Fracture Kinematics and Holocene Stress Field at the Kraﬂa Rift, Northern Iceland

: In the Northern Volcanic Zone of Iceland, the geometry, kinematics and offset amount of the structures that form the active Kraﬂa Rift were studied. This rift is composed of a central volcano and a swarm of extension fractures, normal faults and eruptive ﬁssures, which were mapped and analysed through remote sensing and ﬁeld techniques. In three areas, across the northern, central and southern part of the rift, detailed measurements were collected by extensive ﬁeld surveys along the post-Late Glacial Maximum (LGM) extension fractures and normal faults, to reconstruct their strike, opening direction and dilation amount. The geometry and the distribution of all the studied structures suggest a northward propagation of the rift, and an interaction with the H ú sav í k–Flatey Fault. Although the opening direction at the extension fractures is mostly normal to the general N–S rift orientation (average value N99.5 ◦ E), a systematic occurrence of subordinate transcurrent components of motion is noticed. From the measured throw at each normal fault, the heave was calculated, and it was summed together with the net dilation measured at the extension fractures; this has allowed us to assess the stretch ratio of the rift, obtaining a value of 1.003 in the central sector, and 1.001 and 1.002 in the northern and southern part, respectively.


Introduction
The Northern Volcanic Zone (NVZ) of Iceland represents the emergence of the Mid-Atlantic Ridge and is composed of five parallel rift zones ( Figure 1) that are, from west to east, the Theistareykir, Krafla, Fremrinámar, Askja and Kverkfjöll rifts [1]. Although much research has been focused on the Krafla system [1][2][3][4], the most detailed studies on rift kinematics and geometry have been carried out at the Theistareykir rift [5][6][7][8][9][10]. These works show a complex pattern of kinematics with the presence of transcurrent components of motions that, in particular, become systematic in the northern section of the Theistareykir rift, the Theistareykir Fissure Swarm (ThFS), where a right-lateral component is observed. This has been suggested to be generated by a heterogeneous simple shear with a smoothly increasing strain gradient produced by the WNW-ESE Grimsey Lineament right-lateral shear zone (GRL in Figure 1b) [7]. Another important feature found at the ThFS is the greater development of normal faults and tension fractures north of its central volcano than in its southern portion. South of the central volcano, in fact, Holocene faults and tension fractures are less developed in terms of slip, length and number. This asymmetric development of the rift has been interpreted by Tibaldi et al. [6] as the effect of buttressing induced by another major volcano and its magma feeding system located just east of the southern ThFS, corresponding to the Krafla volcano [14] (Figure 1b), and by the fact that the Krafla rift approaches the ThFS southwards [15], thus contributing to an increase in buttressing induced by repeated dyke injection along the Krafla rift, or Krafla Fissure Swarm (KFS). Based on these observations, the study of the Theistareykir Fissure Swarm and of the Grimsey Lineament suggested that a rift termination can interact with a transversal shear zone, whereas the study of the asymmetric development of the ThFS suggested possible interactions with the KFS. These hypotheses are worth further investigation through an in-depth analysis of the architecture and kinematics of the KFS, which is a major, 100-km-long structure. Moreover, quantifying the spreading direction across a rift zone is of paramount importance for several practical applications, ranging from the assessment of seismic hazard [16] to the evaluation of factors that can contribute to magma uprising, and thus to the assessment of volcanic hazard [17]. However, the precise definition of the possible variation in the spreading direction along a rift requires the knowledge of a series of parameters that include the architecture of the rift, the geometry of each single fault and extension fracture, the timing of the rifting and the kinematics; needless to say, the quality of the collected data must be as good as possible. The most detailed reconstruction of the strain field can be achieved only by collecting a huge amount of horizontal dilation values. In view of the above, we set about analysing, with the greatest possible detail, the geometry and kinematics of the normal faults and extension fractures that characterize the Krafla rift. Here, we present the results of a survey conducted through remote sensing techniques along the whole rift, as well as field surveys in three areas located in the northern, central and southern part of the rift.
Our work on one hand is a contribution to a better understanding of this important seismogenic and volcanic rift, and on the other hand is of more general interest, as it allows for a better understanding of the processes that take place in regions under extension. Moreover, it sheds new light on the mechanisms of plate separation and enables investigating how rifts can interact. Furthermore, our study is of interest to understand the interaction of a transform fault with a rift and can contribute to increasing knowledge about oceanic ridges. The KFS is extremely suitable for such studies because (i) the region is almost unvegetated due to harsh climate conditions; (ii) deformation rates are high, of the order of 17-18 mm/year across the whole Northern Volcanic Zone [18,19]; and (iii) the rocks affected by faulting and fracturing mainly belong to recent deposits (Holocene-historic), so that the effects of erosion are not meaningful, and the structures show preserved features.

