Fracture distribution in a folded fluvial succession: the Puig-reig anticline (South-eastern Pyrenees)

Sedimentary rocks of foreland fold-and-thrust belts typically undergo intensive fracturing as fold grows. The resulting fracture networks can present significant variations depending on the distribution of sedimentary facies and the complex structural characteristics of fold-and-thrust belts. The Puig-reig anticline, located in the south-eastern Pyrenees, mainly exposes proximal fluvial deposits in the north limb and medial fluvial deposits in the rest of the anticline. Thus, this anticline constitutes an excellent case study to investigate the main controls on the distribution of fracture networks in folded fluvial deposits, in terms of structural position and lithofacies variations. Outcrops were selected to be representative of different structural positions, from the fold hinge to its limbs, and of a variety of the main lithofacies, from proximal to medial fluvial deposits. Fracture data were acquired using the linear scanline method. Results indicate that the anticline is affected by four sets of fractures. The north limb is dominated by thick conglomerate bodies with interlayered sandstones deposited from unconfined flash floods and wide-shallow channel streams in the proximal fluvial fan, and presents large fracture spacing and low fracture intensity but relatively large fracture length and aperture. The crest and the crest-limb transition zones are mainly composed of interlayered conglomerates, sandstones, siltstones and clays, deposited from braided channel streams and overbanks in the medial fluvial fan and present fractures with relatively high fracture intensity and variable fracture length and aperture. The south limb, composed of channel filling sandstone layers and stable overbank fine deposits in the medial fluvial fan, is characterised by low fracture intensity and small fracture length and aperture. Based on multiple linear regression analysis, fracture intensity is mainly controlled by the structural position, bedding thickness and lithological associations, with relatively more intense fracturing in thin sandstone layers with multiple interlayers of fine deposits in the anticline crest. The fracture length is mainly controlled by bedding thickness


Introduction
Fracture networks in rocks of gently deformed foreland basins and intensively deformed fold-and-thrust belts promote the formation of vertical and/or lateral fluid migration pathways within different hydrostratigraphic units (Travé et al., 2007;Fischer et al., 2009;Evans and Fischer, 2012;Ogata et al., 2014;Muñoz-López et al., 2020a). Many studies have analysed factors controlling the distribution of fracture networks, particularly how the structural position and the characteristics of sedimentary rocks impact the resulting fracture networks (Underwood et al., 2003;Florez-Niño et al., 2005;Lorenz et al., 2006;Wennberg et al., 2006;Ortega et al., 2010;Ogata et al., 2017). Here we use the term 'fracture' in a wide sense to refer to discrete mechanical discontinuities in the rock mass formed under the action of stress, including low-or zero-offset fractures, joints, microfractures and veins (i.e., sealed fractures) (Peacock et al., 2016), and leave out high-offset faults within large fault zones.
Fracture network attributes, including fracture intensity, orientation, length, aperture and connectivity have been described to be closely related to the structural position of a rock volume within a fold (Peacock, 2001;Bellahsen et al., 2006;Ghosh and Mitra, 2009;Watkins et al., 2015a). Fracture networks in fold hinges or forelimbs tend to have high intensity, with fractures presenting wider apertures and better connectivity than those located in fold backlimbs, due to the greater curvature and finite strain (Nelson and Serra, 1995;Watkins et al., 2015a). Besides, fracture intensity tends to increase in the proximity of large faults .
Other studies show that the intensity of certain fracture sets can vary with the structural position and finite strain, while in other sets it may show less variation across fold sections. Some examples are the Oil Mountain anticline in Wyoming (Hennings et al., 2000) and the Teton anticline in Montana (Ghosh and Mitra, 2009).
Additionally, fractures formed prior to folding can contribute to the mechanical anisotropy of stratified units and thus significantly impact the resulting fracture networks formed during fold growth. For example, the Emigrant Gap anticline in Wyoming features constant fracture characteristics owing to the influence of prefolding fractures (Bergbauer and Pollard, 2004). All these previous studies point out that the position with respect to a structural feature can be a key factor controlling fracture attributes, but there is great variability in their relationship. 3 Apart from the structural position, the characteristics of the hosting sedimentary rocks have also been reported to be key controls on the distribution of fracture networks. The depositional and diagenetic characteristics of a rock unit, including the lithofacies architecture, lithological assemblages, bedding thickness, depositional components, textures, grain size and presence of cements and other diagenetic products determine the rock mechanical properties, including stiffness, cohesion and angle of internal friction (Shackleton et al., 2005;Olson et al., 2007;Ferrill and Morris, 2008;Laubach et al., 2009). Some studies reported a clear negative correlation between fracture intensity and bedding thickness (Huang and Angelier, 1989;Florez-Niño et al., 2005;Wennberg et al., 2007), while others did not reveal systematic relationships (Guiton et al., 2003;Wennberg et al., 2006;Ortega et al., 2010;Awdal et al., 2013). Competent rocks, such as clay-poor carbonates, are typically associated with much higher fracture intensity than clay-rich rocks (Ferrill and Morris, 2008).
