Decrypting Magnetic Fabrics (AMS, AARM, AIRM) Through the Analysis of Mineral Shape Fabrics and Distribution Anisotropy

Anisotropy of magnetic susceptibility (AMS) and anisotropy of magnetic remanence (AARM and AIRM) are efficient and versatile techniques to indirectly determine rock fabrics. Yet, deciphering the source of a magnetic fabric remains a crucial and challenging step, notably in the presence of ferrimagnetic phases. Here we use X‐ray micro‐computed tomography to directly compare mineral shape‐preferred orientation and spatial distribution fabrics to AMS, AARM and AIRM fabrics from five hypabyssal trachyandesite samples. Magnetite grains in the trachyandesite are euhedral with a mean aspect ratio of 1.44 (0.24 s.d., long/short axis), and >50% of the magnetite grains occur in clusters, and they are therefore prone to interact magnetically. Amphibole grains are prolate with magnetite in breakdown rims. We identified three components of the petrofabric that influence the AMS of the analyzed samples: The magnetite and the amphibole shape fabrics and the magnetite distribution anisotropy. Depending on their relative strength, orientation and shape, these three components interfere either constructively or destructively to produce the AMS fabric. If the three components are coaxial, the result is a relatively strongly anisotropic AMS fabric (P' = 1.079). If shape fabrics and/or magnetite distribution anisotropy are non‐coaxial, the resulting AMS is weakly anisotropic (P' = 1.012). This study thus reports quantitative petrofabric data that show the effect of magnetite distribution anisotropy on magnetic fabrics in igneous rocks, which has so far only been predicted by experimental and theoretical models. Our results have first‐order implications for the interpretation of petrofabrics using magnetic methods.

. The cryptodome consists of a porphyritic trachyandesite with amphibole and plagioclase phenocrysts and accessory phenocrysts of titanomagnetite and clinopyroxene   (Burchardt et al., 2019). The amphibole phenocrysts are surrounded by breakdown rims that range from 10 to 100 µm in thickness and consist of small (µm in diameter) crystals of titanomagnetite, pyroxene and feldspar ( Figure 1b). Several amphibole crystals also have oxide inclusions, whereas oxide inclusions are rare in the plagioclase phenocrysts. The groundmass is rhyolitic in composition and comprises euhedral to subhedral plagioclase and alkali feldspar laths, euhedral to subhedral apatite and pyroxene, and anhedral quartz (Figure 1a). Plagioclase phenocrysts constitute about 24 vol. % of the rock, amphibole phenocrysts only about 3-7 vol. %, and magnetite and pyroxene phenocrysts constitute ∼0.5 vol. % and <<1 vol. % of the rock, respectively. Plagioclase phenocrysts in the Cerro Bayo occur in glomerocrysts or as individual "free-floating" crystals oriented largely parallel to the amphibole shape-preferred orientation (Figure 1a). The dominant iron oxide in the Cerro Bayo trachyandesite has been determined to be titanomagnetite with on average 3.5 wt. % TiO 2 and the amphibole phenocrysts have been classified as pargasite and hastingsite (Sun, 2018). Interpretations of magma flow in the Cerro Bayo cryptodome utilizing the AMS data in this study are presented in Burchardt et al. (2019).

Anisotropy of Magnetic Susceptibility and Thermomagnetic Properties
Five representative, oriented block samples  were collected from the Cerro Bayo cryptodome and cored to extract 5, 5, 6, 11 and 6 (21 × 24 mm cylinder) specimens, re-MATTSSON ET AL. spectively. AMS measurements were performed in the Laboratory for Experimental Paleomagnetism at the Department of Earth Sciences, Uppsala University with an Agico Kappabridge MFK1-FA in semi-automatic spinning mode. A field of 200 A/m and frequency of 976 Hz were used for the measurements. Symmetric second rank magnetic susceptibility tensors were determined from the measurements using the least square inversion method of Jelínek and Kropáček (1978). The eigenvalues and eigenvectors of the magnetic susceptibility tensor define the value and orientation of the three orthogonal, principal axes of susceptibility, k 1 ≥ k 2 ≥ k 3 , which can be represented by a triaxial ellipsoid (the magnetic susceptibility ellipsoid) (Khan, 1962). The mean magnetic susceptibility (K m ) is given by the arithmetic mean of the principal susceptibilities: Coe (1966) queries the applicability of describing AIRM using a second rank tensor, taking that study into account we evaluated the calculated AIRM tensor elements and the results of the evaluation are presented in the supporting information ( Figure S2).
Stepwise ARM demagnetization and saturation isothermal remanence magnetization (sIRM) measurements were also performed on the samples used for AARM and AIRM analysis ( Figure S3). During sIRM acquisition, the samples were first magnetized with the PAM1 in DC fields up to 20 mT and later magnetized with an MMPM10 pulse magnetizer from Magnetic Instruments in DC fields between 25 mT and 3 T.

