Frictional melting significantly affects magnetic properties of fault rocks. The newly crystallized mineral assemblage of pseudotachylytes is distinctly different from that of its host rock (Ferré et al., 2012). The rapid quenching leads to a remanent magnetization, which is acquired coseismically but sometimes contains post-seismic superimposed magnetizations, and hence impacts interpretation of paleomagnetism (Ferré et al., 2014; Fukuchi, 2003). Anisotropy of magnetic susceptibility of pseudotachylytes may also record information about the viscous flow of the friction melt (Ferré et al., 2015; Scott and Spray, 1999). Comparison of fault plane geometry and orientation with the magnetic fabric and petrofabric has been used to deduce earthquake kinematics and focal mechanism (Ferré et al., 2015).

The magnetic fabric of a rock is defined by its anisotropy of magnetic susceptibility (AMS), which in turn reflects the sum of individual magnetic responses of the rock-forming minerals (Borradaile, 1987). To use magnetic fabrics for inferring flow direction and sense, the carriers of rock magnetism must be known (Cañón-Tapia and Castro, 2004). In general, minerals respond in three fundamental ways to applied magnetic fields: diamagnetic, paramagnetic or ferromagnetic sensu lato (Butler, 1992; Tauxe, 2010). Depending on which of these behaviors is dominant in a rock specimen, AMS needs to be interpreted in different ways. Low susceptibility of diamagnetic minerals generally makes them subordinate contributors to the bulk rock AMS (Hirt and Almqvist, 2012, and references therein). Most rock-forming minerals are paramagnetic, for which AMS is foremost controlled by crystallography. AMS in paramagnetically dominated rocks reflects the crystallographic preferred orientations of these minerals (Hirt and Almqvist, 2012). However, pseudotachylytes have been shown to contain authigenic magnetite produced during frictional melting (Nakamura et al., 2002). For ferromagnetic minerals, AMS is mainly controlled by grain shape and orientation distribution, with the most notable exception of hematite (Borradaile and Jackson, 2010). With few exceptions, paramagnetic and ferromagnetic minerals express normal AMS fabrics. In such fabrics, the longest grain dimensions coincide with the maximum principal AMS axes (Tarling and Hrouda, 1993). For these cases, the flow direction can be deduced from the magnetic lineation (e.g., Ernst and Baragar, 1992).

An oriented sample of a foliation-parallel fault vein with host rock on either side was collected in the field (sample AB15, schistosity 341/30, mineral lineation LAB15 269/07; Figs. 2 and 3). The hand specimen was cut with a diamond saw into 5 to 10 mm thick slabs parallel to the lineation and perpendicular to the foliation. A thin section was prepared from one of these slabs. The rest of the slabs were cut into lineation-parallel sticks of approximately equal width and height. From these, 116 cube-shaped specimens were cut for magnetic experiments; x axes of the cubes are parallel to Lhr and z axes are perpendicular to Shr. Due to the small spatial distribution of host or fault rock, specimen cubes are unconventionally small (side length 5.3±1.2 mm, volume 0.17±0.13 cm3; uncertainty levels here and throughout the article are 1σ) compared to standard-sized specimens (7 to 11 cm3) used in paleomagnetism (Table S1 in the Supplement). Therefore, the shape and size of cube dimensions were compared to properties of the AMS ellipsoid and uncertainties related to the cube dimension were also investigated. Despite expending particular care to avoid cutting specimens with different types of host or fault rock, specimens with mixed rock types occur. Approximate modal proportions for each rock type per specimen are presented in Table S2 in the Supplement.

Obliquity between shear plane and magnetic fabric may be used to determine the sense of slip. Progressive shearing rotates maximum and intermediate principal axes of strain and AMS toward the shear plane (Borradaile and Henry, 1997). Kinematics are indicated in a plane perpendicular to the shear plane (i.e., fault vein margins) that contains the minimum and maximum AMS axes (cf. Fig. 26 in Borradaile and Henry, 1997, and Fig. 3 in Ferré et al., 2015). In this case, magnetic foliations are inclined toward the slip direction, which gives the sense of shear.

