Tectonophysics 724–725 (2018) 93–115

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Tectonophysics

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Olivine-antigorite orientation relationships: Microstructures, phase T boundary misorientations and the effect of cracks in the seismic properties of serpentinites ⁎ Luiz F.G. Moralesa, , David Mainpriceb, Hartmut Kernc a Scientific Center for Optical and Electron Microscopy (ScopeM), ETH Zürich, Auguste-Piccard-Hof 1, HPT D9, 8093 Zürich, Switzerland b Géosciences Montpellier, Université Montpellier 2, Place Eugène Bataillon, Batîment 22, 34095 Montpellier, France c Institut für Geowissenschaften, Universität Kiel, 24098 Kiel, Germany

ARTICLE INFO ABSTRACT

Keywords: Antigorite-bearing rocks are thought to contribute significantly to the seismic properties in the mantle wedge of Serpentinite subduction zones. Here we present a detailed study of the microstructures and seismic properties in a sample of EBSD antigorite-olivine schist previously studied by Kern et al. (1997, 2015). We have measured crystallographic Olivine-antigorite transformation orientations and calculated the seismic properties in three orthogonal thin sections. Microstructures indicate that Phase boundary misorientation deformation is localized in the bands with high antigorite fractions, resulting in strong crystallographic preferred Effect of cracks in seismic properties orientations (CPOs) with point maxima of poles to (100) parallel to lineation and poles to (001) to the foliation Subduction normal. Olivine CPO suggests deformation under high temperature and low stress, with a [100] fiber texture. The CPO strength varies with grain size, but is strong even in fine-grained antigorite, and larger grains tend to display higher internal misorientation. Orientation relationships between olivine and antigorite are evident in

phase boundary misorientation analysis, (100)ol||(001)atg being more frequent than [001]ol||[010]atg. Two new orientation relationships between olivine and antigorite have been documented. Seismic velocities decrease while anisotropy increases with increasing antigorite modal content. Antigorite grain shape has a weak effect on seismic velocities, but it is important on anisotropy. Comparison between CPO-derived seismic velocities using Voigt, Reuss, Hill averages and geometric mean only showed good agreement in 1/3 of experimental velocities. If the crack porosity of 1.63% measured experimentally at 600 MPa was used in the self-consistent model with two crack orientations with planes normal to Z and Y, good match with all experimental velocities was achieved. The self-consistent model implies important crack porosity in the foliation plane at 600 MPa that reduces Vp normal to the foliation by 0.3 km/s.

1. Introduction et al., 2013; Scambelluri and Philippot, 2001). In particular, antigorite is stable up to pressures of 5 GPa and temperatures around 600 °C In the last 15 years, the minerals of the serpentine group (chrysotile, (Ulmer and Trommsdorff, 1995), it may contain up to 13 wt% of water lizardite and antigorite) have been receiving increasing attention due to in its crystal structure, and its dehydration and subsequent water re- their importance in subduction zone dynamics (e.g. Peacock and lease play an important role in triggering partial melting in the mantle Hyndman, 1999; Hacker et al., 2003a, b; van Keken, 2003; Hyndman wedge (e.g. Ulmer and Trommsdorff, 1995; Green II, 2007). and Peacock, 2003; Faccenda et al., 2009; Hilairet and Reynard, 2009; Currently, there is a debate over the mechanisms responsible for Katayama et al., 2009; Bezacier et al., 2010; Boudier et al., 2010; deformation of antigorite in the mantle wedge (e.g. Escartin et al., Chernak and Hirth, 2010; Plümper et al., 2012; Reynard, 2013; 1997; Hilairet et al., 2007; Chernak and Hirth, 2010; Auzende et al., Amiguet et al., 2014; Auzende et al., 2015; Guillot et al., 2015; Nagaya 2015; Amiguet et al., 2014). Much of this discussion is related to the et al., 2016). Serpentine polymorphs are stable over a wide range of P “brittle-ductile” transition in antigorite, as brittle features such as and T conditions, and are found on multiple levels in subduction zones fractures, kinking, and grain crushing have been observed at high P-T as a direct expression of mantle wedge hydration (e.g. Ulmer and experimental conditions (e.g. Auzende et al., 2015; Amiguet et al., Trommsdorff, 1995; Hacker et al., 2003a, b; Evans, 2004; Schwartz 2014). Nevertheless, the relative mechanical strength of antigorite at