Petrofabric Analyses Using X-Ray Computed Microtomography
In order to assess the petrofabric, the same five representative specimens (CB-15C2, CB-19A1, CB-46A1, CB-55A1 and CB-61B2) were imaged by µXCT. The speciemens were scanned with a Nikon Metrology XT H 225 ST X-ray microtomograph at the Natural History Museum, University of Oslo. µXCT analyses was conducted using a 140 kV acceleration voltage, a current of 300 µA, 1 s exposure time and 3,016 rotational projections and using a 0.25 mm copper filter. The X-rays transmitted through the specimen were collected on a planar 1,920 × 1,536 pixels detector. The resulting voxel (volume pixel) size was about 16 µm 3 (see Table S1).
The obtained stack of 1,534 grayscale images on each core represents the attenuation of the X-rays in the scanned volume, that is, phases of higher densities have lighter grayscale voxels and lower density phases have darker voxels. Magnetite and amphibole grains have comparatively higher densities than the groundmass and can therefore easily be distinguished in the scan slices. Plagioclase phenocrysts could not be separated from the scan slices due to similar densities as the sample groundmass. Beam-hardening effects are visible on the scan slices and are most distinct 1.5-2 mm from the edge of the core. Beam-hardening had no effect on magnetite segmentation due to its high attenuation of X-rays, however amphibole segmentation was strongly affected. As a consequence, a 1.5-2 mm rim of the scanned core was segmented as a single blob and removed from the sample set during the manual separation of the data.
Samples were oriented in the scanner to facilitate direct comparison to AMS and anisotropy of magnetic remanence results. However, minor discrepancies in the comparison between AMS and crystal SPO and spatial distribution data collected with µXCT could have been induced by differences in sample mounting.

Extraction of Grain Properties From X-Ray Micro-Computed Tomography Scans
X-ray microtomography scan slices were subsequently analyzed using Blob3D (Ketcham, 2005). Six hundred slices of 1,534 (∼40% of the scanned volume) were processed for each specimen in order to limit the segmentation time. For specimen CB-61B2, 1,180 of 1,535 slices were processed to separate magnetite crystals. Blobs of segmented crystals were created from the stacked slices in Blob3D using grayscale threshold values. Noise in the scan slices was limited by removing islands below a certain pixel radius, as well as removing already separated components (only for amphibole segmentation; see Table S1 for Blob3D segmentation parameters). The created blobs were then reviewed, and crystal aggregates were manually separated into individual crystals before data extraction. Crystals smaller than 1,000 voxels for amphibole and 500 voxels for magnetite were discarded to avoid imaging artifacts. Crystals intersected by the edges of the core and processed scan slices were mostly discarded, however, if the shape and length of the intersected blob were not compromised by the intersecting surface they were not discarded. For each crystal grain, the volume, center x, y, z coordinates and the length and orientation of the three orthogonal principal axes (long axis v 1 ; intermediate axis v 2 ; short axis v 3 ) were determined by fitting a best-fit ellipsoid to the separated grain volume surfaces in Blob3D.
We validated the accuracy of the phase separation between Blob3D and the commercial software Avizo Fire edition ( Figure S4). In Avizo, magnetite and amphibole were separated from the scanned cores using grayscale thresholding. Magnetite grains smaller than 1,000 to 2,000 voxels and amphibole grains smaller than 3,000 to 4,000 voxels were removed to limit noise and the erosion tool was employed to remove breakdown rims on crystals and imaging artifacts. No individual review of separated crystal volumes was performed in Avizo, which resulted in fast extraction of data, but the crystal volumes extracted largely represent crystal aggregates. The results from Blob3D and Avizo were concordant (see Figure S4): All µXCT data presented below were extracted with Blob3D.

Crystal Orientation and Fabric Determination
The statistical petrofabric analysis was performed with the TomoFab v. 1.3. MATLAB package by using either a set of grain principal axes directions, or a set of grain principal axes directions and lengths (see details and discussion in Petri et al., 2020). The nomenclature used to describe the magnetic fabrics and the petrofabric is given in Table 1.
First, we calculated the mean principal directions (O 1 , O 2 , and O 3 ) by constructing the orientation tensor (OT) for each principal axis group (v 1 , v 2 and v 3 ), as defined by Scheidegger (1965) and Watson (1966) as:  The eigenvalues and eigenvectors of the FT correspond to the three mean axes (V 1 ≥ V 2 ≥ V 3 ). The shape of the FT ellipsoid can then be projected in Ramsay-type diagrams by calculating the V 1 /V 2 and V 2 /V 3 mean axes length ratios, but also by calculating the corrected degree of anisotropy (P') and the shape parameter (T) as done with the AMS tensor elements (see above and Petri et al., 2020). The FT approach described here also allows one to calculate 95% confidence estimates around the mean principal axes using the method of Jelínek and Kropáček (1978). The results of the two approaches are presented in Table 2.