Calcareous amphibole–biotite micaschist hosts the fault veins. Large biotite crystals are oriented subparallel to the foliation (Fig. 4a). Some grains show minor replacement by chlorite. Very fine grained (<5 µm), euhedral Ti-oxides occur in the center of patches where chlorite replaced biotite (Fig. 5a). Amphibole is chloritized and only preserved as pseudomorphs (Fig. 4a); their long axes have acute angles (<45∘) to the foliation plane. The major opaque mineral is ilmenite (Figs. 4a, 5b). Ilmenite breakdown to Ti-oxide is observed at grain boundaries with biotite (Fig. 5b). Boundaries between the brittlely undeformed and fractured host rock or fault or injection veins are sharp (Fig. 4b). In the fractured host rock, alteration of biotite is more pronounced.

Cataclastic fault rock appears bright in thin section and consists of granular lithic and mineral fragments (Fig. 4c). It forms bulky-to-drawn-out patches that grade into compositional flow banding in fault veins mainly composed of pseudotachylyte (Fig. 3). Within cataclasite patches, tens to hundreds of micrometers thin, curved-to-meandering pseudotachylyte veins occur (Fig. 4c). The modal abundance of cataclasite patches decreases from bottom to top of the studied fault vein (Fig. 3).

Such structural evidence includes microcrystallites, sulfide/oxide droplets and spaced survivor clasts, which may display embayed edges witnessing their melt-assisted corrosion (Magloughlin and Spray, 1992; Kirkpatrick and Rowe, 2013). All of these features are expressed in the studied pseudotachylytes. Sulfide/oxide droplets are submicron in size (Fig. 4d). Grain size of survivor clasts is on the order of 20 to 100 µm (Figs. 4d, 5c, d). Their shapes are generally round, although some exhibit concave, serrated edges (Fig. 5d). Quartz clasts are most common. A smaller amount of subhedral calcite occurs in the fault rock, which most likely represents survivor clasts. Furthermore, <5 µm long needle-shaped crystals without obvious shape-preferred orientation occur dispersed in the cryptocrystalline or amorphous matrix (Fig. 5d). The needle-shaped microcrystallites are probably biotite, as energy-dispersive spectroscopic X-ray (EDS) mapping indicates that they are enriched in Al, K, Fe and Mg compared to the matrix. However, their small size prevented an interpretable single-crystal spectrum. In some places, microcrystallites of unknown composition show dendritic patterns, possibly K-feldspar (sanidine and anorthoclase; Lin, 1994; Fig. 5e).

A 4 to 10 mm wide layer in the upper part of the studied fault vein exhibits a bubbly microstructure in transmitted light (Fig. 4e, f). This spherically meandering microstructure represents chlorite alteration fronts replacing pristine pseudotachylyte (Fig. 5e). The fine-grained (5 to 15 µm) chlorite displays no shape-preferred orientation. Where chlorite has replaced pseudotachylyte, micron- to submicron-sized rhomb-shaped Ti-oxide crystals are finely dispersed (Fig. 5f, g). Their grain size decreases from center to rim of the chloritized domains.

Thin (<0.5 mm) antitaxial calcite + quartz veins with sharp edges cut across the host rock and all types of fault rock. They consist mainly of calcite and subordinate quartz. Euhedral pyrite occurs within such veins or in close proximity (<1 mm, Fig. 3c). Vein orientations generally dip at high angles toward the W or are perpendicular to the foliation. Fibrous calcite, quartz and strain fringes around pyrite are compatible with E–W extension. The veins transect the boundaries between different fault rock types and the host rock without being offset at these boundaries.

AMS data for all specimens are summarized in Table 1 and graphically presented in Fig. 6. Magnetic anisotropy in host rock and fault rock specimens displays consistent orientations of principal axes. Maximum principal axes (k1) trend E–W and are subparallel to the host rock lineation for all rock types (Fig. 6). Generally, all rock types show prolate AMS symmetry as indicated by distribution of intermediate (k2) and minimum principal axes (k3) in a girdle perpendicular to k1. Furthermore, shapes and orientations of the 95 % confidence regions for mean k2 and k3 axes reflect the prolate AMS shape (Fig. 6a, c–f). Symmetry of these confidence regions indicates that AMS fabrics are similar for the analyzed specimen groups (Borradaile and Jackson, 2010). However, intermediate and minimum principal axes for host rock specimens occur in two clusters (Fig. 6a). One cluster has k3 axes perpendicular to the host rock foliation and k2 axes lying within the foliation plane (Fig. 6b). The corresponding subfabric AMS ellipsoid approaches an oblate shape (T=0.21±0.19). The magnetic foliation expressed by these specimens is subparallel to the schistosity Shr. In the second cluster, k2 and k3 axes are inversely oriented.