⁎ Corresponding author. E-mail address: [email protected] (L.F.G. Morales). https://doi.org/10.1016/j.tecto.2017.12.009 Received 26 June 2017; Received in revised form 5 December 2017; Accepted 11 December 2017 Available online 10 January 2018 0040-1951/ © 2018 Elsevier B.V. All rights reserved. L.F.G. Morales et al. Tectonophysics 724–725 (2018) 93–115 geological strain rates is much lower than olivine, and for this reason it Table 1 is expected that deformation will localize in antigorite, rather in the Area fractions of olivine and antigorite determined by EBSD in thin sections YZ, XZ and mantle phases (Hirth and Guillot, 2013). This is evident when one looks XY. at the deformation features in serpentinized mantle rocks, where de- ⊥X section YZ ⊥Y section XZ ⊥Z section XY Average formation is mainly accommodated by antigorite (e.g. Hirauchi et al., 2010; Soda and Takagi, 2010; Padrón-Navarta et al., 2012; Soda and Olivine 0.32 Olivine 0.25 Olivine 0.09 Olivine 0.22 Wenk, 2014; Brownlee et al., 2013; Morales et al., 2013; Nagaya et al., Antigorite 0.68 Antigorite 0.75 Antigorite 0.91 Antigorite 0.78 2014). δ Large magnitude shear wave-splitting delay times ( t = 0.2 to 1.4 s) We have performed microstructural analysis and crystallographic with trench parallel Vs1 polarization directions have been observed in preferred orientation (CPO) determinations on three orthogonal thin many subduction zones (e.g. Long and Silver, 2008; Long, 2013). One sections cut parallel and normal to macroscopic fabric elements X, Y generally accepted hypothesis is that these shear wave-splitting ob- and Z. In this reference frame, X is parallel to lineation as defined by servations are related to a strong preferred orientation of antigorite in magnetite elongation and shape preferred orientation of antigorite the mantle wedge and its highly anisotropic single crystal elastic flakes, Y is normal to lineation (X) within the foliation plane, and Z is properties (e.g. Katayama et al., 2009; Bezacier et al., 2010, 2013; normal to foliation, defined by the alignment of platy antigorite grains. Mookherjee and Capitani, 2011; Marquardt et al., 2015). In fact, recent Morales et al. (2013) – Tectonophysics, 594, their Fig. 5) speculated advances in the determination of elastic properties of antigorite, cou- that due to the topotactic olivine-antigorite orientation relationship in pled with antigorite CPO determinations have led to a plethora of pa- two different planes and consequent control of olivine on the antigorite pers about the seismic properties of antigorite bearing rocks (e.g. CPO, the actual lithospheric mantle foliation and lineation in partially Hirauchi et al., 2010; Jung, 2011; Morales et al., 2013; Nagaya et al., serpentinized mantle rocks is at 90° from the antigorite foliation. In this 2014; Watanabe et al., 2014). These data have been complemented case, the mantle foliation is a vertical N-S plane in the pole figures, and ff with ultrasonic measurements in di erent types of serpentine-rich ag- the lineation is a horizontal line, also N-S. Therefore, the mantle gregates via pulse transmission methods (Christensen, 1989, 2004; lineation is parallel to the pole of antigorite foliation in the pole figures, Kern, 1993; Kern et al., 1997, 2015; Ji et al., 2013; Shao et al., 2014). and the mantle foliation is orientated at 90° to the antigorite foliation ff These two methods di er in how the seismic properties are determined. reference frame. The “mantle reference frame” is indicated in red in the For CPO-derived seismic properties (e.g. Mainprice, 1990, 2007), the olivine pole figures. crystal orientations, single crystal elastic constants, the volume of each The CPO measurements of antigorite and olivine were acquired phase and their densities are taken into account in the calculation of the using automatic indexation of EBSD patterns in a scanning electron aggregate elastic tensor. The computation of the wave speeds Vp, Vs1 microscope (e.g. Adams et al., 1993; Prior et al., 1999). The thin sec- and Vs2, with Vp > Vs1 > Vs2, and orthogonal polarization direc- tions were polished via standard methods. Final chemical-mechanical ff tions are calculated using the Christo el equation for each propagation polishing was performed for 2 h with an alkaline solution of colloidal direction. In the ultrasonic method, an elastic wave of known frequency silica on a neoprene-polishing pad. The EBSD measurements were ff is propagated in di erent directions through the volume of rock, and conducted with a FEI Quanta 3D FEG SEM equipped with an EDAX-TSL the travel time is measured by transducers (e.g. Kern et al., 1997; Ji EBSD Digiview camera and the OIM/TSL version 5.31 software (Adams et al., 2013). The experimental data (Vp, Vs1, Vs2 and their polariza- et al., 1993). The measurements were conducted on uncoated thin tions) describe the seismic properties of the rock as a whole, which sections with the SEM operating at low-vacuum conditions (10 Pa of results from the mineral properties and their volume fractions, but also H2O vapor). The acquisition parameters included: accelerating voltage from the presence of micro-cracks, pores, layering and open grain of 20 kV, beam current of 8 nA, working distance of 10 mm and step boundaries, which are sensitive to hydrostatic pressure. sizes of 0.5 μm. For the antigorite indexation, we have used the struc- To shed light on the microstructural evolution of antigorite-bearing ture determination of Capitani and Mellini (2006) with relatively short rocks and to compare seismic properties results from the two ap- a-axis of 35 Å length, which is typical of antigorite at high metamorphic proaches described above, we have performed detailed microstructural grade, as found in the Val Malenco region (Mellini et al., 1987). To analysis and calculations of seismic properties in three orthogonal thin optimize the indexation of antigorite, we have performed the mea- sections from the sample 987 from Kern (1993) and Kern et al. (1997, surements with an image binning of 2 × 2 and a 160 pixel Hough 2015). We also present misorientation analysis in phase boundaries binning. In these conditions, between 7 and 12% of the diffraction (antigorite-olivine) and shape-preferred orientation in terms of crys- patterns acquired during measurements were not indexed properly. tallography of antigorite, and we describe new orientation relationships In order to compare the CPO and seismic properties results in a between olivine and antigorite. common reference frame and investigate the effect of sectioning, we have rotated the datasets obtained in XY and YZ sections into the XZ 2. Sample and analytical methods reference frame commonly used for reporting CPO data in structural geology. All pole figures are presented in this reference frame, in which The serpentinite sample studied here was prepared from the same the plane of the stereonet is the XZ plane, normal to the foliation and block of serpentinite (sample 987) used by Kern et al. (1997, 2015) and parallel to the lineation. The orientation distribution functions (ODF), comes from Val Malenco (Western Alps, Northern Italy). The Malenco pole figures, misorientation, and seismic properties were calculated and serpentinites are antigorite-rich rocks that equilibrated at upper plotted using the MTEX toolbox for Matlab, version 4.2 (Hielscher and greenschist facies and possibly represent the hydrated subcontinental Schaeben, 2008; Mainprice et al., 2011). We have used the raw data as ff mantle of the Adriatic lithosphere (Trommsdor et al., 1993). The obtained from the measurements, and for the calculations we have ff general chemistry of the protolith is lherzolitic (Trommsdor and considered only indexed points with confidence index (CI) higher than Evans, 1980), and several generations of metamorphic minerals can be 0.1. The ODFs were calculated with axially symmetric de la Vallee fi identi ed. The upper greenschist assemblages occur not only as Poussin kernel, with half-width of 10° (band-width of 28 in spherical medium grained serpentinites as in this study, but also in veins. In the harmonic coefficients). The ODF texture index, also called the J-index fi eld, these rocks have strong variations in composition and micro- (Bunge, 1982) was quantified in two ways. Firstly we used the Boot- structures, and mantle mineralogy is still preserved in some areas as strap method (e.g. Efron and Tibshirani, 1993), which is non-para- small crystals of olivine, clino and orthopyroxene. The studied sample metric approach to statistical inference. To characterize the antigorite contains only antigorite and olivine (area fractions given in Table 1), J-index as function of grain size, we ran 1000 statistical experiments, with minor amounts of magnetite and chlorite (> 1%).