Distribution Anisotropy Analysis
We evaluated the spatial distribution of grains, that is, DA, by calculating directional cosines l, m, n of the vector defined by two grain centers, for each couple of grains in the sample segmented using Blob3D. The sets of directional cosines, were then used to compile a distribution anisotropy tensor, similar to an OT, and defined as: Each vector of the directional cosines is here weighted by the w-factor of Stephenson (1994), defined as: with  1 and  2 being the volumes of the two grains, and r the distance between the same two grains. The use of the weighting factor implies that large grains that are spatially close together have a stronger influence on the result compared to small and distant grains. This also avoids the calculated DA to be affected by the shape of the sample (two grains at each side of an elongated sample are unlikely to impact the DA). The spatial distribution of grains is deduced from the corrected degree of anisotropy (P') and the shape (T) of the ellipsoid defined by the eigenvectors and associated eigenvalues of the DA (λ 1 ≥ λ 2 ≥ λ 3 ): Low degree of anisotropy (low P') indicates that grains are randomly distributed; high degree of anisotropy (high P') indicates that grains are strictly distributed, either in planes if the shape of the DA is oblate (T > 0) or along lines if the shape of the DA is prolate (T < 0). The orientation of the planes or lines onto which grains are distributed are determined by the DA eigenvectors, λ 1 being the line, and λ 3 the pole to the plane. This method is implemented in the Tomofab MATLAB code (version 1.3). We analyzed the DA of the complete data set but also as three equivalent subsets of grains based on their volume.
At sub-zero temperatures, thermomagnetic susceptibility (T-X) curves of samples CB-19 and CB-46 show an increase in bulk magnetic susceptibility between −180 to −160°C before the susceptibility slowly decreases until −50°C, this represents the Verwey transition (Figures 2l and 2m). A Verwey transition feature is not observed in samples CB-15, 55 and 61, instead susceptibility steadily decrease from −194°C to −120°C before steadily increasing toward 0°C (Figures 2k, 2n and 2o). During heating from 25°C to 400°C, all samples show an inflection at around 300°C. Samples CB-15, 55 and 61, that do not display a Verwey transition, exhibit the most abrupt increase in susceptibility (50%-75%), whereas CB-19 and CB-46 exhibit relatively modest increase in susceptibility (20%-40%). Heating from 400 to 700°C reveals a prominent decrease in susceptibility in all samples between 450°C and 580°C; samples CB-19 and 46 peak between 550°C to 580°C, while samples CB15, 55 and 61 exhibit broader peaks ranging from 450°C to 550°C. For all, irreversible cooling curves are produced, and the 300°C inflection recorded during heating is absent. Samples 10.1029/2021JB021895 8 of 23   Tomofab-FT  CB-15 and CB-55 show a ∼20% decrease in magnetic susceptibility after cooling, CB-61 exhibits a modest 5%-10% increase and samples CB-46 and CB-19 display a marked increase in susceptibility of 40% and 500% respectively (Figures 2k-2o).
The observation of a Verwey transition at around −170°C and/or Curie temperatures between 540°C and 580°C show that a low titanium titanomagnetite is the main ferrimagnetic phase in the samples (Dunlop & Özdemir, 1997;Lattard et al., 2006). The irreversible inflection at around 300°C on all heating curves indicates that the magnetic mineralogy changed during the experiment. In CB-15, CB-46 and CB-55, a relatively modest change of <20% is recorded and this may be attributed to the combined effect of titanium exsolution from titanomagnetite and the modification of maghemite during the high temperature experiment (Bilardello, 2020; Dunlop & Özdemir, 1997;Özdemir et al., 1993). Abrupt increases in susceptibility in CB-46 and especially in CB-19 show that a substantial amount of new magnetite has formed during the experiment. For simplicity, we will refer to low Ti-magnetite as magnetite in subsequent paragraphs.
The ARM AF demagnetization of the samples shows M/Mmax = 0.9 (i.e., when 90% of the imparted field is gone) at around an AF of 50 mT for CB-15, 55 and 61 and around an AF of 70 mT for CB-19 and 46 (Figure S3). The sIRM acquisition curves show that CB-19 and 46 reach 95% saturation in fields ≥400 mT (Figure S3). Sample CB-19 has the highest coercivity range of all of the samples studied and the thermomagnetic susceptibility experiment shows that this sample also has a very prominent Hopkinson peak (Figure 2l).
MATTSSON ET AL.
10.1029/2021JB021895 9 of 23 Table 2 Continued  Abbreviations: AARM, anisotropy of anhysteretic remanent magnetization; AIRM, anisotropy of isothermal remanent magnetization; AMS, anisotropy of magnetic susceptibility. a The errors associated with the tensor calculation is much smaller when using the 12-position measurement scheme. See Table S2.  Together these data indicate that single domain or pseudosingle domain magnetite is present and may play a dominant role in the magnetic fabric in this sample (cf. Dunlop & Özdemir, 1997). Sample CB-46 returns a similarly high coercivity spectra and also exhibits a prominent Verwey transition and notable Hopkinson peak on the thermomagnetic susceptibility curve (Figures 2m and S3). In contrast, CB-15, 55 and 61 reach 95% saturation at an applied field of ∼300 mT ( Figure S3), and exhibit a more gradual Curie temperature peak and record no Verwey transition (Figures 2k, 2n and 2o). This points toward the dominance of a relatively low-coercivity ferrimagnetic phase in these samples. The absence of a Verwey transition indicates the presence of non-stoichiometric likely oxidized magnetite and/or superparamagnetic (SP) magnetite grains in these samples (Moskowitz et al., 1989;Özdemir et al., 1993).

Magnetic Fabrics
While AMS parameters in the Cerro Bayo intrusion show significant variation between samples (P' = 1.008 to 1.081 and T = −0.799 to 0.974; Burchardt et al., 2019), sub-samples or specimens collected from each sample return highly consistent results. The samples selected for detailed petrofabric µXCT analysis were purposefully chosen from a range of samples to include a broad selection of AMS fabric types.

CB-15
The mean AMS ellipsoid for CB-15 AMS has a P' = 1.07 (ranging from 1.068 to 1.073) and a T = −0.39 (ranging from −0.442 to −0.361), this defines a moderately prolate fabric. Sub-sample AMS axes define very narrow confidence ellipses ( Figure 2 and Table 2). Both the AARM and AIRM principal axes are coaxial to the AMS axes, but have higher P' values ( Figure 2 and Table 2).

CB-19
The mean AMS ellipsoid for CB-19 has a P' = 1.01 (ranging from 1.012 to 1.015) and a T = −0.5 (ranging from −0.675 to −0.309), this defines a very weak, moderately prolate fabric. The k 1 axes are clustered and k 2 and k 3 axes define a broad girdle ( Figure 2 and Table 2). The principal axes of the AMS, AARM and AIRM ellipsoids are slightly oblique and diverge by 15-30°. The pAARM R 3 axes of CB-19A1 are coaxial to the 12-position calculated AARM principal axes, but not the 15-position calculated principal axes (Figures 2, S5  and Table S2).