Measurements of anisotropy (Pj, T) scatter over similar ranges for all rock types (Fig. 7a). The anisotropy degree Pj shows highest variation for host rock specimens (1.02<Pj<1.45) and lowest for altered pseudotachylyte (1.06<Pj<1.25). However, the median Pj values are similar in all rock types (1.1<Pj<1.2) and the middle 50 % of these data overlap when shown in box-and-whisker plots (Fig. 7b). The symmetry of the magnetic fabric shows no co-variation with the degree of anisotropy (Fig. 7a). Shapes of AMS ellipsoids for individual specimens of all rock types range from oblate to prolate (Fig. 7c). Overall, neither degree nor shape of the AMS ellipsoid defines a magnetic fabric distinctive for one rock type or a group of several rock types. Nevertheless, the volume-normalized mean susceptibility of altered pseudotachylyte specimens is approximately twice as high (median km=4.7×10-3 (SI)) as that of all other rock types (median km=2.7×10-3 (SI); Fig. 8).

All samples were measured with the three available frequencies used for the MFK1-FA. Figure 9 shows a comparison between mass-dependent susceptibilities measured at frequencies F1 (976 Hz) and F3 (15 616 Hz). Most samples fall along the 1:1 relationship, but it is possible to differentiate samples of pristine pseudotachylyte that have a relatively higher susceptibility compared to other samples (host rock, fractured host rock, cataclasite and altered pseudotachylyte). There is significant scatter in the data, particularly for the pristine pseudotachylytes. The length of the error bars shown in Fig. 9 represents 1 standard deviation based on repeated measurements, with at least three measurements per sample. However, there is a tendency for pristine pseudotachylyte samples to have slightly higher susceptibility at F1 (976 Hz) compared to measurements made at F3 (15 616 Hz).

Thermomagnetic curves for heating and cooling of host rock, as well as for pristine and altered pseudotachylyte, are presented in Fig. 10a–c. With increasing temperature, host rock thermomagnetic data exhibit steadily decreasing magnetic susceptibility, followed first by a rapid increase to about twice the initial value at ca. 500 ∘C and then followed by a rapid decrease at ca. 580 ∘C (specimens AB15-115, AB15-116; Fig. 10d). During cooling, host rock specimens show a prominent rise in susceptibility at temperatures <600 ∘C and a peak at ca. 430 ∘C. Pseudotachylyte specimens (AB15-12, AB15-13/61, AB15-62) show a small but noticeable drop in susceptibility at 550–590 ∘C (Fig. 10e). During cooling, susceptibility rises sharply for all pseudotachylyte specimens at temperatures <590 ∘C (Fig. 10b). Altered pseudotachylyte exhibits progressively decreasing susceptibility with increasing temperature without any significant drops (specimens AB15-43, AB15-67; Fig. 11f). During cooling, susceptibility progressively increases to a peak at ca. 300 ∘C and then gradually decreases again. For specimen AB15-43, there is a small sharp increase in susceptibility at 590 ∘C observed in the cooling curve.

Magnetic hysteresis measurements show that all rock types respond dominantly paramagnetically to applied high magnetic fields (Table 2, Fig. 11a, e, i). Hysteresis results for pseudotachylyte-free specimens show either no or very minor ferromagnetic response. They have saturation magnetizations (Ms=2.3±1.3×10-4 A m2 kg-1) about 1 order of magnitude below those specimens containing pseudotachylyte (Ms=1.73±0.6×10-3 A m2 kg-1) (Table 2). Furthermore, pseudotachylyte-free specimens have generally very open slope-corrected hysteresis loops, which do not display branches characteristic of ferromagnetic minerals (Fig. 11b, j) (Paterson et al., 2018). Slope-corrected hysteresis curves for these specimens accordingly also display atypical shapes, which may result from an artificial correction to the data (Fig. 11c, k). Contrastingly, hysteresis loops for pseudotachylyte-bearing specimens show a ferromagnetic contribution in magnetic response. This is expressed weakly in the unprocessed hysteresis loop (Fig. 11e), and more clearly after linear high-field slope correction (Fig. 11f; although hysteresis loops generally fail to close at high fields). Based on hysteresis parameters, pristine pseudotachylyte-rich specimens have the highest saturation remanent magnetization (Mrs=3.9±1.8×10-4 A m2 kg-1), compared to host rock (Mrs=6.6±7.5×10-5 A m2 kg-1) and altered pseudotachylyte specimens (Mrs=1.2±0.5×10-4 A m2 kg-1). Magnetic hysteresis raw data are available in Table S3 in the Supplement.