Grain size has a significant effect on fracture propagation, in a way that increasing grain size has been found to reduce crack coalescence and crack damage thresholds (Eberhardt et al., 1999). The rock mechanical properties can also greatly evolve with progressive diagenetic events, thus affecting the evolution of fracture networks (Di Naccio et al., 2005;Laubach et al., 2009;Barbier et al., 2012).
Foreland basins and their adjacent fold-and-thrust belts contain significant hydrocarbon resources (Mann et al., 2003), and also show high potential for CO 2 storage (Sun et al., 2020). As important fluid migration pathways and potential reservoir space, fracture networks have been widely studied in thrust belts composed of carbonate deposits due to their abundant hydrocarbon resources, e.g., in the Zagros fold-and-thrust belt (Stephenson et al., 2007), the Bighorn Basin (Bellahsen et al., 2006), the Apennines (Van Dijk et al., 2000) and the Oman Mountains (Gomez-Rivas et al., 2014). However, studies of fracturing of thrust belts composed of sandstone deposits are significantly less well documented (Watkins et al., 2015a). An example of understudied systems is alluvial-fluvial fans, which are the main deposits in non-marine foreland basins at their active margins (Horton and Decelles, 2001).
The southern Pyrenees presents multiple fold and thrust related alluvial-fluvial fans, which are buried as subsurface reservoirs or exposed as outcrops (e.g., Arenas et al., 2001;Jones, 2004;Sáez et al., 2007;Yuste et al., 2004). Such alluvial-fluvial strata in the subsurface show high potential to become effective reservoirs. For example, the eastern part of the Puig-reig anticline in the south-eastern Pyrenees was assessed as a potential site for gas storage (Instituto Geológico y Minero de España, 1995). Besides, the well-exposed outcrops can provide excellent reservoir analogues to investigate fracture distributions in folded alluvial-fluvial successions at basin margins. However, most studies of the southern Pyrenees focused on unravelling the different 4 tectonic events and/or analysing the fingerprints of fluids to decipher the evolution of fluid flow (Travé et al., 2000;Beaudoin et al., 2015;Taillefer et al., 2017;Cruset et al., 2018Cruset et al., , 2020Lacroix et al., 2018;Nardini et al., 2019;Muñoz-López et al., 2020b), while only a few studies focused on the formation or distribution of fractures (e.g., Tavani et al., 2011Tavani et al., , 2020Gutmanis et al., 2018). Here we present a systematic analysis of the fracture network of a folded fluvial succession exposed in the Puig-reig anticline. Fracture attributes from different structural positions and sedimentary facies were collected and analysed, with the overarching aim of determining what are the main depositional and structural controls on fracture distributions.

Geological setting
The Pyrenees is a doubly verging orogenic belt that formed during the continental collision between the Iberian and European plates from Late Cretaceous to Miocene (Muñoz, 1992;Vergés et al., 2002). This orogenic belt is characterised by an antiformal stack of basement-involved thrusts (the Axial Zone) surrounded by two fold-and-thrust belts that were transported to the north and south over the Aquitanian (France) and Ebro (Spain) foreland basins, respectively (Choukroune, 1989;Roure et al., 1989;Muñoz, 1992). The eastern part of the Ebro Basin displays an irregular shape bounded by the Pyrenees to the north and the Catalan Coastal Range to the southeast ( Fig. 1A and B) (Vergés, 1993;Vergés et al., 1998). The Vallfogona thrust represents the major frontal thrust between the SE Pyrenean thrust sheets and the Ebro Basin. The Busa syncline and the Puig-reig anticline developed along the footwall of the Vallfogona thrust during Late Eocene and Oligocene (Vergés, 1993).
Based on the available seismic profiles across the Puig-reig anticline (Fig. 1C), the anticline was interpreted to have been formed as a consequence of a duplex stack in depth (Vergés, 1993). In the lower part, the Banyoles and Igualada formations (Middle-to-Upper Eocene) consist of marine marls. They were duplicated by thrusting and detached above the Beuda (Middle Eocene) evaporitic formation Serra-Kiel et al., 2003a, 2003b. In the upper part, the Berga Group and the Solsona Formation (Upper Eocene to Oligocene) were deposited during the endorheic stage of the Ebro Basin (Puigdefàbregas et al., 1986(Puigdefàbregas et al., , 1992, after a rapid transition from marine to continental environments of deposition at around 36 Ma during the Priabonian (Costa et al., 2010). During Oligocene, Vallfogona footwall was folded forming the km-scale south-verging gentle anticline of Puig-reig. The fold-trend is ESE/WNW, slightly oblique to the main Pyrenean structures (Vergés, 1993).  (Vergés, 1993).
(C) Geological cross section of the frontal part of the SE Pyrenean fold-and-thrust belt and the Ebro Basin (Vergés, 1993).
The seismic profile (Line S-2) is from the Spanish Geophysical Information System (Instituto Geológico y Minero de España, 1977). (D-E) Distribution of the Berga Group and the Solsona Formation and location of outcrops. The strata distribution in Fig. 1D is based on the regional geological map of Catalonia (Institut Cartogràfic i Geològic de Catalunya, 2006). The formation subdivision of the Berga Group follows the scheme of Williams et al. (1998). Fig. 1E is modified from Williams et al. (1998) and Barrier et al. (2010).