CB-46
The mean AMS ellipsoid for CB-46 AMS has a P' = 1.02 (ranging from 1.018 to 1.023) and a T = 0.29 (ranging from 0.522 to 0.131), this defines a weakly anisotropic, transitional oblate fabric. Sub-sample AMS axes are tightly clustered (Figure 2 and Table 2). The principal axes of the AMS, AARM, AIRM and pAARM ellipsoids plot close to each other ( Figure S5 and Table S2).

CB-55
The mean AMS ellipsoid for CB-55 has a P' = 1.07 (ranging from 1.064 to 1.087) and a T = 0.9 (ranging from 0.91 to 0.599), k 3 axes are tightly clustered; k 1 and k 2 axes plot along a girdle defining an oblate ellipsoid ( Figure 2 and Table 2). The maximum and intermediate axes of the AMS, AARM and AIRM ellipsoids plot along the same girdle, whereas the minimum axes of the AMS, AARM and AIRM are coaxial. The R 3 axes of the pAARM and AARM are nearly coaxial ( Figure S5 and Table S2).

CB-61
The mean AMS ellipsoid for CB-61 has a mean P' = 1.05 (ranging from 1.046 to 1.055) and a T = 0.85 (ranging from 0.639 to 0.974). k 1 and k 2 sub-sample axes define a girdle and k 3 axes are clustered, these data describe a strongly oblate fabric (Figure 2 and Table 2). The AMS, AARM and AIRM maximum and intermediate axes plot along a single girdle and the corresponding minimum axes are coaxial to one another. The pAARM R 3 principal axis are nearly coaxial to the AARM R 3 ( Figure S5 and Table S2).

Grain Shape
In total, 15,112 magnetite and 23,966 amphibole grains were separated from the five representative scanned cores (see details in Table 2). Magnetite and amphibole both occur as individual "free-floating" grains in the groundmass and as aggregates (Figures 1a-1f). Even though the whole core was not processed with Blob3D, the limited treated volume still yields >2,000 separated crystals per mineral phase and specimen, which is adequate for crystal population statistics (cf. Mock & Jerram, 2005;Morgan & Jerram, 2006). In all five specimens magnetite grains have similar crystal habits (Figure 3). Separated single magnetite grains are equant, display a nearly cubic crystal habit and have an average v 1 /v 3 axis ratio (aspect ratio) of 1.44 (0.24 s.d.) and v 1 /v 2 axis ratio of 1.21 (0.15 s.d.) (n = 14,828) ( Figure 3a). Visual inspection of magnetite crystals with a scanning electron microscope show that magnetite clusters consist of both individual crystals with distinct margins and intergrown crystals (Figures 1b and 1c). The v 1 lengths of extracted crystals range from 0.15 to 0.9 mm and the bulk (∼80%) of the total analyzed volume of magnetite in the samples is carried by grains with v 1 lengths of between 0.18 and 0.5 mm (Figures 4a and 4b). Crystals that were intersected by the edge of the core and scans were excluded from the crystal size distribution and crystal shape analyses. The average distance between magnetite crystal centers to its nearest neighbor ranges from 0.53 to 0.42 mm ( Table 2; Mattsson et al., 2021). About 50%-60% of the magnetite crystals in the analyzed samples have a d/r ratio >0.5 and between 40% to 50% of the crystals have a ratio >0.8 to its nearest neighbor (see Introduction for description of ratio).
The amphibole grains in all specimens are dominantly prolate with an average v 1 /v 3 axis ratio of 3.49 and v 1 / v 2 axis ratio of 2.71 (n = 22,243) ( Figures. 1a, 1b, 1e, 1f and 3b). The v 1 lengths of amphiboles extracted from the scanned cores range between 0.2 to 5.4 mm (Figure 4c).

CB-15
The magnetite long axis (v 1 ) orientations present a moderately defined E-W striking girdle (Figure 5a). Conversely, the magnetite short axis (v 3 ) orientations are characterized by a horizontal N-striking cluster. The analysis of the FT shows that V 1 is located at 105 / 47 and V 3 at 006 / 08, both are coaxial with the OT (Figure 5a and Table 2). The fabric parameters derived from the FT indicate a moderately defined oblate fabric (T = 0.54, P' = 1.08), which is consistent for all crystal sizes (Figure 6a; Table S3). The constrained FT-foliation is oriented 186 / 82 (dip-direction). In contrast to magnetite, amphibole grains document a fabric that is more clearly defined (Figure 5b). v 1 orientations present a distinct cluster to the east. Conversely, v 3 orientations plot along a weak N-S striking girdle that dips moderately to the west. The FT governed by the amphibole v 1 , results in a V 1 at 091 / 40, which is oriented very close to the O 1 , whereas the V 3 plots on the v 3 girdle at 288 / 49, far from the O 3 . The fabric parameters obtained by the FT analysis indicate a strongly anisotropic, prolate fabric (P' = 1.66; T = −0.68), with a weakly constrained foliation at 108 / 41 (dip-direction).

CB-19
The v 1 of magnetite grains are aligned along a steeply dipping E-W girdle and v 3 axes cluster at the poles of the Schmidt net (Figure 5c). The V 1 at 121 / 48 is not aligned with respect to O 1 but still located on the v 1 -defined girdle ( Figure 5c and Table 2). The V 3 axis at 018 / 11 is almost identical to the O 3 . The FT fabric parameters indicate an oblate (T = 0.75) and moderately anisotropic fabric (P' = 1.08) with a defined foliation at 198 / 79 (dip-direction).
The amphibole v 1 axes define a weakly developed, moderately southward dipping girdle; v 3 axes define a northward dipping wide cluster (Figure 5d). The V 1 and V 3 are oriented at 175 / 48 and 001 / 42, respectively (Table 2). A triaxial neutral fabric is indicated by the FT fabric parameters (T = 0.08) with a strong degree of anisotropy (P' = 1.38). The foliation defined by the FT of amphibole lies at 181 / 48 (dip-direction).