94 L.F.G. Morales et al. Tectonophysics 724–725 (2018) 93–115 each randomly sampling 200 grains with replacement from the total stiffness tensor of ith inclusion and Csc is self-consistent solution for population of 3051 grains in the XZ section. Replacement in this context aggregate. Using this ratio (Ai) we can define the ensemble averages of means any grain may appear multiple times in the one sample, which is stress 〈σSC〉 and strain 〈εSC〉 where the standard procedure for the Bootstrap method. For each random in= in= sample of 200 grains we calculated the ODF and the J-index. From these SC SC SC SC SC −1 〈〉=σVCAεVAσε∑∑iii,,C 〈〉=ii =〈〉〈〉 fi data, we calculated the mean and the ± 95% con dence intervals. For in= in= (1) reference we also calculated the ODF and J-index for all grains using sc sc their area weighting. Secondly, we calculated the ODF of all grains As the solution for C occurs on both sides of the equation, the C is using the mean orientation for each grain, also known as the “one point found by iteration (e.g. Mainprice, 1997). The seismic properties were per grain” (oppg) method. This method reduces the influence of larger plotted in the same antigorite structural reference frame described grains with respect to smaller grains as no grain area weightings are above. To assess the role of olivine and antigorite on the seismic ff used. From the oppg ODF we calculated the ODF J-index and pole properties of the studied sample in di erent sections, we have varied figure texture indices (PfJ) for (001), (100) and (010). the modal content of both phases between 0 and 100% with 10% steps, We also calculated the grain orientation spread (GOS), which is in a similar way as the rock recipe modeling of Lloyd et al. (2009).To ff based on the calculation of misorientation of each orientation pixel verify the e ect of antigorite grain shape on the seismic properties and with respect to the mean orientation of the grain. The GOS is then the to have a better approximation to the Hashin-Strickman formalism, we ff ff average of all misorientation angles from the grain mean orientation. have performed di erential e ective media (DEM) composite modeling The misorientation between grain boundaries (antigorite-antigorite, of olivine and antigorite (e.g. Mainprice, 1997; Morales et al., 2013; olivine-olivine) and phase boundaries (olivine-antigorite) were also Watanabe et al., 2014). The DEM has been shown to give estimates of determined from the EBSD data. We have developed a new approach the elastic properties of composites that lie within the Hashin- for shape preferred orientation (SPO) analysis, where orthogonal long, Shtrikman upper and lower bounds (McLaughlin, 1977). We calculated intermediate and short axes of antigorite crystals are plotted in the several olivine and antigorite elastic constant end-members using the antigorite crystallographic reference frame as an inverse pole figures VRH and SC schemes. For olivine with an ODF texture index of 1.83 x (IPF). As the EBSD maps are 2D entities, the intermediate axes pre- uniform, the VRH has Vp and Vs anisotropies 5.3% and 4.0%, respec- sented here were calculated as the cross product of the long and short tively. For the olivine SC with spherical grains, the values of Vp and Vs axis vectors extracted from these maps. Grain sizes were determined are exactly the same as VRH. For antigorite with an ODF texture index from the EBSD maps and are given as 2D equivalent diameter, without of 8.33 x uniform the VRH has Vp and Vs anisotropies 29.0% and 31.4% any geometrical correction (see Heilbronner and Barrett, 2014). For the respectively. For the antigorite SC with spherical grains, the values of grain size calculations, we considered a cut-off misorientation angle of Vp and Vs anisotropies are exactly the same as VRH, just like olivine. 