To the north, at the footwall of the Vallfogona thrust, the Berga Group consists of more than 2,000 m-thick 6 alluvial and proximal fluvial conglomerates interbedded with minor sandstones and claystones, which display growth strata geometries (Ford et al., 1997;Suppe et al., 1997). To the south, the Berga deposits became progressively finer-grained and thinner-bedded fluvial conglomerates, sandstones and claystones of the Solsona Formation (Williams et al., 1998;Barrier et al., 2010). Finally, the Solsona deposits translated downstream to terminal deposits of a distal fluvial system, which graded into evaporites and calcareous lacustrine deposits towards the centre of the Ebro Basin (Del Santo et al., 2000;Sáez et al., 2007;Barrier et al., 2010).

Data and methods
The Puig-reig anticline exposes excellent outcrops along four roads perpendicular to the axial direction of the structure, roughly in a north-south direction, between the villages of Sant Llorenç de Morunys in the north and Solsona in the south ( Fig. 1B and D). Seven high-resolution stratigraphic logs with a total length of over 3,000 m were built based on the data collected from outcrops along these roads (Fig. 1D). Our study mainly focused on the Camps de Vall-Llonga (a sub-formation of the Berga formation) and Solsona formations (Upper Eocene to Lower Oligocene; Carrigan et al., 2016), which cover most areas of the anticline. The ca. 9 km-long geological cross-section of the Puig-reig anticline (sections A and B, Fig. 1E) lies roughly parallel to the thrust direction of the south-eastern Pyrenees and displays the transition from proximal to medial fluvial deposits.
Three main sampling methods for collecting fracture data are widely used and discussed in the literature, namely the linear scanline, window sampling and circular scanline methods (e.g., Zeeb et al., 2013aZeeb et al., , 2013bWatkins et al., 2015b;Healy et al., 2017 and references thereof). The linear scanline method was adopted in this study because of the nearly vertical outcrops present in the Puig-reig anticline (Fig 2A), which prevented the use of other fracture sampling methods. The linear scanline method is a fast technique for recording a wide range of fracture attributes (listed in Table 1), including fracture orientation, length, spacing, intensity, aperture and fracture filling. The scanline locations were chosen to be representative of different structural positions as well as of different sedimentary facies and stratigraphic arrangements (e.g., variable bed thickness, lithological associations, etc.). We acquired data from 53 scanlines that add up to around 1,600 m in total scanline length (Table 2), along the three western-most roads (Fig. 1C). The fracture data was acquired in groups of at least two people, with the aim of reducing subjective acquisition biases (Andrews et al., 2019). Around 1,800 fractures with lengths greater than 20 cm intersecting the scanlines were measured. In this study, we did not include large faults with high offsets and obvious fault zones. Small-scale fractures (with length smaller than 20 cm) were difficult to collect using the linear scanline method, especially in conglomerate layers containing 7 abundant fractures confined to only one or a few clasts. To overcome this limitation, the window sampling method was used in zones with abundant small-scale fractures. Conglomerate layers from different structural positions were photographed using a rectangle frame with size dimensions of 45×55 cm (Fig. 2B). Cracked clasts located inside the frame were identified and such fracture data manually collected. The intensity of fractured clasts in conglomerates was defined as the ratio of the number of fractured clasts with respect to the number of identifiable clasts. Although we could not quantitatively distinguish fold-related fractured clasts from clasts in other times, such as those with fractures inherited from the source rocks or formed during clast transport, we assume a similar proportion of non-fold-related fractured clasts in different areas. Thus, we only used the intensity of fractured clasts in conglomerates as an indicator to show the relative fracture intensity in different structural positions.
To study fracture-filling cements, vein samples were collected from different structural positions. 60 polished thin sections of calcite veins were made for petrographic analysis, which was carried out using a Zeiss

Anticline structure
The Puig-reig anticline trends ESE/WNW and has a wavelength of more than 10 km. The ca. 9 km-long geological cross-section (sections A and B in Fig. 1E) exposes continuous outcrops in different structural positions. In this study, the anticline was divided into five structural positions from north to south, i.e., north limb, crest-north limb transition zone (NTZ), crest, crest-south limb transition zone (STZ) and south limb ( Fig.   1E). We did not use the terms proximal and distal to name the structural positions, as other previous studies did (e.g., Ge et al., 1997;Martínez-Martínez et al., 2002), to avoid the potential confusions with common terms to divide environments of deposition in sedimentary systems (i.e., proximal, medial and distal). 9 In the anticline crest, the bedding angles mainly range from 5 o to 15 o . In the north, the bedding dominantly dip towards the north in sections A and E. In the south, the strata mainly dip towards the south in sections B and D. The orientation of the fold hinge was estimated based on the distribution of bedding attitudes in the anticline crest, with a resulting strike of oriented 105 o . In the anticline crest a system of fractures was observed, including abundant joints and some strike-slip and normal faults with displacements smaller than 20 m and a few small low-angle reverse faults with displacements lower than 2 m, and previously observed also in other studies (Cruset et al., 2016). In the NTZ and north limb of the anticline, the strata mainly dip between 10

Sedimentology
The Camps de Vall-Llonga and Solsona formations in the Puig-reig anticline were deposited as part of proximal-medial deposits of a fluvial fan system. The north limb is dominated by proximal fluvial fan deposits characterised by unconfined flash floods and wide-shallow channel streams. Clast-or reddish matrix-supported pebble to cobble conglomerates are the prevailing deposits, especially in the northwest of the anticline. The conglomerate bodies tend to present a massive structure, thick sheet geometries, unscoured or scoured basal surfaces, and broad distributions ranging from a few hundred meters up to three kilometres. Fine to coarse sandstone interlayers display stable tabular geometries or pinch out laterally as sandstone lens. The NTZ, crest and STZ of the anticline are dominated by medial fluvial fan deposits characterised by braided channel streams and overbanks. These deposits are composed of interlayers of conglomerates, sandstones, siltstones and clays.