CB-46
The v 1 of magnetite grains are aligned along a N-S striking girdle that dips moderately to the west and the v 3 axes cluster to the east (Figure 5e). The V 3 axis constrained by the FT at 098 / 55 correlates well with O 3 , whereas the V 1 at 202 / 10 is slightly misoriented with respect to O 1 ( Table 2). The analysis of the FT fabric parameters shows a strongly oblate (T = 0.96) and moderately anisotropic fabric (P' = 1.09); the defined foliation stands at 278 / 35 (dip-direction).
The amphibole v 1 axes plot in a moderately developed, sub-vertical NNE-striking girdle with a cluster around the poles of the Schmidt net; v 3 orientations define a sub-horizontal cluster (Figure 5f). The mean V 1 and V 3 are coaxial to the OT and oriented at 004 / 22 and 104 / 24, respectively ( Table 2). The fabric is oblate (T = 0.42) with a strong degree of anisotropy (P' = 1.4). The foliation defined by the FT of amphibole lies at 284 / 66 (dip-direction).

CB-55
The fabric of CB-55 is very well developed for both magnetite and amphiboles. Magnetite grains v 1 define a clear vertical NW-SE-striking girdle, whereas v 3 orientations occur in a narrow sub-horizontal cluster (Figure 5g). Both orientations and fabric parameters obtained with OT analysis corroborates with the FT analysis ( Table 2). The V 1 axis is oriented 319 / 07; V 3 axis lies at 228 / 10; and the fabric is strongly oblate and moderately defined (T = 0.79, P' = 1.1). The compiled foliation defined by the V 1 -V 2 plane lies at 048 / 80 (dip-direction).
Similarly, amphibole v 1 axes define a vertical, NW-SE-striking girdle and a narrow v 3 cluster (Figure 5h). The FT constructed using the amphibole individual axes and length is coaxial to the OT and points to a V 1 at 343 / 72 and V 3 at 226 / 08 with a strongly developed oblate fabric (P' = 1.6; T = 0.85), and a well-defined foliation of 046 / 82 (dip-direction).
MATTSSON ET AL.

CB-61
In CB-61, magnetite grains v 1 are distributed in a weakly defined vertical NW-SE-striking girdle, whereas v 3 orientations plot in a sub-horizontal cluster in the SW (Figure 5i). Both orientations and fabric parameters obtained by OT analysis corroborate results with the FT analysis ( Table 2). The V 1 axis is oriented 129 / 55; V 3 axis trend and plunge 238 / 14; and the fabric is oblate (T = 0.56), but with a relatively low degree of anisotropy (P' = 1.06). The foliation defined by the V 1 -V 2 plane is oriented 129 / 55 (dip-direction).

Distribution Anisotropy of Magnetite
Here we report the results of the DA of magnetite; results for the DA of amphiboles can be found in the supporting information.

CB-15
The magnetite grains of CB-15 are distributed on a NE-SW girdle (P' = 1.25, T = 0.12; Figure 6a). The DA λ 1 axes (089 / 38) plots close to the V 1 FT axes and together with λ 2 define a foliation oriented 117 / 41 (dip-direction) ( Table 2). The analysis of the different grain size categories shows that the magnetite DA is strongly anisotropic for small and intermediate grain sizes, but both the orientation and shape of the DA vary (Figure 6a).

CB-19
The magnetite grains of CB-19 have a triaxial and moderately defined distribution, as indicated by the fabric parameters of the DA (P' = 1.21, T = −0.01; Figure 6c). The λ 1 and λ 2 eigenvectors are distributed on a southward dipping girdle and define a foliation plane oriented 187 / 44 (dip-direction) that is sub-parallel to the magnetite FT foliation. The analysis of the different grain size categories shows that the small grain MATTSSON ET AL.  sizes have a relatively strong and transitional prolate distribution coinciding with the southward-dipping girdle. Large and intermediate volume grains define a prolate and transitional prolate fabric with a lineation plunging moderately to the SW (Figure 6c; Table S3).

CB-46
The degree of anisotropy and shape of the DA (P' = 1.29 and T = 0.86) indicates that magnetite grains are distributed along planar structures (Figure 6e). The orientation of these planes can be assessed by the DA eigenvectors, with λ 1 being 204 / 58 and λ 3 at 106 / 05. The compiled planar structure along which grains are aligned are defined by a plane oriented 286 / 86 (dip-direction). The DA of the different grains size categories display transitional oblate shapes with a high degree of anisotropy (Table S3). However, all the DA foliations are oriented at a high angle to the mean FT axes (Figure 6e).

CB-55
The DA of magnetite grains in CB-55 (Figure 6g) shows an oblate distribution (T = 0.46) that is moderately anisotropic (P' = 1.26). Magnetite grains are distributed along planes, where the pole to these planes λ 3 (220 / 05) lies close to V 3 . Although λ 1 (317 / 56) is highly misoriented with respect to V 1 , the compiled foliation defined by the grain spatial distribution (040 / 85, dip-direction) is very close to the foliation defined by the shape and the orientation of the grains (i.e., the FT). These characteristics are consistent for all grain size categories except for intermediate volume magnetite crystals that have a triaxial distribution (Figure 6g).