10° and a minimum number of indexed pixels of 10 per grain. Antigorite has more pronounced grain shape than olivine, so we used ff fi For the calculations of the elastic properties of the aggregates we two di erent speci cations of the grain shape. Firstly, we used the grain fi used the complete EBSD datasets and the elastic constants of olivine shape speci ed in sample coordinates X:Y:Z = 10:10:1 that results in all (Abramson et al., 1997) and antigorite (Bezacier et al., 2010). The antigorite grains shapes being exactly parallel the foliation plane. Sec- fi elastic constants for the aggregates were averaged via the Voigt-Reuss- ondly, we used the grain shape de ned along orthogonal crystal- Voigt Reuss −1 lographic reference frame in each grain, such that a*:b:c = 10:10:1. For Hill scheme, where C =[∑iViC(gi)], C =[∑iViS(gi)] and CVoigt-Reuss-Hill =(CVoigt +CReuss) / 2. We also calculated the geometric shape X:Y:Z = 10:10:1 the Vp and Vs anisotropies 31.6% and 34.3% mean, which can be described by CCgdVGeometricMean = exp[1 ∫ ln ( ) . respectively. For the shape a*:b:c = 10:10:1 the Vp and Vs anisotropies V i ff The mathematical details of the aforementioned methods can be found 30.6% and 34.2% respectively. All these calculations indicate the e ect in Matthies and Humbert (1993, 1995), Mainprice and Humbert (1994) of grain shape does not result in large variations of Vp and Vs aniso- and in the recent review of methods by Almqvist and Mainprice (2017). tropy and even VRH average would provide reasonable end-member for In these equations, the local stiffness tensor is C(g ) and S(g ) is the olivine and antigorite. We calculated two end-members using the Hill i i ff compliance tensor, with orientation defined by Bunge Euler angles averages for aggregate elastic sti ness tensors, one for olivine a second for antigorite, using their respective CPO in the sections XZ, YZ and XY gi={φ1Φ φ2}, and volume fraction Vi. The local compliance tensor is given by S(g ). A physical estimate of the moduli should lie between the and then rotated the tensors into a common reference frame of XZ. We i ff Voigt and Reuss average bounds, as the stress and strain distributions have averaged the elastic tensors of the three di erent sections for are expected to be somewhere between uniform strain (Voigt bound) olivine and antigorite, and used these data as end-members for the DEM and uniform stress (Reuss bound). Hill (1952) observed that arithmetic model. The model was performed by incrementally adding inclusions of mean of the Voigt and Reuss bounds, sometimes called the Hill or Voigt- polycrystalline antigorite to the background of polycrystalline olivine ff Reuss-Hill (VRH) average, is often close to experimental values. The and then recalculating the new e ective background olivine-antigorite averages of Voigt, Reuss, Hill and Geometric mean allow direct com- tensor at each increment to construct the two-phase composite model. parison with previous results of Kern et al. (2015) using the Geometric The tensor equations for DEM is as follows: mean. As Kern et al. (2015) reported a crack porosity of 1.63% at a DEM dC 1 DEM fi = ()CCi − Ai con ning pressure of 600 MPa, we also use the self-consistent method dV(1− V ) (2) to model the effects of open cracks on the seismic properties. The self- consistent (SC) method has been formulated in several ways; here we To evaluate the elastic moduli (CDEM) at a given volume fraction V will use the scheme proposed by Willis (1977). The SC method is based one needs to specify the starting value of CDEM, which is the olivine on introduction of elastic inclusion (e.g. grains, cracks etc.) into to a aggregate end-member elastic stiffness tensor. To obtain accurate re- − background matrix, which is estimated using the average elastic tensor sults, a small volume increment of dV = 10 3 was used; further tech- of the all crystals in the aggregate. The elastic ellipsoidal inclusion nical details can be found in Mainprice (1997). In summary, to examine problem was solved by Eshelby (1957) by using a Green's function 4th the effect of antigorite grain shape on the seismic properties of an an- rank tensor G and evolves the numerical ellipsoidal integration in three tigorite bearing rock, we have progressively added “inclusions” of an- dimensions for the general case. In the formulation of Willis (1977) he tigorite with constant aspect ratio in specimen coordinates of introduces a simple ratio (Ai) to relate the strain inside and outside the X:Y:Z = 10:10:1 (flattened crystals parallel to the foliation) to the oli- sc −1 inclusion as Ai = [I + G(Ci − C )] . In this equation, I is 4th rank vine background medium. We then recalculated the new effective unit tensor Iijkl = 1/2 (δik δjl + δil δjk), where δik is the Kronecker delta, media properties at each step, for different compositions, from 0% to G is the symmetrical 4th rank tensor Green's function, Ci is the elastic 100% antigorite.