Channel lag deposits are dominated by clast-supported pebble to small cobble conglomerates with grey sand matrix. The conglomerates commonly present a massive structure, scoured basal surfaces, and channelised geometries. The interlayers of massive and laminated sandstones and overbank fine deposits tend to have tabular geometries. The south limb is also dominated by medial fluvial fan sediments. However, the conglomerate channel lags are replaced by (pebbly) sandstone channel lags, and the south limb is composed of more fine deposits from overbanks than the NTZ, crest and STZ. The distal fluvial fan is located southward of our study area, and is composed of terminal lobes representing low lake-level stages and fluvial-dominated deltas and interdistributary bays representing high lake level stages (Sáez et al., 2007). Four fracture sets (F1, F2, F3 and F4) were identified in the Puig-reig anticline (total 1778 fractures measured) based on fracture orientation and their relationships with the fold hinge ( Fig. 3 A). The F1 and F2 sets have a NNW-SSE orientation and an ENE-WSW orientation, respectively. They are the predominant fracture sets observed at the target structure, accounting for 44% and 28% of the total fractures analysed, respectively. The F3 set is characterised by a WNW-ESE orientation and strikes roughly parallel to the anticline hinge. This set is less frequent and accounts for 17% of the total fractures. The F4 set with a NNE-SSW orientation is very limited along the selected scanlines, because they are sub-parallel to the directions of most scanlines. The lack of outcrops located parallel to bedding planes prevents the identification of systematic where I is the true intensity of different fracture sets, S t is the true fracture spacing, S a is the apparent fracture spacing, and θ is the acute angle of fracture and scanline. The F4 set is sub-parallel to the directions of most scanlines, resulting in limited fractures intersecting scanlines and very small acute angles between fractures and scanlines. The corrected intensity is too sensitive to fracture number and the acute angles, leading to high uncertainty to the results. Thus, we only corrected the fracture intensity of the F1, F2 and F3 sets using this method. The F1 set presents high intensity in all structural positions, while the F2 and F3 mainly presents high intensity in the crest and STZ of the anticline (Fig. 8A). Similar to the distribution of the apparent fracture intensity, the sum of the true fracture intensity of the three sets presents the highest intensity in the crest ( (1.39 m on average). Furthermore, channelised conglomerate bodies tend to present longer fractures than sandstone layers (1.52 m and 1.30 m on average, respectively) (Fig. 5B). Fracture length distributions should normally be corrected for size bias, because the probability of small fractures to cut the scanline is significantly lower than that of large fractures, causing an underestimation of short fractures on the statistical distribution of the whole network (Zeeb et al., 2013a). The probability of collecting fractures greater than or equal to a certain length can be corrected according to the longest fracture length (Zeeb et al., 2013a). The corrected dataset does not fit to an exponential or a power-law distribution, and only a log-normal one presents a 16 reasonable good fit (Fig. 6B).

Fracture aperture and filling
Fracture apertures resulting from stress related to the anticline growth could have potentially been affected by the subsequent stress release during the uplift and exhumation of the anticline. To avoid this uncertainty, in this study we only focus on fractures (now veins) filled with calcite cement precipitated during the anticline growth, where vein widths can represent fracture apertures not affected by the subsequent rock uplift and exhumation. Fracture apertures mainly range from 1 to 5 mm on average and present significant variation across the different structural positions (Fig. 4C). The north limb presents the largest fracture aperture, which mainly ranges between 1 mm and 5 mm but sometimes reaches up to several centimetres. The crest, NTZ and STZ present similar fracture aperture distributions that mainly range from 1 to 3 mm. The south limb has the smallest fracture aperture with all aperture values below 2 mm. Moreover, fracture aperture also varies 18 significantly across the different sedimentary facies and lithofacies. Fractures in the proximal fluvial fan, especially within the conglomerate bodies with interlayered sandstones, present distinctively large apertures, mainly ranging from a few millimetres to a few centimetres. In the crest, NTZ and STZ, channelised conglomerate bodies present wider fractures (1.99 mm on average) than sandstone layers (1.41 mm on average).