CB-61
The DA of magnetite grains in CB-61 ( Figure 6i) is oblate (T = 0.46), with a moderate degree of anisotropy (P' = 1.23). Magnetite grains are distributed along moderately S-dipping planes, where the pole to these planes (λ 3 at 002 / 41) coincides with magnetite V 2 . λ 1 (130 / 36) plots close to V 1 and the compiled foliation defined by the grain spatial distribution (182 / 49, dip-direction) is almost at a right angle to the FT foliation. The fabric shape and orientation vary between different grain sizes. The smallest and largest volume grains have a prolate distribution and the intermediate volume grains have an oblate distribution (Figure 6i).

Interpretation and Discussion
Based on our results, the AMS fabric of the Cerro Bayo trachyandesite may be attributed to three sources: (a) The SPO of magnetite grains (Ferré, 2002;Hrouda, 1982); (b) the spatial distribution of the magnetite grains across the sample (Cañón-Tapia, 1996, 2001Gaillot et al., 2006;Hargraves et al., 1991;Stephenson, 1994;Grégoire et al., 1995); and (c) the amphibole CPO and composition (Biedermann et al., 2015. The analysis of these three components of the petrofabric shows contrasting relationships in our samples.

Comparison Between Magnetic Fabrics and Rock Fabrics
The AMS k 1 and AARM R 1 principal axis in CB-15 are coaxial with the V 1 and O 1 of both magnetite and amphibole (Figure 7a). The magnetite and amphibole SPO are coaxial in terms of maximum principal direction, but not the intermediate direction. The shape parameters that can be derived from the AMS, AARM, amphibole FT, and OT-derived indexes indicate a moderate to strong prolate fabric. The magnetite DA has a triaxial shape and is co-axial to amphibole FT and AMS, AARM and AIRM principal axes, but not the magnetite FT (Figure 7a). The magnetite DA and the amphibole SPO therefore likely control the principal directions of the AMS ellipsoid. The non-coaxial oblate magnetite components of the petrofabric may destructively interfere, which induce prolate magnetic fabrics controlled by the amphibole SPO and/or the intersection lineation between the magnetite components of the petrofabric.
In CB-19, the magnetite FT displays an oblate fabric and the amphibole FT a triaxial fabric with a similar east-west strike of the foliation planes, although the inclination of the amphibole FT foliation is distinctly shallower (Figures 5c, 5d, 6c and 6d). Magnetite DA is triaxial and plots close to the amphibole FT. The AMS and AARM fabrics of CB-19 are prolate and k 1 and R 1 plunge toward the north, whereas amphibole V 1 and magnetite λ 1 plunge toward the south. Amphibole V 3 and magnetite λ 3 , in turn correlate with k 1 and AARM R 1 . The AIRM fabric is transitional oblate and R 1 is co-axial to magnetite V 3 (Figure 7b). The AMS and AARM fabrics are therefore inverse relative to amphibole FT and magnetite DA, whereas the AIRM fabric is inverse relative to the magnetite FT fabric (Figure 7b). The three contrasting petrofabric components therefore seem to neutralize the AMS fabric, resulting in very low degree of anisotropy (P'). The AMS ellipsoid still reflect the analyzed components of the petrofabric, albeit the principal axes position has been flipped relative to the principal axes of the petrofabric ellipsoids.
In CB-46, the k 1 , k 2 and AIRM R 1 , R 2 , as well as the λ 1 and λ 2 of magnetite plot along a subvertical NNE-SSW girdle (Figure 7c). The amphibole FT foliation is parallel to the AMS foliation, but dips moderately toward west and amphibole v 1 axes are clustered toward the poles of the Schmidt net (Figure 5f). The magnetite FT shows, however, a strongly oblate fabric that dips gently toward west, although with a similar strike of the foliation plane as the amphibole shape and magnetite DA fabrics (Figures 5e, 5f, 6e and 6f). The AMS signal correlates well with the magnetite spatial distribution in terms of its foliation (k 1 -k 2 plane), but the k 1 orientation is in better agreement with the amphibole SPO (Figures 6e and 7c). All petrofabric elements that may contribute to the magnetic fabrics are oblate but not co-axial (Figure 7c). The misorientation of the petrofabric components results in a competition that neutralizes the AMS shape factor and lowers the degree of anisotropy. Among the three components of the petrofabric, the magnetite DA governs the AMS foliation, as indicated by their close spatial correlation. However, the orientation of the k 1 axis is clearly related to the SPO of amphibole and, to some degree, the magnetite SPO ( Figure 7c).
In CB-55, the AMS k 1 and k 2 , AARM and AIRM R 1 and R 2 principal axes plot along the same NW-SE oriented steeply dipping girdle as the amphibole and magnetite O 1 , V 1 and O 2 , V 2 , whereas the AMS k 3 and AARM R 3 and the V 3 , O 3 are horizontally clustered to the NE and SW (Figure 7d). Both the magnetite and the amphibole in sample CB-55 display a strong v 1 girdle distribution and the FTs yield a high shape factor (T) (Figure 5g). The AMS shape factor also indicates a strongly oblate fabric. The DA of magnetite displays an oblate shape that is coaxial to the other fabric elements (Figure 7d). The principal axes of the magnetic fabrics of sample CB-55 are therefore controlled by a combination of magnetite SPO, the magnetite spatial distribution and amphibole SPO. The concordance of the three components of the petrofabric in CB-55 accentuates both the shape parameter and degree of anisotropy.
The volume of the core processed was increased for CB-61 magnetite relative to the other samples because the magnetite petrofabric components display a large variation in fabric orientation in the different grain sizes (Figure 6i). These large variations in magnetite SPO between different grain sizes result in a relatively low degree of anisotropy for the magnetite components of the petrofabric. Magnetite FT is oblate in CB-61 with a NW-SE striking foliation (Figures 5i and 6i). The orientation of the magnetite FT foliation contrasts the magnetite DA and amphibole FT foliations, which are oriented E-W ( Figure 6i and Table S3). The AMS, AARM, and AIRM ellipsoids are oblate and their foliation strikes NE-SW (Figure 7e). The magnetite DA and amphibole SPO are coaxial, whereas the magnetite SPO is oriented at right angle to the amphibole SPO and the magnetite DA foliation (Figure 7e). The AMS fabric seems to reflect the competition between the relatively weakly anisotropic magnetite DA and magnetite SPO, resulting in the misorientation relative to the analyzed components of the petrofabric (Figure 7e). The V 1 , k 1 , R 1 , λ 1 plot close to each other, whereas the magnetite V 3 plot along the same girdle as the k 2 and k 3 and R 2 and R 3 anisotropy of anhysteretic remanence magnetization (AARM) and anisotropy of isothermal remanence magnetization (AIRM) principal axes. V 1 and magnetite V 1 are both located on the magnetite distribution anisotropy (DA) foliation plane, that is, they point in the direction of the plane in which magnetite grains are spatially distributed. (b) CB-19A1. k 1 and AARM R 1 plots close to amphibole V 3 and magnetite λ 3 and is inverse relative to amphibole V 1 and magnetite λ 1 . The magnetite FT foliation strike parallel to the amphibole FT foliation and magnetite DA foliation, however, is more steeply inclined. Fabric parameters show that magnetite FT is oblate, whereas the AMS fabric is prolate, amphibole FT and magnetite DA are triaxial. (c) CB-46A1. The amphibole V 1 plots close to the k 1 and R 1 principal axes. The magnetite shape fabric is distinctly oblate and dips shallowly to the west and the anisotropy of magnetic susceptibility (AMS) k 1 principal axis is located on the magnetite V 1 and V 2 girdle. However, the AMS foliation is steeply dipping and is similar to the magnetite DA foliation. (d) CB-55A1. The V 1 , V 2 of the amphibole and magnetite crystals population and the k 1 , k 2 , R 1 , R 2 AMS, AIRM and AARM principal axes, as well as the magnetite λ 1 and λ 2 plot along a NW-SE girdle. All fabrics analyzed are parallel as indicated by the tightly clustered short (x 3 ) axes of the different fabrics. (e) CB-61B2. All fabrics are oblate as indicated by the fabric shape factors. The magnetite fabric tensor (FT) foliation plane is oriented at a right angle to the magnetite DA and amphibole FT planes. The AMS, AARM and AIRM foliation is oriented between the magnetite FT and DA foliations.