95 L.F.G. Morales et al. Tectonophysics 724–725 (2018) 93–115

Fig. 1. Optical microstructures of the sample 987 in the XZ surface. (a) Irregularly spaced banding with alternating highly and weakly orientated antigorite crystals. Note the sharp contact between bands. (b) The strong foliation is marked by the dimensional alignment of antigorite plates with at least two orientations indicated by the blue and red colors. (c) Olivine porphyroclasts are still visible in some regions with strong antigorite foliations wrapping around them. (d) Domains are characterized by the typical interpenetrating texture of antigorite with two dominant orientations at high angle to each other. (e) Locally well-developed intersecting foliations are also observed. (f) At higher magnification the grain boundaries are better visualized in thin sections that are slightly thicker than 30 μm standard thin sections. (g) In the section XY grain boundaries are not visible, apart some flakes in weakly orientated domains. (f) The dominant blue/red colors when using the gypsum plate confirm the strong preferred orientation observed in hand specimens. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

96 L.F.G. Morales et al. Tectonophysics 724–725 (2018) 93–115

the regions with weaker foliations the antigorite flakes can be fairly large and may reach lengths of 500 μm(Fig. 1d). In detail, the anti- gorite crystals may present undulate extinction and locally subgrain boundaries (Fig. 1d), while the olivine crystals that occur in the lenses present intense fracturing oblique to the main olivine foliation (Fig. 1c). In the section YZ the foliation is apparently not very strong and a number of antigorite crystals appear at high angles to the main folia- tion. Due to the sectioning normal to the lineation and the foliation, the aspect ratio (visually determined) of the antigorite is much smaller than in the sections parallel to the lineation (Figs. 1f and 2). The presence of two orientations of antigorite flakes is clearly seen with the aid of the gypsum plate, with the dominant orientation appearing as blue/pink and a less common orientation appearing as yellow or green. Grain boundaries are better visualized in slightly thicker thin sections. In the section parallel to the foliation (XY), grain boundaries in antigorite are barely visible and it is hard to see individual antigorite flakes, but the dominance of blue or pink colors confirm the presence of a strong preferred orientation. Subgrain boundaries are easily seen in this sec- tion, and appear as a smooth variation on the blue colors when the gypsum plate is inserted. The microscopic inspection of the three or- thogonal sections (Figs. 1 and 2) gives clear evidence for marked micro- inhomogeneity of our sample. The area fractions of olivine and antigorite were determined using the EBSD data from the three perpendicular sections (Table 1), each area representing approximately 2 mm2. The olivine area fractions vary from 0.09 in the XY section to 0.32 in the YZ section, with an average value of 0.22 for the 3 sections. The antigorite area fractions vary from 0.68 in the YZ section to 0.91 in the XY section with average of 0.78 for the 3 sections. The average values for the olivine area fraction could be expressed as 0.22 (+0.10, −0.13) and for the antigorite as 0.78 (+0.13, −0.10), so that a difference of about 10% would occur if only one section was used to determine the area fractions. The modal pro- portions determined by EBSD compare fairly well to those obtained by point counting by Kern (1993) and Kern et al. (1997) in three ortho- gonal sections of the same sample used here.