In the south limb, the fracture aperture of the medial fluvial fan is keeping below 2 mm (Fig. 5C). Fracture apertures present a good fit to a power-law in a cumulative distribution plot (Fig. 6C) or elongated crystal morphology with crystal size mainly ranging from 0.1 to 3 mm ( Fig. 9A and B). Veins formed by multi-episodic crack-seal events are also occasionally observed ( Fig. 9A and B). The second generation (Cc2) precipitated mainly in fractures and rarely in interparticle pores. Cc2 presents dull orange luminescence and blocky or elongated crystal morphology with slightly larger crystal size than Cc1, mainly ranging from 0.2 to 5 mm ( Fig. 9C and D). The third (Cc3) and fourth (Cc4) cement generations only precipitated in fractures. Cc3 presents dull luminescence and euhedral blocky crystal morphology ranging in size from a few millimetres up to several centimetres ( Fig. 9E and F). Cc4 is not luminescent and presents elongated crystal morphology or palisade structure made of bladed crystals with sizes generally smaller than 1 mm ( Fig. 9G and H). This cement occasionally fills space originated by the reopening of veins hosting older cements ( Fig. 9G and H).

Controlling factors of fracture spacing and intensity
Fracture spacing presents a log-normal distribution, mainly ranging between 0.2 m and 1.2 m (Fig. 6A).
However, the fracture spacing and intensity still vary significantly across the different structural positions (  (Bellahsen et al., 2006;Iñigo et al., 2012;Awdal et al., 2013). If flexural slip was the dominant folding mechanism, then the thin and soft layers in limbs would be ones subjected to the highest strain. However, our field data better matches the first option because the anticline crest features more intensive fracturing than the limbs. Besides, a neutral line can divide a fold into an outer-arc extensional area and an inner-arc shortening area. Sets of layer-perpendicular extensional fractures are typical outer-arc extensional structures (Frehner, 2011). However, only a few normal faults developed in the crest of the Puig-reig anticline, which lacks systematic extensional fractures. Moreover, the analysis of Frehner (2011) reveals that when the 21 fold is gentle (as in the case of the Puig-reig anticline) only a small area at the outer arc would undergo extension. These observations suggest that the anticline probably did not experience intensive out-arc extension.
Fracture intensity has been described to be closely related to the bedding thickness (Ladeira and Price, 1981).
Some studies reported a clear negative correlation between fracture intensity and bedding thickness (Huang and Angelier, 1989;Florez-Niño et al., 2005;Wennberg et al., 2007). However, other studies did not reveal systematic relationships (Guiton et al., 2003;Ortega et al., 2010;Awdal et al., 2013). In this study layers with same lithology and located in the same structural position were chosen for comparison to determine the real relationship between fracture intensity and bedding thickness. Fig. 10B1 reveals a clear negative correlation between fracture intensity and bedding thickness for both conglomerate and sandstone layers in the anticline crest. Fig. 10 B2 shows a similar negative correlation for sandstone layers in the south limb and conglomerate layers in the north limb. Furthermore, conglomerate layers generally tend to be thicker than sandstone layers, thus resulting in lower fracture intensity for the same structural position, e.g., in the anticline crest (Fig. 10B1).
Moreover, fracture intensity decreases more significantly in sandstone layers compared to that in conglomerate layers. This can be observed from difference on slope of the trend lines in Fig. 10B1 and B2.
The grain size of host rocks has been frequently considered as a critical factor affecting rock strength (Přikryl, 2001;Suorineni et al., 2009). Both physical experiments and numerical simulations have shown that the strength of brittle rocks decreases with increasing grain size (Fredrich et al., 1990;Yu et al., 2018). Fracture intensity is generally related to the rock strength or brittleness, and is higher within the stronger and more brittle rocks (Nelson, 2001). Thus, coarse-grained rocks tend to present higher fracture intensity than finegrained rocks, especially in carbonates (Hugman and Friedman, 1979;Hanks et al., 1997). However, a negative correlation between fracture intensity and grain size has also been reported in sandstones (Watkins et al., 2015a). In the present case, there also seems to be a subtle negative correlation between fracture intensity and grain size with relatively higher intensity in sandstone layers and lower intensity in coarse conglomerate layers.