Geological and Tectonic Background
Iceland is a 300 × 500 km platform located in the Northern Atlantic Ocean, at the junction between the Kolbeinsey Ridge in the north and the Reykjanes Ridge in the south [20]. Its location makes it a unique site for geology, since it is situated both along a divergent plate boundary (between the Eurasian and American plates) and on top of a hotspot [21]. From a geological point of view, Iceland is characterized by the widespread presence of Neogene and Pleistocene basalts, bordering the active rift systems that cut through the island from SW to NNE. Such active rifts are made of swarms of faults, extension fractures and basaltic volcanoes, and are marked by the occurrence of eruptions, representing the surface expression of the mid-ocean ridge [20]. Their formation is due to plate-pull associated with mid-oceanic ridge activity and magma upwelling. Thus, Iceland is the result of the combination of hot spot and mid-ocean ridge magmatism [21][22][23][24]. Nowadays, there are 30, presently active, 40-150 km long and 5-20 km wide volcanic systems, all hosting a central volcanic edifice [20]. The spreading direction, holding the North America Plate fixed, is given with a plate velocity vector of 18.2 mm/year in a direction of 105 • for Central Iceland [21]. This spreading process, in the northern part of the island, is accommodated by the NVZ, the northern part of which joins with the offshore Tjörnes Fracture Zone. This is made of three WNW-oriented transform areas: the Húsavík transform fault (or the Húsavík-Flatey Fault, HFF), the Grímsey oblique rift (or Grimsey Lineament, GRL) and the Dalvík zone [21,[25][26][27][28]. The center of the Icelandic hotspot is situated in the southern sector of the NVZ [29]. As mentioned above, the NVZ consists of five volcanic systems, which are volcano-tectonic rift zones [1,30] (Figure 1) composed of swarms of normal faults, extension fractures and eruptive fissures, as well as a main central volcano [25]. The trend of the 5-20 km-wide and 60-100 km-long rift zones is N-S to NNE-SSW. The KFS is the second westernmost rift of the NVZ, and is made of the Krafla active central volcano, normal faults and extension fractures, as well as numerous eruptive fissures that stretch north and south of the volcano. These structures cut Pleistocene and, mostly, post-Late Glacial Maximum (LGM) deposits emplaced since~12,000 years BP [31]. All structures are mostly N to NNE oriented and have been the site of volcano-tectonic deformation for the last 100 ka [1,13,14,32,33]. The Krafla central volcano is marked by a major caldera (about 8 km wide) that is thought to have formed during a large ignimbrite-forming eruption about 110 ka ago [33,34]. After caldera formation, it has widened about 2 km in an E-W direction as a consequence of plate spreading [33]. Although the Krafla volcano is mainly basaltic, silicic deposits can be found near the caldera [33,35]. Below the volcano, a magma chamber of irregular form is located: its top lies at a depth of 3 km and its bottom is situated above 7 km depth [36]. Ground deformation [37] and geochemical data [38] suggest that, below this main magma chamber, deeper magma reservoirs may occur.
Within the NVZ, major rifting episodes were observed, respectively, in 1618 at the ThFS, in 1724-1729 at the KFS and in 1874-1876 at the Askja volcanic system [39]. In 2014, a dyke intrusion from the Bárðarbunga volcano migrated northward, affecting the NVZ [40,41]. One of the most recent rifting activity in the NVZ has taken place within the KFS and its central volcano. Two rifting episodes have occurred here in the last 1140 years: the 1724-1729 "Mývatn fires episode" and the instrumentally recorded 1975-1984 Krafla rifting episode. During both episodes, intense earthquake activity and fault displacements (often with graben subsidence) took place within the fissure swarm. Rifting processes were accompanied by fissure eruptions [33,42]. The volcano-tectonic processes that took place in the KFS from 1975 to 1984 [39,43,44] were marked by about 20 rifting events and nine lava eruptions. During each rifting event, magma escaped from the chamber below the Krafla volcano and intruded in the form of dykes [45]. These typically propagated to the surface in the caldera area and to a depth of about 3 km at the northernmost end of the KFS [46]. During these events, rapid subsidence within the Krafla volcano was instrumentally documented, followed by earthquake swarms directed away from the caldera and into the fissure swarm. All the above was associated with graben subsidence in the respective section of the fissure swarm and sometimes with eruptions near the caldera. [43,47]. Although the 2-cm-yr spreading rate proceeds in a constant manner [48], the spreading that is observed at individual fissure swarms, such as the KFS, is episodic [49,50]. This is because the fractures within the fissure swarms are mainly activated during rifting episodes, when dykes intrude along fissure swarms, often triggering fissure eruptions [49,51].
With regard to the spreading direction in the whole NVZ, Drouin et al. [18] measured a value of N112 • E, for a limited time window of 4 years and based only on GPS data. Two other works, on the basis of GPS data and focusing on the 1997-2011 and 2006-2010 time intervals, provide values of N109 • E and N115 • E, respectively, for the northern part of the NVZ [52,53]. On the other hand, researchers that considered also geological data provided lower values for the Icelandic spreading direction, such as De Mets et al. [48], who provided a value of N104 • E for the whole Iceland considering both GPS and geological data. From the plate velocity model of [48], Hjartardóttir et al. [13] calculated a value of N106 • E for the NVZ. Finally, Bonali et al. [9,10,54] proposed a N103-108 • E range, after completing an extensive UAV-based survey and conducting a major data collection campaign within Holocene units at the ThFS, located immediately west of the KFS.