3.2. Crystallographic orientations

Fig. 2. “3D orientation maps” for antigorite and olivine constructed from 2D EBSD sec- The CPO of antigorite is very strong, as can be seen in the or- tions orientation maps on three orthogonal tectonic sections normal to lineation X (YZ ientation maps, where each section shows grains with similar colors section to the left), normal to Y (XZ section to the right) and normal foliation Z (XY the (Fig. 2). The antigorite CPO occurs with two different patterns. The CPO top section). All the EBSD data from 3 maps were collected with the same step size of measured directly on the XZ and YZ sections is characterized by an μ fi 0.5 m. (a) Orientation maps colored using inverse pole gure (IPF) color code (see text). orthorhombic symmetry distribution with the poles of (001) parallel to (b) Phase maps showing the distribution of antigorite in red and olivine in green. The edges of maps do not join due to material loss during thin section preparation. (For in- the pole of the foliation (Z), the poles of (100) parallel to the lineation terpretation of the references to color in this figure legend, the reader is referred to the (X) and the poles of (010) parallel or slightly oblique to Y (Fig. 3). The web version of this article.) CPO measured on the section XY section on the other hand describes a fiber texture with poles of (001) defining the symmetry axis parallel to 3. Results Z axis, with continuous girdles of (100) and (010) parallel to the fo- liation, with the maxima of (100) parallel to the lineation and the 3.1. Microstructures maxima of (010) parallel to Y (Fig. 3). The sum of the CPO measured in the 3 sections and plotted in the XZ reference plane describes again a fi In the XZ section, the dominant structure is an irregularly-spaced, ber texture slightly weaker than the one measured in the XY plane. In fi mm-scale banding (Fig. 1a) where a strong foliation marked by the all the antigorite pole gures, the stronger CPO is given by the maxima dimensional alignment of antigorite crystals (Fig. 1b) is interleaved of (001) poles. The J-index of the antigorite CPO is always > 8 x uni- with bands of weakly orientated antigorite blades. The contact between form and tends to increase with increasing grain size, up to a maximum μ these two bands is sharp, and in our specimen both bands occur in of ~16 x uniform when the grain sizes are between 20 and 25 m approximately equal proportions. While the bands with strong foliation (Fig. 4). The J-index calculated from the ODF of all grains in the or- are dominated by antigorite that locally wrap around elongated lenses ientation map of the XZ section is slightly lower than the average J- fi of olivine crystals (Figs. 1c and 2), in the bands with weaker foliation index quanti ed via the Bootstrap method described above. The CPO of the antigorite occurs mixed with remnants of olivine. In these bands, individual sections does not exactly match the CPO measured by syn- ff there are two orientations of antigorite flakes lying at an angle between chrotron X-ray or neutron di raction due to poor counting statistics of 60° to 90° to each other, resulting in an interpenetration texture (Wicks an individual section (Kern et al., 2015, their Fig. 5), but the combined fi and Whittaker, 1977; Hirauchi et al., 2010)(Fig. 1d). Antigorite grain data from 3 sections compares favorably with the pole gure distribu- sizes are quite variable; the regions with stronger foliations normally tions and times uniform values of the antigorite CPO reported by Kern have smaller grains (between 10 and 100 μm-Figs. 1b and 2), while in et al. (2015). Due to the small volume fraction of olivine in their sample, they did not report the olivine CPO.

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Fig. 3. Pole figures of crystallographic preferred orientations of antigorite and olivine for the 3 orthogonal sections. For monoclinic antigorite, the pole of (100) is not parallel to [100] and the pole of (001) is not parallel [001], whereas the pole of (010) is parallel [010]. Nevertheless, as beta (the angle between a-axis and c-axis) is 91.16°, the angular differences are small, and the angular difference between the pole of (100) to [100] and the pole of (001) to [001] = 1.16°. The data from YZ and XY sections have been rotated into the X to the right and Z to the top reference frame after acquisition. Additionally we had to rotate the XY sample due to a mirror effect during sample preparation. The data from XZ, YZ and XY in common XZ reference frame have been summed and renormalized and displayed as the ‘TOTAL’ pole figures. Scale is given in multiples of uniform distribution (MUD), X, Y and Z represent the tectonic reference frame based on the antigorite foliation and lineation, and the maximum concentration is given for individual pole figures in top left on each pole figure. Note that, as we assume that the mantle foliation-lineation is at 90° to the antigorite foliation, the olivine pole figures have a red vertical N-S plane and a red horizontal line that should be used as reference for reading the olivine pole figures. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The olivine CPO is more variable than antigorite, but the [100] axes (Fig. 5d) shows that olivine has no real correlation between GOS and are either concentrated in maxima predominantly parallel to the pole of grain diameter, whereas antigorite displays a weak correlation between the antigorite foliation, or along discontinuous single girdles spreading GOS and grain diameter, probably reflecting their different origins. The from Z to Y. The [001] axes are distributed in discontinuous girdles newly undeformed small grains of antigorite crystallized from olivine. parallel to the antigorite foliation, with maxima parallel to the anti- As the transformation from olivine to antigorite proceeds during de- gorite lineation, while [010] axes have a more complex distribution formation, the structure of antigorite becomes progressively more dis- with no clear pattern. From the pole figure analyses there is a clear torted, and hence larger antigorite grains tend to have higher GOS orientation relationship between the maxima of poles of (001)atg and values. [100]ol and poles of (100)atg and [001]ol in all the sections, which be- The misorientation angles of the olivine-antigorite phase boundaries comes more obvious when all the sections are added together (Fig. 3). and antigorite-antigorite grain boundaries are presented as measure- ments in the form of histograms for neighboring crystals (red bars in the histograms), classically called correlated misorientations. The calcu- 3.3. Misorientation and shape preferred orientation lated theoretical uncorrelated misorientation is given as the blue line in the histograms of Fig. 6. This distribution is calculated in the MTEX In the maps, there is a clear predominance of low Grain Orientation toolbox directly from the ODF spherical harmonic coefficients as an Spread (GOS) for both phases, particularly for the fine-grained anti- uncorrelated misorientation distribution function (MDF). The un- gorite and olivine (Fig. 5a and b respectively). The plot of mean GOS vs. correlated theoretical distribution only reflects therefore the influence grain diameter (Fig. 5c) shows that most grains of antigorite or olivine of the CPO and nothing else. Such an approach differs from the nu- have a very low GOS of about 0.5°, except for one olivine grain with merical random finite number of sampling methods used by some mean GOS of 2.3°. The plot of individual GOS vs. grain diameters