However, the variation of fracture intensity can be caused by other factors. There is not a clear relationship between fracture intensity and grain size when other factors, i.e., structural position and bedding thickness are well controlled (Fig. 10C1 and C2). This indicates that grain size is not a significant factor controlling fracture intensity in the Puig-reig anticline, compared to structural position or bedding thickness. In addition to the structural position, bedding thickness and grain size, in this study we explore the effect of lithological associations on fracture intensity. To mitigate the influence of other factors, the scanlines selected for comparison are those that correspond to layers with the same lithology, similar bedding thickness and that are located in same structural position. Fig. 11A presents three typical lithological associations in the anticline crest, where sandstone layers with multiple thin interlayers of fine sediments (Layer C-1) show relatively smaller fracture spacing than sandstone layers in between thick overbank fine deposits (Layer C-2) and those in between thick channel lag conglomerate bodies (Layer C-3). Similarly, Fig. 11B shows that sandstone layers 23 with multiple interlayers of fine deposits (Layer S-1) present relatively smaller fracture spacing than those in between thick fine deposits (Layer S-2) in the south limb. In the north limb, Fig. 11C shows that conglomerate bodies with sandstone interlayers (Layer N-1) have smaller fracture spacing than other conglomerate bodies with a limited amount of sandstone lenses (Layer N-2). The high competence contrast at distinct mechanical stratigraphic positions (e.g., at the interfaces between carbonate or sandstone layers and fine deposits) favours the development of joints or faults (Sibson, 1996;Wilkins et al., 2014). In this study, the interlayers between competent sandstone layers and thin incompetent fine deposits result in a high competence contrast, which favours the formation of fractures in the competent sandstone layers (i.e., Layer C-1 and Layer S-1 in Fig. 11A and B). However, sandstone layers developed between thick incompetent fine deposits present relatively larger fracture spacing (Layer C-2 and Layer S-2 in Fig. 11A and B), compared to those having thin interlayers of fine deposits. This is probably because thick incompetent lithologies are capable of accommodating greater amounts of pre-failure strain, e.g., by means of inter-granular sliding, pressure solution, pore collapse and associated dewatering (Ferrill and Morris, 2008). Sandstone layers developed between thick conglomerate bodies (Layer C-3 in Fig. 11A) also present relatively larger fracture spacing. This is mainly because the competence contrast between competent sandstones and conglomerates is lower than that between competent sandstones and incompetent fine deposits. In the north limb, the competence contrast of interlayered conglomerate and sandstone layers is higher than that of conglomerate layers with limited sandstone lens.
24 Figure 11. Typical lithological associations in different sedimentary facies and their cumulative distributions of fracture spacing. (A) Massive sandstones with multiple interlayers of fine deposits (Layer C-1), massive sandstones between thick fine deposits (Layer C-2), and massive sandstones between thick conglomerate bodies (Layer C-3) in the anticline crest.
(B) Massive sandstones with multiple interlayers of fine deposits (Layer S-1) and massive sandstones between thick fine deposits (Layer S-2) in the south limb. (B) Conglomerate bodies with stable sandstone interlayers (Layer N-1) and conglomerate bodies with limited sandstone lens (Layer N-2) in the north limb. 25 Based on the above analysis, we can conclude that fracture intensity is controlled by the structural position, bedding thickness and lithological associations, while the host rock's grain size only has a limited effect on fracture intensity. To quantitatively compare the relative importance of each factor for controlling fracture intensity, multiple linear regression analysis using SPSS software (IBM Corp, 2017) was employed in this study. First, lithological associations were classified and digitalised based on their effects on fracture intensity.
The lithological association of competent layers with multiple thin incompetent layers (e.g., Layer C-1 and Layer S-1 in Fig. 10) is assigned a value of 1 because it is conducive to the development of fractures. The lithological association of competent layers between thick incompetent layers (e.g., Layer C-2 and Layer S-2 in Fig. 10) and the lithological association of interlayered competent conglomerate and sandstone layers (e.g., Layer C-3 and Layer N-1 in Fig. 10) are assigned a value of 2. The lithological association of competent conglomerate layers with limited sandstone lens is assigned a value of 3, because it is not favourable for the development of fractures. Then, a multiple linear regression equation for fracture intensity can be used: where, X, X n , � , X max and X min are the actual, normalised, average, maximum and minimum values for each parameter, respectively, I n is the normalised fracture intensity, P 1 to P 4 are the normalised influence factors on fracture intensity, of structural position (distance to the anticline hinge), bedding thickness, lithological association, and lithology (grain size), respectively, and c 1 to c 4 are the standardised regression coefficients of the four influence factors, respectively. Finally, the relative importance of each factor for controlling fracture intensity can be determined based on the standardised regression coefficient of each factor. The data of 53 scanlines reached the following multiple linear regression equation: Thus, this analysis confirms the qualitative observations that fracture intensity is mainly controlled by the structural position and is also moderately affected by bedding thickness and lithological associations, while the host rock's grain size has a very limited effect on fracture intensity.

Controlling factors of fracture length and aperture
Data displayed on Fig. 12A1 and A2 show positive correlations between fracture length and bedding thickness, for conglomerate and sandstone layers in the anticline crest and sandstone layers in the south limb of the anticline. Furthermore, fracture length is approximately equal to the bedding thickness in these cases. 26 On the other hand, in the north limb the fracture length of many conglomerate layers is larger than the bedding thickness, while some thick conglomerate layers present anomalous small fracture lengths (Fig. 12A2). These anomalous values correspond to the tabular conglomerate bodies in the northwest zone of the anticline. The limited outcrop size in this area can exert an important effect on the collected data of fracture length due to the so-called 'censoring bias' (Zeeb et al., 2013a).
The types of fracture intersections with bedding interfaces are significantly affected by their strength.