Remote Sensing
Our work has been mainly focused on updating and classifying a major fracture set provided by Hjartardottir et al. [1], where all fractures were mapped using digitalised aerial photographs, without distinction between faults and extension fractures. We used aerial photos, satellite images and field surveys to assess the categories of brittle structures and define their geometry and kinematics. Aerial photos were obtained from Loftmyndir Inc. (Reykjavík, Iceland), with a resolution of 0.5-1 m/pixel, compared with aerial photos from Samsýn Inc. (0.5 m/pixel) and satellite images from the US/Japan ASTER project (15 m/pixel). All the considered aerial photographs were more recent than the latest Krafla event (1975)(1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984).
In order to analyse the rift architecture, we considered structures affecting both Post-LGM and Pre-LGM/LGM units as a unique dataset, because available information does not allow to assess which structures in the older units have been active also in the Holocene: such a classification would require a more detailed and extensive field survey on each single fracture, as demonstrated by Tibaldi et al. [55], who observed active fractures affecting a LGM hyaloclastite in the NW sector of the KFS. All the fractures have been classified as extension fractures, normal faults, eruptive fissures and caldera faults, also considering the geological map of the NVZ at a 1:100,000 scale [31]. To perform the classification, we used the above-cited materials, also with the aid of satellite images, the 30-m JAXA AW3D Digital Elevation Model and the shaded view of the high-resolution DSM from Loftmyndir Inc (https://www.map.is/base/ (accessed on 15 January 2021)). Normal faults were recognized and distinguished from extension fractures thanks to the presence on the DSM and on aerial photos of the shaded or better-lit slopes, which allowed also to distinguish between the E-dipping and W-dipping faults, respectively (Figure 2a,b). Extension fractures, instead, are expected to form by normal stress or fluid pressures and to open in a direction parallel to the minimum compressive principal stress (that is tensile near the surface), without any clear evidence of the shear components. Normal faults are excluded from this definition [56]; in fact, extension fractures do not show any well-lit slope or vertical offset.
In some cases, the presence of eruptive fissures could be directly identified on highresolution aerial photos thanks to the recognition of volcanic deposits emplaced along the same fractures, whereas in other cases they were traced based on some morphometric parameters of related eruptive centres: the elongation of the cone base, the elongation of the crater and the alignment of cones were considered parallel to the strike of the feeding fracture, as summarised in Tibaldi and Bonali [57]. Finally, caldera faults were recognized on aerial photos with the aid of the DSM and the geological map, and were not considered in the detailed analysis of the present work.

Field Data Collection
In addition to the overall mapping and classification of all the structures in the KFS, three areas of the rift were surveyed in the field to a greater detail, so as to collect structural measurements along both the extension fractures and normal faults (Figure 2c,d). Structures were classified as normal faults when they showed a continuous vertical offset >0.50 m, whereas they were considered extension fractures when they were characterized by a vertical component <0.50 m, including both structures with a pure extensional opening and those with a lateral component.
At the extension fractures, we collected the local azimuth, amount of opening and opening direction where piercing points were detectable. In total, we collected 4086 measurements from a total of 1362 structural stations where piercing points were detectable, and 556 azimuth and dilation measurements from 278 sites, where piercing points were not visible. The net direction and amount of opening were quantified by measuring, respectively, the strike and the length of the line connecting the two piercing points (Figure 2c). Wherever piercing points were not observable, we measured the dilation amount orthog-onally to the extension fracture walls. In order to measure the dilation amount, we used a tape or a laser rangefinder. To avoid the effect of erosion and gravity, we measured the dilation amount in the lower portions of the fractures, and only where fracture walls were clearly visible. In fact, sedimentation, erosion and weathering can cause a widening of the fracture on the surface, leading to possible overestimation of the amount of opening [10]. Along normal faults, we collected a total of 653 vertical offset values at intervals of 50 m. Where the scarps were in the order of meters, we used a tape or a laser rangefinder, whereas in the case of higher scarps, we used GPS measurements, calculating the difference in elevation between the two blocks.