The Origin of the Magnetic Fabrics
Depending on their relative strength and orientation, the magnetite SPO and DA and amphibole SPO either constructively or destructively interfere to produce the AMS fabric in our samples. If all petrofabric elements are coaxial (CB-55), the AMS P′ is relatively large and the AMS T reflects the near rotational oblate shape of the mineral shape fabric (Figure 7d). In samples where the magnetite DA and amphibole SPO are coaxial and their foliations are oriented perpendicular to the magnetite SPO foliation (CB-15 and 61) the AMS P′ is also moderate to strong (Figures 7a and 7e). The distinct differences in the orientation of the petrofabric components may result in a AMS fabric dominated by some components of the petrofabric (CB-15) or magnetic fabrics that represent a mix of the components of the petrofabric (CB-61). However, when the magnetite DA, magnetite SPO and amphibole SPO foliations strike parallel, but have different inclinations (CB-19 and 46) the AMS P′ is weak (Figures 7b and 7c). The competition between the components of the petrofabric may therefore neutralize the degree of anisotropy and the AMS ellipsoid shape.
The larger P' values of the AARM and AIRM tensors compared to the AMS tensor are expected and reflect magnetic anisotropies of the remanence carrying phases (cf. Jackson, 1991;McCabe et al., 1985;Stephenson et al., 1986) (Figure 7 and Table 2); the high bulk magnetic susceptibility of our samples (>10 −3 SI) and the positive correlation between AMS, AARM and low-field AIRM indicates that the AMS signal is primarily controlled by MD magnetite (Stephenson et al., 1986). Yet, the amphibole FT and AMS are largely co-axial in our samples (Figure 7). Single-amphibole-crystal AMS show that the k 1 axis may correlate with the short or intermediate axes (crystallographic a and b axis) of a amphibole crystal and hence not with the macroscopic shape fabric (long axis lineation, c axis) for amphibole of a given composition (Biedermann et al., 2015. This may hamper the direct correlation between the amphibole FT (its SPO) and AMS. However, magnetite inclusions in paramagnetic minerals have been suggested to amplify the mineral AMS signal, which is likely due to the fact that the inclusion shape reflects the shape of the host-silicate crystal and cleavage planes (Lagroix & Borradaile, 2000;Renne et al., 2002;Selkin et al., 2014). The small size of micrometer-scale magnetite inclusions (likely SD/SP grains) in amphibole alteration rims in our samples precludes any analysis of their SPO due to the resolution of our µXCT data. Yet, the AMS signal may be largely controlled by their shape and/or spatial distribution (DA), this would explain why AMS and amphibole SPO results are often coaxial when the magnetite SPO is non-coaxial. Plagioclase is the most abundant phenocryst phase in the Cerro Bayo trachyandesite and it has previously been shown that plagioclase host magnetite inclusions, which may affect the magnetic fabrics of a rock (cf. Ageeva et al., 2020;Feinberg et al., 2006). However, compared to the amphibole phenocrysts, few magnetite inclusions are observed within plagioclase phenocrysts in the Cerro Bayo samples (cf. Figure 1b); we therefore consider that the amphibole related fabrics are more likely to influence the magnetic fabrics of the samples rather than the plagioclase related fabrics.
Information on the expected SP/SD contribution to each sample's magnetic fabrics is garnered from its coercivity spectra because SD magnetite has higher coercivity than MD magnetite (Dunlop & Özdemir, 1997). CB-19 and 46 display relatively higher coercivity and require fields of 300-600 mT to achieve 95% saturation. In contrast CB-15, CB-55 and CB-61 are saturated in fields ≤300 mT ( Figure S3). Together with the susceptibility temperature dependence experiments (Figures 2k-2o), these data suggest that SP/SD magnetite makes a relatively greater contribution to the magnetic fabrics of CB-19 and CB-46. Notably, the components of the MD magnetite petrofabric in CB-19 and 46 are non-coaxial (Figures 6 and 7). These components are expected to interfere destructively with each other and result in a lower degree of anisotropy. To investigate the fabric of higher coercivity grains in our samples we employed pAARM. In all samples except CB-19, the pAARM R 1 and R 2 plot along the AMS k 1 -k 2 girdle ( Figure S5, Table S2). The R 1 and R 2 pAARM principal directions of CB-19 plot on a NE-dipping girdle and the pAARM R 2 axes have flipped position with the AIRM and AARM R 3 axes (Figures 7b and S5). In CB-19, the magnetic fabrics are inverse relative to the three components of the petrofabric, however, the fabric is not magnetically inverse as indicated by the co-axial k 1 and AARM R 1 (Figure 7e). Hence, the AMS fabric of CB-19 is the result of the destructive interference between petrofabric components, which lowers the degree of anisotropy and causes higher coercivity magnetite grains, likely SD, to influence the position of the k 1 axis. The magnetic fabrics in CB-19 may thus be classified as intermediate fabrics (cf. Ferré, 2002), due to the competing components of the petrofabric and the MD and SD (magnetite) magnetic fabrics.