Fracture terminations are more likely to occur at very weak bedding interfaces between competent and incompetent layers, such as at interfaces between sandstone and clay, whereas strong bedding interfaces that put in contact competent layers favour fracture propagation across the interface (Cooke and Underwood, 2001).
In the crest, crest-limb transition zones and south limb, where interbedding of conglomerates or sandstones and clays are common in the medial fluvial fan, more fractures tend to abut at the weak bedding interfaces. In this case, the fracture length is limited by the bedding thickness when fractures are stratabound (Wennberg et al., 2006). In the north limb, the fine deposits are very sparse in the proximal fluvial fan, commonly resulting in strong contacts between adjacent conglomerate bodies or between conglomerates and sandstones. These relatively strong bedding interfaces in the proximal fluvial fan may promote the propagation of some long fractures but fewer facture population.
In addition, the fracture length may be structurally controlled and tend to be larger in higher strained zones to accommodate deformation during folding. For instance, Ghosh and Mitra (2009) calculated greater average fracture lengths in hinge zones compared to fold limbs. However, in the present case, the relatively higher strained crest corresponds to relatively higher fracture intensity but not larger fracture lengths. Besides, there is no clear correlation between the fracture length and intensity when other factors, i.e., structural position and lithology, are well constrained ( Fig. 12B1 and B2). Therefore, for the case study, the fracture length is not significantly affected by the structural position. In the Puig-reig anticline, fracture apertures are generally smaller than 2 mm, while relatively larger values are mainly concentrated in conglomerate layers (Fig. 5C). This indicates that the sedimentary and diagenetic characteristics of the host rocks are the main controlling factor in terms of apertures rather than their structural position. This observation differs from some previous studies that suggested that wide apertures may be expected in high-strain zones (Jamison, 1997), e.g., fracture apertures widen from the low-strain backlimb to the high-strain hinge (Iñigo et al., 2012). However, there is no clear correlation between fracture aperture and fracture intensity in this study (Fig. 13A), but we observe a subtle positive correlation between fracture aperture and length (Fig. 13B). This is consistent with other studies that reported that longer fractures tend to present wider apertures (Vermilye and Scholz, 1995;Olson, 2003;Ellis et al., 2012). We interpret this as an indication that these thick and massive conglomerate layers are not easily fractured, and thus strain tends to be accommodated by lengthening, widening and reopening of existing fractures rather than by developing new fractures, thus resulting in larger fracture length and aperture but lower fracture intensity. The large aperture and prevalent calcite veins in conglomerate bodies are discussed in section 5.2.

Fracture patterns in the Puig-reig anticline
Based on the above analysis, Fig. 14 shows a schematic diagram that summarises the main fracture patterns of the Puig-reig anticline (Fig. 14). The crest of the anticline, which is dominated by medial fluvial deposits

Rock fracturing and vein formation
Fractures can potentially act as conduits for fluid flow and as depositional sites for cement precipitation.
Therefore, fracture-filling cements are very useful to understand the conditions in which precipitation took place, including stress, strain, pressure, temperature, fluid composition and fluid origin during vein growth (Bons et al., 2012, and references therein). Structures and microstructures of calcite veins can be used to reveal fracture spatial and temporal distribution and even the fracturing and filling process in different structural positions and rock units (Gomez-Rivas et al., 2014). In the Puig-reig anticline, fractures are filled by four generations of calcite (Cc1 to Cc4) that formed veins (Fig. 8). Among these, the Cc1 and Cc2 veins are the dominant generations, which are closely related to fluid flow during the anticline growth (Cruset et al., 2016).
The clumped isotope thermometry data presented by these authors indicate that Cc1 and Cc2 precipitated from fluids at 92 • C to 129 • C and 77 • C to 93 • C, respectively. These temperatures are greater than the maximum temperature of 42 ºC reached by formation fluids during burial according to the maximum burial of 1.7 km and a geothermal gradient of 25ºC/km, indicating the input of hydrothermal external fluids. Besides, most Cc1 and Cc2 veins present a syntaxial microstructure with blocky calcite growing from the vein wall to the centre.
Syntaxial veins with strong growth competition, formed by crystal growth into fracture porosity, probably reveal advective transport of fluid along fractures and fracture networks (Bons et al., 2012). Thus, fractures acted both as conduits for fluid flow and as depositional sites for calcite precipitation in the Puig-reig anticline during fold growth. More samples and experimental data (e.g., geochemical data) are still required in order to carry out a more systematic in-depth study to reveal the origin of calcite cements and the temporal and spatial relationships between calcite cementation, fluid flow and fracture development. However, this is beyond the scope of the present study.