Data Analysis
The azimuth and length of each mapped structure were calculated in a GIS environment (ArcMap v.10.6), together with the X and Y coordinates of the mean point, enabling to correlate these parameters and to analyse their possible variations in space. Moreover, we counted the number of structures along 97, N106 • E-striking transects, each spaced 1 km in a N-S direction, to quantify the structure density variation along the rift. Along each transect, we also measured the rift width, considering the distance between the easternmost and the westernmost structure, and the average spacing. These analyses were carried out considering all types of structures at first, and then distinguishing between all the subsets (extension fractures, normal faults and eruptive fissures).
In the three field surveyed areas, we analysed all the collected data to check whether the different measured parameters showed correlations or spatial variations. Starting from the local azimuth and the opening direction values, it was possible to calculate the lateral component of motion present in each structural site, to include this parameter in the analysis. Finally, we cumulated the dilation values along three transects, one for each area, striking N106 • E, considering both extension fractures and normal faults, to calculate and compare the stretch values in three different sectors of the rift and with other rift zones in Iceland.

Fracture Geometry
In the KFS, a total of 20,483 structures were recognized and classified as normal faults (8353-40.8%), extension fractures (11,807-57.6%) and eruptive fissures (296-1.5%) (Figure 3a). Of the remaining 27 structures, 8 were identified as caldera rim faults, whereas the very few remaining fractures were not classified, due to uncertainty on the available DEM and aerial photos.   Furthermore, strike and length values were related to the UTM X and Y coordinates (WGS84-UTM zone 28N). At a general level, by considering the whole set of fractures (Figure 4a), it is possible to observe that data distribution covers an about 100-km-long area, and that in the northern part of the rift, the azimuth values present a greater range than in the southern part, except for its southernmost part, which seems to be represented by extension fractures (Figure 4b). Additionally, it can be noticed that this range abruptly changes north of the Y coordinate 7,290,000, corresponding to the central caldera. This observation is also confirmed for the extension fractures set ( Figure 4b In Figures 6 and 7, the strike and length, respectively, of the fractures and faults were related to the X coordinates (WGS84-UTM zone 28N). Regarding the strike values, considering the whole set of fractures (Figure 6a), the range is greater in the central part, near the X coordinate value 420,000, also corresponding to the Krafla caldera longitude, and decreases moving towards E and W to values included between NW and NE; towards the W, the decrease is more evident. Values between NNW and NNE are generally always represented. Such a pattern also can be noticed for the extension fractures and normal faults subsets (Figure 6b   In Figure 8, the strike and length of all the datasets were related, showing that the greatest lengths are associated with the N-S-oriented fractures, with strikes between N0 and 10 • E (Figure 8a). Generally, longer structures (all sets) are in the N-NE range; the longest are mainly represented by normal faults and eruptive fissures with a similar relation between the azimuth and length as observed above (Figure 8c,d). The extension fracture set shows a similar pattern but with a shorter length (Figure 8b).

Fracture Density and Spacing
In order to detect fracture density variation, we traced 97 transects, striking N106 • E, spaced 1 km from each other and parallel to the average spreading direction of the region [13]. Along each transect, we counted the number of intersecting fractures, first considering them all (Figure 9), then distinguishing between extension fractures (Figure 10), normal faults ( Figure 11) and eruptive fissures ( Figure 12). For each dataset we also measured the width of the fractured area, namely, the distance between the easternmost and the westernmost structure intersecting each transect, and the average spacing. The latter was calculated with the ratio width/number of structures, considering both the rift width ( Figure 9c) and the width of the fractured area obtained considering only a specific type of structure. In Figure 10c (Figure 11f,g).
Finally, eruptive fissures can be observed only in the central part of the rift, between transects 31 and 77, whereas they disappear moving away from Krafla volcano (Figure 12b). The number of eruptive fissures reaches a maximum (5) in the proximity of the caldera, at transects 44 and 49, and decreases going northward and southward. The same pattern can be observed considering the width of the fractured area, whose maximum is reached in the caldera, at transect 49, with a value of 6 km; however, except for this transect, the width is always less than 4.1 km (Figure 12c). The average spacing considering the whole dataset of structures reaches a value up to 17.7 km at transect 57, due to the limited number of eruptive fissures if compared to the extension fractures and normal faults in the rift (Figure 12d). On the contrary, considering just the eruptive fissure dataset, the average spacing shows a maximum value of 2.05 km at transect 58, with a decrease going northward and southward (Figure 12e).