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uncorrelated and uniform distributions, with peaks at 90° and 120°, well above the calculated distributions (Fig. 6a–d). The grain boundary map showing the olivine-antigorite boundaries with No.4 Burgers misorientation relationship is shown in Fig. 6d. The approximate mis- orientation angles associated with Burgers relationships 1 to 4 are marked on the XY section histogram, both coinciding with the very strong maxima in the histogram at 90° and 120° (Table 4). The uniform misorientation axes distribution for olivine-antigorite phase boundaries has a complex form as shown in Fig. 7a. The dis- tribution's fundamental region requires an entire upper hemisphere due to the combination of the orthorhombic symmetry of olivine and the monoclinic symmetry of antigorite. In addition, there is the constraint that grain 1 (olivine) cannot be exchanged with grain 2 (antigorite) because they are clearly different physical entities. Therefore, there is no exchange symmetry across a phase boundary (e.g. Morawiec, 1997). The principle axes [100], [010] and [001] of olivine are conveniently used as axes for this space as they are orthogonal, and all labels refer to the olivine reference frame unless otherwise specified. The olivine [100], [010] and [001] directions have the minimum times uniform value of ~0.7 x uniform. A maximum value of 1.6 x uniform is found along the approximate integer directions < 12 6 10 > . These direc- tions are marked with the misorientation axes of the associated No.1 and No.3 orientation Burgers relationships and their symmetry equivalents marked by ‘*’ (Fig. 7a, see Table 2 for further details). In the Fig. 7b–d the measured axes distribution for all misorientation angles (ω) between 0° and 120° are plotted for the sections YZ, XZ and XY respectively. In agreement with the histograms of Fig. 6, the axes distributions of sections YZ and XZ are also similar (Fig. 7), and show a weak preferred orientation, with a maximum of 2.6 x and 2.1 x uniform, respectively. Weak maxima occur close to the misorientation axes of No.1, 2 and 4 Burgers relationships. In Fig. 7d the misorientation distribution of the XY section shows an extremely strong preferred orientation with max- imum of 17 x uniform. In the XY section the misorientation axes of No.1, 3 and 4 Burgers relationships show strong maxima of about 10 to 12 x uniform. All maxima lie approximately in the planes normal to − [504] or [504], and both planes intersect with [010] axis. The strongest − − maximum is however parallel to both the[594] in olivine and [1144] antigorite crystal reference frames. As in the XY section antigorite re- ff presents 91% of the area, we plot the pole figures of antigorite to clarify Fig. 4. (a) Antigorite ODF texture index (J-index) for di erent grain size intervals for bins − with at least 200 grains using a random sampling from total population of 3051 grains the nature of [1144] direction of antigorite in sample coordinates. The − and Boot strapping method to calculate the ± 95% confidence intervals (see text for pole figure of [1144] shows a similar maximum as the [010], which is details). Note the trends of texture index with grain size are similar for mean 200 grains normal to maxima in [100] and [001] pole figures. and all grains in XZ section. (b) The texture ODF index and pole figure texture indexes The misorientation angle distribution ω for antigorite is presented were calculated using an ODF defined mean orientation per grain with no area weighting, – also called one point per grain (see text for details). The variation of the pole figure in Fig. 8a c, together with the calculated distribution of uncorrelated indices for (001), (100) and (010) show that (100) and (010) have weaker indices and and uniform distributions. As the analysis is for antigorite-antigorite (001) has much higher x uniform values, this to be expected because of the axial (001) boundaries, exchanging grain 1 (antigorite) with grain 2 (antigorite) is fiber texture of the antigorite. The ODF index and all pole figures indices show a similar permitted and the misorientation space is half that of misorientation μ μ evolution with grain size, with minimum near 10 m and maximum near 20 m. All between olivine and antigorite (e.g. Morawiec, 2004). In this case, the measurements in XZ section. −− − misorientation axes [uvw]or[uvw] are equivalent and hence the mis- orientation axes are represented in half of the upper hemisphere commercial EBSD packages. The uncorrelated theoretical distribution (Fig. 8d–o). The measured correlated misorientation angle histograms can be calculated for a single phase (using the ODF of olivine) or be- in the range from 0° to 180° for the monoclinic symmetry of antigorite tween phases (using the ODFs of olivine and antigorite). The uniform (Fig. 8a–c) do not agree well with the calculated uncorrelated or uni- distribution (green line) on the other hand is calculated via the MDF form angle distributions. The angle histogram for the YZ section using an analytically calculated uniform ODF for any crystal symmetry (Fig. 8a) shows a moderate peak of approximately 10% at low mis- (Fig. 6). This line essentially shows the misorientations expected in the orientation angles (< 15°) corresponding to misorientations within case of a uniform misorientation distribution of grains in an aggregate antigorite grains as defined in this study. At the other extreme, the (e.g. Morawiec, 1997). histogram bin corresponding to 180° misorientation angles has a fre- The angle distributions for sections YZ and XZ are very similar, with quency of 35%, the highest values found in any section. Misorientation a central peak at 90° in all three distributions. There is a very close angles from 15° to 170° have low frequencies (~2.5%). The angle his- agreement between all distributions with calculated uniform distribu- togram for the XZ section (Fig. 8b) shows a different pattern, with very tion. In the XZ section the maximum at 90° is slightly higher than the high frequency of low misorientation angles (~18%) and two other bins uniform distribution. The angle distributions in the XY plane are very with higher frequencies at 60° and 120. The angle histogram for the XY different, and the neighbor misorientation differs considerably from the section (Fig. 8c) shows another different pattern, with high frequency of