As discussed in section 5.1, the lower fracture intensity in the north limb is likely caused by its larger bedding thickness and lower strain compared to the crest, NTZ and STZ. When strain is high enough to cause brittle failure, fewer fractures develop in thick conglomerate bodies compared to sandstone layers. Besides, strain can also be accommodated by the cracking of clasts in conglomerates. Progressive stretching caused by folding can be accommodated by the propagation and/or re-opening and widening of previous fractures or by the formation of new ones (Watkins et al., 2015a). Strain accommodation by fracture propagation versus new fracture nucleation depends on the rock strength in a way that propagation rates decrease with increasing ductility (e.g., Gomez-Rivas et al., 2015). Moreover, layer rotation (e.g., due to folding), as well as mechanical anisotropy, can also reduce the fracture propagation rate (Gomez-Rivas and Griera, 2012). Eberhardt et al. (1999) found that longer grain boundaries and larger intergranular cracks, resulting from increasing grain size, 30 provide longer paths of weakness for growing cracks to propagate along. This in turn promotes a reduction of the rock strength once the longer cracks begin to coalesce and interact. The propagation, re-opening and widening of existing fractures and the formation of new ones can operate at the same time in all structural positions and lithofacies. However, we observe that it is difficult to form many new fractures to accommodate strain in the north limb due to the relatively lower strain in this structural position and the higher strength of these thick conglomerate bodies. Moreover, the existing fractures and veins in these thick conglomerate bodies act as weak parts compared to the host rock with high strength. Thus, the propagation, re-opening and widening of the existing fractures can accommodate strain when it is not strong enough to form many new fractures. As a result, the conglomerate bodies in the north limb present relatively larger fracture length and aperture but lower intensity (Fig. 5). Besides, the re-opening or widening of existing fractures can also be proved by the observed multi-episodic crack-seal structure ( Fig. 9A and B). Similarly, in the medial fluvial fan in the crest, NTZ and STZ, the channelised conglomerate bodies also present longer fractures with wider veins than those of sandstone layers.

Implications for reservoir potential
Fracture networks have a significant impact on reservoir performance. They can play a fundamental role in both controlling fluid migration and reservoir quality, especially in low-permeability and tight reservoirs in foreland fold-and-thrust belts (Casini et al., 2011;Wang et al., 2020). However, systematic fracture assessment in subsurface rocks is limited by the inability of sampling subseismic-scale fractures and large fractures that have much larger dimensions than that of the accessible rock volumes in boreholes (Ortega et al., 2006;Iñigo et al., 2012). Thus, a common strategy is to use outcrop analogues to extend sampling demonstrations, understand the controlling factors of fracture networks and reduce uncertainties in subsurface predictions (Sanderson, 2016;Miranda et al., 2018). In the Pug-reig anticline, the distribution of fracture networks is significantly affected by the structural position and the host rock sedimentary characteristics, including bedding thickness, lithology and lithological associations. Although many fractures are sealed by calcite cements, this anticline can still be used as a reservoir analogue to explore the fracture distribution pattern and reservoir potential in folded clastic sediments, especially in the research context that fracturing in siliciclastic thrust belts is much less well documented than that in carbonate ones (Watkins et al., 2015a). The fluvial deposits present very low matrix porosity due to prevailing calcite cements, generally ranging from 0 to 4%.
Among conglomerate and sandstone layers, only medium to coarse sandstones in the medial fluvial fan tend to present relatively high porosity (2.8% on average). Fracture intensity is mainly affected by structural position and sedimentary characteristics, with the relatively high values developing in the sandstone layers of 31 the medial fluvial fan in the crest, NTZ and STZ of the anticline. The results indicate that the channel filling sandstone deposits, especially in the high strain zones, present relatively higher potential to be effective reservoirs. Certainly, a more detailed and comprehensive study considering sedimentology, structural geology and diagenesis and further reservoir modelling are needed to apply the analogue study in the exploration of subsurface reservoirs.

Conclusions
The Puig-reig anticline, located in the south-eastern Pyrenean fold-and-thrust belt, is an excellent example of a folded fluvial depositional system, which exposes deposits of different sedimentary facies from the north to the south limb. A linear scanline method has been used to systematically collect fracture data, allowing the investigation of fracture distributions and their depositional and structural controlling factors. We reach the following conclusions: (1) Four main sets of fractures have been identified, i.e., the NNW-SSE, ENE-WSW, WNW-ESE and NNE-SSW sets.
(2) Fracture attributes are indeed strongly influenced both by their position within the fold and by the depositional characteristics of the sediments. Based on multiple linear regression analysis, fracture intensity is mainly controlled by the structural position, the bedding thickness and lithological associations, while grain size has a very limited effect on fracture intensity. Fracture length is mainly controlled by the bedding thickness and is affected by lithological associations. Fracture aperture is mainly controlled by lithology, with relatively larger values developed in conglomerate layers.
(3) Thick and massive conglomerate bodies can accommodate strain by the propagation and re-opening of existing fractures apart from the formation of new fractures during fold growth, especially in the proximal fluvial fan in the north limb where low strain is not high enough to promote the formation of a significant number of new fractures. Thus, compared to thin sandstone layers, these conglomerate bodies tend to present relatively low fracture intensity but large fracture length and aperture.
(4) The study of the Puig-reig anticline reveals the fracture pattern in a folded fluvial succession, which can provide an analogue for the prediction of subsurface fractured reservoirs with low matrix quality in fold-andthrust belts. 32