Fracture Kinematics and Dilation
In the field, we collected data of the extension fracture local strike, opening direction and amount of opening at 1362 different sites (Figure 13a), for a total of 4086 structural measurements along fractures affecting the Post-LGM units. Such sites are mainly located in three areas, two of which north of the caldera and one south of it (Figure 13b-d). It is worth noting that, in 278 sites where the opening direction was not recognizable, we collected only the strike and dilation amount of the extension fractures, reaching a total of 4642 structural measurements at 1640 different sites. Along the normal faults, we collected 653 vertical offset values in order to estimate the stretch over the three areas. Opening direction values present a wide range, between N39 • and 148 • E, with an average value of N99.5 • E (SD 14.8 • ) (Figure 13a). In the northern area, the opening directions have a range between N48.5 • and 148.5 • E, with an average of N103.2 • E and a SD of 15.7 • (Figure 13e). In the sector situated north of the caldera, the range is the greatest (N39 • -148 • E), with an average of N98.7 • E and a SD of 14.7 • (Figure 13f). Finally, in the southern sector, values are comprised between N78.5 • and 138.5 • E, with an average of N107.7 • E and a SD of 12.4 • (Figure 13g). In Figure 14a, we show the relation between the opening direction and northing: the greatest range is in correspondence with the sector located north of the caldera, whereas in the northern part of the rift and south of the caldera, it decreases. In the southern part, we can observe a clockwise rotation of the opening direction values going northward, towards the central caldera. Regarding easting, we notice that the range of values is greatest in the central part of the rift, decreasing towards the E and W (Figure 14c).  As far as net dilation is concerned, we found a maximum value of 5.9 m, with an average of 0.7 m (SD 0.5 m). With respect to northing, the greatest values are in the central sector, and in the northern part of the rift we notice greater values than in the southern sector (Figure 14b). In the E-W direction, the maximum values are reached at the centre of the rift, decreasing going towards its sides (Figure 14d). Dilation values tend to be greater for the opening direction values between N90 • and 113 • E (Figure 15b).  Figure 13a). We have related these values to the opening directions, showing that a clockwise rotation of the latter corresponds to an overall clockwise rotation of local strike (Figure 15a). Considering the average values of the opening direction and fracture strike in the rift, we thus obtained an overall small right-lateral component of motion of 1.5 • (Figure 13a). Actually, we have analysed the results more in detail, distinguishing between pure extension fractures (when the local lateral component was <5 • ) and fractures with a lateral (right or left) component of motion (when the local lateral component was >5 • ), finding out that 453 fractures are characterized by pure extension, whereas 497 fractures have a right-lateral component and 412 a left lateral component (Figure 15c,d). Right-lateral component values reach a maximum of 81 • , while left-lateral ones have a maximum of 65 • (Figure 15c,d). With a clockwise rotation of the fracture strike, lateral components tend to switch from right-lateral to leftlateral (Figure 15c), whereas with a clockwise rotation of the opening directions the lateral component behaviour is the opposite (Figure 15d).
Finally, in order to measure the stretch along the rift, we traced three transects, one for each area, oriented in the overall regional spreading direction (N106 • E) [13] (Figure 13b-d). Along these transects, the dilation values were added up, considering both extension fractures and normal faults: at the extension fractures, we measured dilation as explained in the methodology section, whereas at normal faults, we calculated the heave starting from the measured vertical offset, considering a fault dip of 75 • . All transects have a length of 9.75 km, and the resulting cumulative dilation is 13.87 m in the northern area, 27.50 m in the central area and 14.70 m south of the caldera. Considering these resulting values, we thus obtained a stretch of 1.0014 in the north, 1.0028 in the central part and 1.0015 in the southern sector.