Specimen cube dimensions deviate moderately from neutral shapes. Their long edges are between 4.1 % and 20.9 % longer than their short edges. Prolate and oblate shapes are equally common (Fig. 12a, Table S1). The shape parameters of specimen dimensions (Td) and magnetic anisotropy (T) are independent of each other (Fig. 12b, Table S1). The degree of anisotropy of specimen shape and magnetic susceptibility show no significant correlation (Fig. 12c).

Raw measurements of mean susceptibility (km) and anisotropy degree (Pj) are inversely proportional (Fig. 13a). The km standard error shows significant correlation with sample volume (Fig. 13b) and degree of anisotropy Pj (Fig. 13c). Additionally, the standard error of km decreases with increasing specimen volume and decreasing mean magnetic susceptibility (Fig. 14). Consequently, the AMS data are dependent on specimen size. Small specimen volumes result in larger uncertainties, which in turn causes higher Pj values. This observation is further discussed in Sect. 6.4 which also discusses the limitation of specimen size in studies using AMS.

Thermomagnetic heating curves for host rock specimens show a decrease in magnetic susceptibility with increasing temperature until 400 ∘C, which is characteristic of paramagnetic behavior (Fig. 10d) (Hunt et al., 1995). Formation of new magnetite at temperatures above 400 ∘C is indicated by the peak and sudden decrease in magnetic susceptibility at 580 ∘C, the Curie temperature of magnetite (Hunt et al., 1995). These results, together with magnetic hysteresis data (Table 2, Fig. 11), show that the magnetic susceptibility of the host rock micaschist arises from paramagnetic minerals. It follows that the AMS in the host rock is controlled by the crystallographic orientation of the paramagnetic minerals (Borradaile and Jackson, 2010). An AMS subfabric in host rock specimens has parallel magnetic and mineral lineations and subparallel magnetic and ductile foliations (Fig. 6b). Shape-preferred orientation of tabular biotite crystals in the host rock (Fig. 4a) implies that crystallographic c axes values of biotite are oriented perpendicular to the schistosity. This AMS subfabric is therefore inferred to originate from crystallographic preferred orientation of biotite, which in single crystals exhibits k3 axes subparallel to biotite crystallographic c axes (Borradaile and Henry, 1997; Martín-Hernández and Hirt, 2003). The mean magnetic susceptibility km of host rock specimens (km=2.62±0.46×10-4 (SI)) is in the range of typical of schists (km=0.026-3.0×10-3 (SI); Hunt et al., 1995). Single-crystal bulk susceptibility values of biotite, muscovite and chlorite are on the same order of magnitude (around 10-4 (SI)) (Martín-Hernández and Hirt, 2003). In the absence of magnetite, the host rock AMS most likely arises from these sheet silicates. Fractured host rock and cataclasite specimens without pseudotachylyte display the same magnetic properties as host rock specimens (Figs. 7, 8, Tables 1, 2). This conformity suggests the same paramagnetic source of the AMS with contributions from biotite, white mica and chlorite.

Pseudotachylyte thermomagnetic data show a distinct drop in susceptibility from 550 to 590 ∘C, which indicates the presence of magnetite (Fig. 10e). Hysteresis results of pseudotachylyte-bearing specimens show mixed paramagnetic and ferromagnetic behaviors (Table 2, Fig. 11e–g). The AMS of pseudotachylytes thus reflects the sum of paramagnetic and ferromagnetic minerals in these specimens. The narrow range of km does not offer the opportunity to isolate subsets (Table 1, Fig. 8), which is a common approach to separate AMS subfabrics caused by paramagnetic and ferromagnetic minerals (Borradaile and Jackson, 2010). The presence of magnetite does not seem to increase km to values significantly higher than the (fractured) host rock and/or cataclasite specimens (Fig. 8). The ferromagnetic contribution to the pseudotachylyte AMS is consequently small. The pseudotachylyte AMS is therefore likely controlled by crystallographic preferred orientation of its paramagnetic minerals, i.e., most probably biotite, with a subordinate contribution from the shape-preferred orientation of magnetite (Sect. 5.2). The nearly absent ferromagnetic response in the slope-corrected hysteresis curves likely means that values of Ms and Mrs are largely artifactual, and samples are dominated by the paramagnetic signal. The exception is pristine pseudotachylyte that does show a weak ferromagnetic behavior after slope correction.

