicator, deformation undergone, area, simulate, ramsay, introduction, predictive capability, fault-propagation, deformation data, present-day, mathematical model, deformation simulation, deformation mechanism, steeply plunging, la, alonso, vein, presented, located, numerical format, footwall, medwedeff equation, algorithm employed, structure analyzed, fold, wa, aapg bulletin, application, result, carboniferous limestone, north limb, equation, strain parameter, geological interpretation, predicted set, bulletin, geological structure, blue colour, limestone, mitra, jamison, minimum deformation, letouzey, zone, fault-propagation fold, masini, dip moderately, undeformed footwall, scale, restoration, ?nite deformation, detachment, specic area, restored loose, journal structural, structural interpretation, malvern, restored, london, tension, julivert, trabajos, analysis, ax, order, basal detachment, los, point, thrust ramp, dip, los fuejos, foldedfaulted region, layer-parallel, marker, model, small, small-scale structure, bed number, villasecino anticline, including, orientation, average difference, large number, tectonic structure, savage, fuejos, slickensides measured, elsevier, fry, simulate deformation, interpretation, frontal syncline, bulnes, argentina, journal structural geology, sitter, mcconnell, fault, journal, minimum, strain ellipsis, technique, marcos, observed, allmendinger, gash, maximum deformation, main, fold axis, distribution, hall