Rift Architecture
We have performed an in-depth reconstruction of the architecture of the KFS through the detailed mapping of all its structures, as well as an assessment of their geometry, distribution and kinematics; we have also distinguished between extension fractures, normal faults and eruptive fissures. This represents an outstanding result, especially considering the width of the KFS, which extends onshore for a length of 97 km and reaches a maximum width of 17.9 km south of the central caldera (Figure 9c). Moreover, we have quantified the strike and length of all KFS structures: normal faults are longer than extension fractures, suggesting that, along the rift, the latter might represent an earlier stage of evolution before developing into faults. This has also been observed in the field, where some normal faults turn into extension fractures at their tips. On the other hand, normal faults can further develop by propagating both vertically and laterally through linkage and nucleation, and this has the effect of increasing their vertical offset and length [58,59]. Regarding the relation between the length and orientation of structures, it is worth highlighting that all structures with a N-S and NNE-SSW orientation have greater lengths (Figure 8): being perpendicular to the regional spreading direction (N106 • E) [13], the development of these structures is facilitated by regional tectonics, more so than for those with different orientations.
Considering the distribution of normal faults vs. extension fractures, our data show that the former are prevalent in the southern part of the rift, whereas the latter dominate in its northernmost sector (Figures 10b and 11b). This distribution of the structures has also been observed at the adjacent ThFS [7,9], suggesting a northward propagation of both rifts, as observed also by Saemundsson [60]; in fact, normal faults show a clear decrease in length and frequency moving northward (Figure 5c). Considering all the above, it can be argued that the northernmost sector represents an earlier stage of rift formation, where faults still have not fully developed. Regarding structure distribution, it is worth highlighting that, within transects 35-52, the decrease in fracture frequency can be influenced by the presence of historic lava flows (<870 AD [31]), covering the older fractures and causing an underestimation of the result. This occurs also south of the central volcano, within transects 58-72, where historical and prehistorical lavas (<2.9 ka BP [31]) crop out.
Eruptive fissures are only found within a distance of 20 km north of the central volcano, and 30 km south of it, whereas they disappear further north or south (Figure 12b). This can be interpreted as a consequence of the lateral shallow propagation of dykes from the central volcano, which tend to deepen with distance [46], inducing surface deformation represented mainly by dry extension fractures. This is coherent with other volcanic systems in Iceland (e.g., the Askja Fissure Swarm) [61], and also with the observations made during historic rifting episodes, when eruptive fissures were detected at the surface in the first 6-7 km from the central volcano, whereas extension fractures were observed as far away as tens of kilometres [14,47]. Eruptive fissures further away can also be explained by lateral feeding, as had occurred in the Holuhraun eruption in 2014, where the event started with a dyke propagating from the Bárðarbunga central volcano and reaching the surface when the seismicity reached north of the Vatnajökull glacier, triggering the eruption when the dyke was about 48 km long [62].
The propagation of eruptive fissures at a greater distance south of the central volcano than in the northern part of the rift might just be a coincidence, or it may be explained by the presence of an additional deep magmatic source in this region, as suggested by Saemundsson [33]. Supporting this hypothesis, chemical analyses by Jónasson [63] have shown that all the eruptive fissures situated in the south-eastern sector of the rift are part of the Heiðarsporður volcanic system, already considered as a separate volcanic system by Saemundsson [25], together with the Bláfjall ridge more to the south; this additional magma source could also influence the width of the rift, and would help explain its widening, as observed in the southernmost sector, where the Bláfjall ridge is located (Figures 9c and 13a). The greater width in this sector could be explained also by the presence of Pre-LGM units affected by fractures (the age of the units is from Saemundsson et al. [31]; Figure 16a); they could have simply recorded a longer time of extensional deformation and, eventually, moved apart by rifting events. This southernmost sector is affected mostly by normal faults (Figure 16b) and extension fractures (Figure 16c), whereas eruptive fissures are not present (Figure 16d). Furthermore, Pre-LGM/LGM units crop out also in correspondence of the caldera, in the central part of the rift, where another increase in rift width can be observed (Figure 16a). Fractures affecting the Pre-LGM units seem, in general, longer than those affecting the Post-LGM units: this can be simply due to the fact that older faults had more time to develop and thus became longer.
The extension fractures peak observed at transect 34 mentioned above, characterized by a decrease in the number of normal faults, is situated at the intersection with the HFF prolongation, as observed also by Hjartardottir et al. [1]. This feature has also been noted in the ThFS by Tibaldi et al. [5,8] and Bonali et al. [9], who suggested the prolongation of the HFF as a buried fault further to the south-east. The hypothesis made on the continuation of the HFF as far as the KFS, which is also suggested by Hjartardottir et al. [13], is based on three observations: (i) the migration of earthquakes along the HFF that was observed for a few hours during the dyke intrusion of January 1978 in the KFS; (ii) the widening of the KFS central graben; and (iii) the increase in fracture density at the intersection between the KFS and the HFF prolongation, as also confirmed by our work. The different propagation pattern of eruptive fissures north and south from the central volcano could have been influenced by the presence of the HFF as well, which may reduce their northward propagation. Moreover, we observed a greater range in the azimuth values for both the extension fractures and normal faults where the HFF prolongation intersects the KFS (Figure 4a-c), with more structures oriented NNW-SSE and NW-SE, if compared to what is observed in the other sectors of the rift. This is another similarity with the ThFS, where the presence of the HFF is considered as responsible for the anti-clockwise rotation of structures [7,64], and of a greater range of azimuth values within a distance of 500 m from the HFF [5].
The range of structure strike increases in the southernmost part of the rift: this can be linked to the presence of a WNW-oriented belt acting as a transform zone, as interpreted by Hjartardottir et al. [1]. In fact, these authors observed the presence of several WNWoriented fractures in the southernmost part of the KFS; this fracture system extends to the northernmost sector of the Kverkfjoll Fissure Swarm, thus forming a WNW-oriented belt across the NVZ. Due to its geometry, crossing the southernmost part of the KFS and the northernmost part of the Kverkfjoll Fissure Swarm, this belt has been interpreted as a transfer zone, which shifts the spreading of the NVZ westward. On the other hand, from east to west, the greater range of fracture strikes is observed along the axial part of the rift (Figure 6), thus suggesting a greater structural complexity than in the lateral sector, where deformation is more coherent with regional tectonics.