The Role of the Distribution Anisotropy
In our samples, the AMS fabric shows a clear correlation to the spatial distribution (i.e., DA) of magnetite. As previously established, the effect of the DA of magnetite on AMS becomes significant when ferrimagnetic grains are located close enough to each other to magnetically interact (Cañón-Tapia, 1996, 2001Gaillot et al., 2006;Grégoire et al., 1995Grégoire et al., , 1998Hargraves et al., 1991;Stephenson, 1994). The DA of amphibole, although being a fabric element that is easy to see in the field, is therefore not significant since amphibole is paramagnetic and does not interact magnetically. About 50%-60% of the magnetite crystals in the analyzed samples are located close enough to their neighbors to interact magnetically (see Section 4.1.), which validates the observed effect of the DA on the AMS ellipsoid. Our results further corroborate the results of the two-crystal experimental setup of Gaillot et al. (2006), which showed that the degree of anisotropy of AMS becomes stronger when the DA is parallel to the SPO compared to when the DA is not parallel to the SPO of magnetite crystals. The presence of discordant magnetite DA can overtake the magnetite SPO, leading to AMS sub-fabrics, a good example of this relationship is the CB-61 AMS foliation plane (Figure 7e). Notably, neither AARM nor low-field AIRM are coaxial to the magnetite FT in samples with competing magnetite components of the petrofabric 19,46 and 61). Instead, they display a similar relationship to the magnetite DA as the AMS fabric. This suggests that the magnetic interaction between MD magnetite grains can also influence the AARM and AIRM fabrics.

Implications for the Interpretation of the Anisotropy of Magnetic Susceptibility Fabric
Our results indicate that if rocks include clustered magnetite grains, DA may be the dominant factor controlling AMS, even if a sample is volumetrically magnetically dominated by MD magnetite crystals. Silicate SPO may also contribute to the AMS fabric in samples with high magnetic susceptibility if SP/SD magnetite is present in mineral breakdown rims and in inclusions. In our samples, the degree of anisotropy reflects how each petrofabric component contributes to the AMS and anisotropy of remanence fabrics. Samples with relatively high degrees of anisotropy have subfabrics that constructively interfere, that is, the DA is parallel to the mineral shape fabrics (FT, OT) of the sample. In the samples with low degrees of anisotropy, different components of the petrofabric are generally non-coaxial and destructively interfere with each other. The AMS may then (a) reflect a combination of shape and DA fabrics of magnetite; (b) be dominated by one petrofabric element, but is influenced to some extent by the other sub-fabrics; or (c) be affected by SD/ SP ferrimagnetic grains and result in inverse fabrics relative to the SPO and DA of MD magnetite.

Conclusions
In this study we investigated the source of the AMS, AARM and AIRM fabrics in the Cerro Bayo trachyandesite by using µXCT and novel and established statistical methods to analyze the petrofabric. Specifically, magnetite in the Cerro Bayo trachyandesite occurs in clusters, which makes it an ideal target to test how far DA influences the orientation and shape of the AMS, AARM and AIRM tensors in a rock dominantly carrying MD magnetite. Our results show that: • The AMS fabric is related to three components of the petrofabric in the Cerro Bayo trachyandesite: The amphibole shape fabric, magnetite shape fabric and magnetite spatial distribution. • The DA of magnetite may dominate the AMS, AARM and AIRM fabrics when MD magnetite is the main magnetic carrier. This indicate that clusters of magnetite that magnetically interact behave as single crystals and can bias the magnetic fabrics. • Amphibole SPO may have a secondary effect on the AMS of the samples. The DA of SP/SD magnetite in amphibole breakdown rims and as inclusions can affect the overall AMS fabric and essentially reflects the amphibole SPO.
The quantitative information provided by µXCT, can therefore help guide the interpretation of AMS and AARM, and considerably improve the use of AMS and AARM as quantitative fabric indicators.