In altered pseudotachylyte specimens, a successive decrease in magnetic susceptibility without significant drop at 580 ∘C during heating indicates dominant paramagnetic behavior. This behavior suggests that magnetite present in pristine pseudotachylyte has been altered to an unknown phase in chloritized pseudotachylyte (Fig. 10f). Magnetic hysteresis results confirm bulk paramagnetic behavior for altered pseudotachylyte (Table 2, Fig. 11i–k). For the mean magnetic susceptibility for altered pseudotachylyte, being about twice as high as that for other rock types (Table 1, Fig. 8b), the AMS of altered pseudotachylyte apparently has an additional or a different mineral source than the other rock types. Notably, this observation is also made in the high-field susceptibility obtained from hysteresis measurements, which is nearly an order of magnitude higher than in other samples, including the pristine pseudotachylyte (Table 2). Bulk magnetic susceptibility for single-crystal chlorite without high-susceptibility mineral inclusions is about twice that of biotite and muscovite single crystals (Martín-Hernández and Hirt, 2003). These sheet silicates were also argued to collectively cause AMS in host rock specimens, but in altered pseudotachylyte chlorite it is much more abundant, forming up to ca. 50 % of the mode (Figs. 4e, f, 5e–g). We infer that AMS in altered pseudotachylyte dominantly reflects the orientation distribution of chlorite. An alternative explanation for the high susceptibility in the altered pseudotachylytes is the formation of metallic iron during faulting. Zhang et al. (2018) have noted formation of micron-sized iron spherules in pseudotachylytes that were heated within a range of 1300–1500 ∘C, leading to increased magnetic susceptibility. However, no such spherules are directly observed with scanning electron microscopy (Fig. 5), which makes it difficult to evaluate this potential origin for increased susceptibility.

The margins of the fault vein are parallel to the slip plane in the Finntjärnen fault zone. Seismic faulting occurred parallel to the schistosity Shr along subhorizontal, shallowly W-dipping shear planes (Figs. 2, 3). The slip direction is indicated by subhorizontal E–W-trending magnetic lineation in all fault rock types (Fig. 6). This direction is consistent with mineral and stretching lineations expressed in the ductilely deformed host rock. These orientations also coincide with the extension direction defined by crosscutting normal faults (Fig. 2b). Obliquity between the pseudotachylyte magnetic foliation and fault vein margins would indicate the kinematics of seismic slip (Ferré et al., 2015). However, the AMS of both cataclastic and friction melt-origin fault rocks displays prolate symmetry and magnetic lineations that are parallel with the vein margins. These results show that neither a magnetic foliation nor obliquity with the shear plane is developed, as would be expected from non-coaxial deformation (Borradaile and Henry, 1997). The observed AMS data raise several questions: (1) If such a kinematic model does not agree with the observed fault rock AMS, what process aligned the maximum principal axes? (2) How is it possible to explain the distribution of intermediate and minimum principal axes in a girdle perpendicular to the k1 axes? (3) Why are AMS fabrics of all rock types compatible? The questions are challenging to answer but they are likely related, given that (1) the magnetic fabrics are coaxial in host rock and pseudotachylytes and (2) the petrofabric and magnetic fabric are coaxial, even though a pronounced magnetic foliation has not developed.