Rift Extension Rate
The cumulative dilation and stretch values were quantified in the northernmost part of the rift and just north and south of the caldera structure, passing through Holocene units (Figure 13b-d). The greatest total dilation value, which is 27.5 m, is reached in the central area, a few kilometres north of the caldera, where the most recent lava flows could have hidden some fractures, causing an underestimation of the resulting value. This value is very similar to the one calculated by Dauteuil et al. [65], who estimated a total extension of 30 m just north of the 1984 Krafla lava flow. Moving to the northernmost part of the rift and just south of the caldera, according to our data the total dilation value is about 14 m.
Furthermore, the stretch ratio that we calculated for the same area, 1.003, is in the same order of magnitude of Dauteuil et al. [65], who obtained a stretch ratio of 1.009. To the north and to the south, stretch values are about 1.001 and 1.002, respectively. A higher value than 1.003 has been calculated in the KFS in a previous research by Bonali et al. [4], but since this value takes into account also older units, it cannot be considered for comparison; the same goes for the stretch value of 1.036-1.046 from Paquet et al. [66], which has been calculated across the Tertiary Alftafjördur dyke swarm, thus describing a deformation that lasted at least 1 Ma. We suggest that the stretch value calculated in the present work, and by Dauteuil et al. [65], can be representative of tectonic and magma forces working together, also considering that in the central area of the rift some eruptive fissures are present. Assuming an age of 11.5 ± 0.5 ka BP for the post-LGM lava units [31], we obtained an extension rate of 2.4 ± 0.7 mm/yr in the central area, and 1.2 ± 0.7 mm/yr in the northern part. Regarding the southern area, it is mostly affected by younger lava flows, which have covered faults and fractures. Our transect is the only one that intersects old-enough lavas to possibly provide a meaningful result, as it crosses through three small lava units of uncertain ages. The results from the southern profile are therefore more uncertain than the profiles north of Krafla.
All these rates are much slower than the GPS velocity field measured after the 1975-1984 rifting/dyking period (3-4.5 cm/yr) [45], suggesting, in agreement with Bonali et al. [4], that the latter values are not representative for the long-term deformation field of the KFS. From another point of view, our values represent a fraction of the extension of the whole NVZ, which corresponds to 1.8-2.3 cm/yr [48,67].

Rift Kinematics and Spreading Direction
Focusing on the kinematics of extension fractures, the collected data suggest an overall average (av.) spreading direction of N99.5 • E and a SD of 14 [52,53]. Our spreading directions in the northern and southern area are closer to the values that take into account geological data covering a larger time window, such as those of Hjartardóttir et al. [13] (N106 • E) and of DeMets et al. [48] (N104 • E), although the latter refer to the whole Iceland, whereas they are instead slightly rotated anti-clockwise with respect to spreading directions based only on GPS data [18,52,53]. Furthermore, our data indicate a more pronounced anti-clockwise rotation of the spreading direction just north of the caldera border and the central volcano, where eruptive fissures are present and where shallow dyking is reported in the literature [55].
The overall fracture strike is suggested to be orthogonal to the spreading vector range discussed in the above section; in fact, longer and thus more developed fractures (in terms of extension fractures and normal faults) and eruptive fissures show an azimuth between N-S and NNE-SSW (Figure 8), confirming the observation made by Hjartardóttir et al. [13]. Furthermore, we investigated the presence of strike-slip components of motion along the extension fractures, with a predominance of right-lateral with respect to leftlateral components of motion, which is coherent with what has been observed in the neighbouring ThFS, where 854 fractures (52%) out of 1633 were characterized by a rightlateral component [7]. Another similarity with the ThFS pertains to the relation with opening directions; in fact, also in the ThFS, a shift from the left-lateral to right-lateral components has been observed alongside a clockwise rotation of the opening direction values [7]. Recent research efforts support the hypothesis that such lateral components can be induced by local perturbations exerted by dyking at shallow depths, as shown for the 2014-2015 Bárðarbunga dyking event [68], and as suggested in the ThFS [7][8][9][10] and by field data by Bonali et al. [4] in the KFS. Furthermore, as suggested by Einarsson and Brandsdóttir [15], magma was injected during the July 1978 event at a total distance of 30 km from the caldera into the northern fracture swarm through lateral dyke propagation. Other dykes propagated even further into the fissure swarm, such as in January 1976 (60 km) and January 1978 (45 km) [14,69].

General Considerations
The approach used in the present work, based on a detailed survey of all the structures of a rift and their differentiation as normal faults, extension fractures and volcanic fissures, was proven effective in assessing the possible propagation direction of a rift. This result is based on an evaluation of the frequency of faults vs. extension fractures, assuming that the latter might develop earlier than the former [3]. This approach can be applied as an alternative to the evaluation of rift propagation based on the reconstruction of fault slip profiles. This considers that single faults develop in the direction where their slip profile tapers out [70]. Both methods have been tested at the ThFS rift [6,8], giving the same result of a preferential northward-directed rift propagation. However, we believe that, on one hand, the slip profile methodology is very time consuming, as it implies the continuous measurement of the offset along each fault for all the structures of a rift, but on the other hand it allows for a better definition of the propagation direction of single structures within the general trend of a rift. At the ThFS, in fact, it was documented that single faults can develop outward from the central volcano, suggesting that they might be related to the outward propagation of dykes from the magma chamber [8]. This double outward propagation of faults has been observed also at the Ado'Ale volcano, located in the Ethiopian Rift [71], implying that this model can be of wider relevance. We thus suggest that, in the future, an analysis of fault slip profiles at the Krafla rift should be carried out, in order to assess if, also at this rift, faults are propagating outward from the central volcano.
The finding of a preferential northward-directed development of both the ThFS and the Krafla rift is relevant for the evaluation of the geodynamics of northern Iceland, as it might suggest that the whole North Volcanic Zone is propagating in that direction. This is important also at the local scale, because it hints at the possibility that new fractures may preferentially develop in the northern part of the rifts, or existing fractures may lengthen northward.
With regard to the dilation amount and dilation directions, the differences between our data, which pertain to the Holocene time span and GPS-based ones [18,52,53], which are related to much shorter time intervals, in the order of years, highlight how much a deformation field can be perturbed as a consequence of a transient event. The Krafla rift, in fact, has been affected by a major intrusive episode, which happened between 1975 and 1984, known as the "Krafla Fires", during which around 20 dykes were injected along the rift [44]. We thus assume that caution should be exerted when using GPS data for geodynamic studies in rift zones where recent dyking has taken place. A more reliable assessment of dilation direction and amount should instead be derived from data related to Holocene structures, which bear information over a longer time span. Similarly, attention should be paid to the presence of huge volcano edifices or calderas; our data show that the dilation amount and rift spreading direction change in correspondence to the Krafla caldera system, with rotation of the dilation direction also in the order of ten degrees.
Finally, the discovery of transcurrent components of motion along the fractures of the Krafla rift increases awareness of this phenomenon. This has been partly explained as induced by the obliquity of some fractures in comparison with the regional tectonic stress field, but in part it is independent from this process. Recently, some authors have suggested that transcurrent components of slip at volcanotectonic rifts may derive from the lateral (horizontal) propagation of magma along dykes [55,62,68,72]. The presence of strike-slip components at the fractures of the Krafla rift, which are supposed to be linked to shallow dyke injection, shed further light on the frequent occurrence of this process.

Conclusions
We have studied the geometry, kinematics and offset amount of the structures that form the active, N-S-trending KFS, mapping and analysing all the extension fractures, normal faults and eruptive fissures of the rift by remote sensing and field survey. Furthermore, in three areas distributed in the northern, central and southern part of the rift, we have collected detailed structural measurements through extensive field surveys along the post-LGM extension fractures and normal faults, obtaining the following conclusions: (1) Regarding structure geometry, normal faults are longer than extension fractures. This suggests that, along the rift, extension fractures might represent an earlier stage of evolution before developing into faults. Normal faults are prevalent in the southern part of the rift, whereas extension fractures dominate in the northernmost sector.
This structure distribution has also been observed at the adjacent ThFS, suggesting a northward propagation of both rifts; in fact, normal faults show a clear decrease in length and frequency going northward. Structures with N-S and NNE-SSW orientations are longer: being perpendicular to the regional spreading direction (N106 • E), their development is facilitated by regional tectonics, more so than for those with different orientations. (2) Eruptive fissures are present only within a distance of 20 km north of the Krafla volcano, and 30 km south of it. This can be interpreted as a consequence of the lateral shallow propagation of dykes from the central volcano, which tend to deepen with distance, causing surface deformation represented mainly by dry extension fractures. Funding: This study was conducted in the framework of the International Lithosphere Program-Task Force II (Leader A. Tibaldi).

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.