Foliation-parallel fault veins, bound by narrow domains of fractured host rock, crosscut the ductile host rock fabric (Figs. 2–4). Their formation thus postdated ductile upper-greenschist to amphibolite facies deformation, which is in line with previous work (Beckholmen, 1982, 1983, 1984). The fault veins contain unmolten cataclasite, frictional melt-origin pseudotachylyte and altered pseudotachylyte in varying modal amounts. Spaced survivor clasts, microcrystallites and submicron sulfide/oxide droplets in pseudotachylyte identify these fault rocks as quenched, coseismic friction melts (Figs. 4, 5) (Magloughlin and Spray, 1992; Cowan, 1999; Rowe and Griffith, 2015). Chloritization of the pseudotachylyte groundmass and pronounced replacement of biotite by chlorite in fractured host rock domains indicate that hydrothermal alteration was associated with faulting. The chlorite microstructure suggests that recrystallization was static (Fig. 5). After pseudotachylyte formation, ambient temperature conditions in the fault zone are therefore inferred to be of lower greenschist facies (cf. Di Toro and Pennacchioni, 2004; Kirkpatrick et al., 2012). We deduce seismic faulting and subsequent alteration of fault rocks in the Finntjärnen fault zone occurred in the brittle–ductile transition zone near the base of the brittle crust. Assuming a typical temperature range of 300–350 ∘C, depending on the thermal gradient, the faulting occurred at ca. 12±4 km depth (Sibson and Toy, 2006).

Brittle faults and fibrous calcite + quartz veins crosscut both the ductile host rock fabric and the fault veins at high angles. Their orientations relative to the fault vein geometry, together with microscopic and macroscopic observations (Figs. 2–5), suggest that these E–W extensional structures formed latest. These structures are consistent with other extensional structures related to the Røragen Detachment west of the Tännforsen Synform (Fig. 1) (Gee et al., 1994; Bergman and Sjöström, 1997). In summary, seismic faulting in the Finntjärnen fault zone occurred after the formation of the upper greenschist- or amphibolite-facies schistosity and prior to late-stage E–W extensional brittle structures. Structural overprinting relations imply transport of thrust sheets in the Köli Nape Complex during exhumation of these nappes from the middle to the upper crust. The sense of faulting, however, cannot be deduced from the here presented data. Nevertheless, previous work in the area indicated that thrusting was toward the ESE (Bergman and Sjöström, 1997; Bender et al., 2018).

Structural and magnetic analyses of pseudotachylyte-bearing fault veins and their ductilely deformed host rocks reveal that petrofabric and AMS are co-parallel. The accordance of these data indicates that ductile host rock fabrics and brittle fault rock fabrics developed in the same strain field. However, the orientations of AMS and petrofabric in host rock versus fault rock specimens could not be used to deduce the kinematics of ductile or seismic shear. Nevertheless, crosscutting relations show that pseudotachylite formation in the Finntjärnen fault zone predated E–W extensional deformation.

There is an apparent inverse relationship between km and Pj, as well as a linear relationship between degree of anisotropy and standard error of mean susceptibility. This effect appears to be caused by specimen size. The larger specimens (by volume) have in general higher bulk susceptibility, and Pj tends towards lower values ranging from 1.01 up to 1.10. Normalization for specimen volume has little impact on removing this bias, and it is therefore evident that specimens with very small sizes are more likely to produce a large scatter in the degree of anisotropy. Although this seems evident, it is important to remark on. The issue with volume is an undesired artifact and it demonstrates the limitation of using small sample cubes in the current setup with the MFK1-FA system. The effect is furthermore emphasized by the increase in km standard error as a function of Pj.

Observations of magnetic anisotropy made in this study raise the issue of measuring AMS of specimens with small volume. Current equipment that exists commercially is not designed for handling small specimen volumes, and in most applications the intended volume ranges from 7 to 11 cm3 (representing standard size cubes and cylinders used in paleomagnetic and AMS studies). However, there is a growing interest for measurements of small specimens, as many AMS studies target geological structures that occur on the centimeter to sub-centimeter scale (e.g., Ferré et al., 2015). One of the challenges in using smaller specimens is clearly an increased uncertainty in manufacturing specimens that have appropriate dimensions. However, specimens can be constructed with care to compensate for this effect, and in this study we have demonstrated that the non-equidimensional effect is secondary in importance to the specimen volume. Furthermore, our AMS data show a consistent magnetic fabric in the different rock types, which suggests that they most likely represent the true rock fabric, although the magnitudes are variable. It is clear that great care has to be taken when evaluating the anisotropy parameters as a function of sample volume and the bulk susceptibility when small samples are measured. At the same time, there is a desire for further study with smaller samples as this increases the scope of AMS measurements to different geological applications.