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Fig. 5. Grain orientation spread (GOS) for antigorite (a) and olivine (b), with maximum spread of 3°. The grains with highest GOS in antigorite have very high axial ratio. Although on average these values are rather low, there is a progressive increase of the GOS with increasing grain size (c, d). In addition, the values are slightly higher for antigorite and tend to increase for larger grain sizes. low misorientation angles (~12%) and two other bins with high values the YZ section has its maximum at [001] with a value of 90 x uniform, at 60° and 120° with frequencies of 4% and 23%, respectively. It is whereas XZ and XY sections have their maximum at {100}, with values remarkable that each section has a different misorientation angle dis- 60 x and 90 x uniform in XZ and XY, respectively. tribution pattern and none agree with the calculated uncorrelated or The microstructure associated with peaks in the MDF sections at uniform distributions. ω = 60°, 120° in XY and 180° in the YZ plane are shown in Fig. 9a–d. The low misorientation angles below the 15° grain boundary seg- The [001]/60° misorientation boundaries are mainly composed of long mentation angle are illustrated using a fixed angle of 5°. All sections at straight lines in Fig. 9a. In contrast the [001]/120° misorientation ω = 5° have a similar axes distribution with a maximum value near the boundaries in Fig. 9b are composed of short straight segments forming [010] axis, with the highest maxima value for the XZ section. MDF approximately circular domains. The density of [001]/120° boundaries maximum values at ω = 5° correlate with the frequency of low angle is clearly much greater than [001]/60° in agreement with the angle misorientations for each section, as shown in the Fig. 8a–c, with XZ histogram (Fig. 8c) for the XY section. For the microstructure associated (17%), XY (12%) and YZ (10%). The presence of low misorientation with misorientation peaks ω = 180° in YZ, MDF shows two peaks, the − subgrain boundaries in antigorite and wavy contacts between olivine- strongest one associated with poles (100) and (100), and a weaker one antigorite are also observed in TEM scale. associated with [001]. In Fig. 9c we have plotted the boundaries for Now we can consider the MDF sections at ω = 60° and 120°, that (100)/180° and in Fig. 9d the boundaries for [001]/180°. Clearly these appear as misorientation angle peaks for XZ and XY. In the Fig. 8g–i, for two figures give the same physical boundaries on the map. MDF sections at ω = 60°, and in the Fig. 8j–l for MDF sections at The shape preferred orientation analysis of antigorite shows a wide ω = 120°, the patterns are similar, with section YZ showing no mis- distribution of the long axes (aspect ratios from 2:1 to 8:1), pre- orientation near [001] and moderate peak of 20 x uniform near [100], − dominantly parallel to the poles of (310) and (410), with a secondary (100) and (100) or family of {100}. In contrast, the 60° and 120° MDF concentration parallel to the poles of (001) (Fig. 11a). The poles of sections show an identical pattern with a single strong peak near [001] intermediate axes (Fig. 11b) are less spread and concentrate pre- with values of 90 x uniform for XZ and 150 x uniform for the XZ and XY dominantly parallel to (410), while the short antigorite axes (Fig. 11c) sections. Finally, for ω = 180°, the misorientation axes are strongly are very strongly correlated parallel to the pole of (001). parallel to {100}, as well as [001]. There are however, differences as

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Fig. 6. The correlated olivine-antigorite phase boundary misorientation. Angle histograms for the YZ, XZ and XY sections, where the red bars show the misorientation between neighboring olivines and antigorites (correlated distribution), the blue line shows the misorientation of non-neighbor pairs (uncorrelated distribution) and the green line shows the theoretical misorientation distribution in the case of a random crystallographic orientation. The No.1, 2, 3, and 4 mark the approximate misorientation angles for Burgers orientation relationship misorientations given in Table 2 on the histogram for the XY plane. The position of the boundaries with No.4 orientation relationship misorientation are marked on EBSD map of the XY plane in red. The antigorite-antigorite boundaries in blue are most common and olivine-olivine boundary are quite rare in green. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 7. The olivine-antigorite phase boundary misorientation angles and axes. Panel a shows the calculated phase boundary misorientation axes for uniform distribution for all angles from 0° to 120°. Note here the fundamental region for MDF is the upper hemisphere. The peaks of this uniform distribution are nearly coincident with misorientation axes for phase transition given in Table 2. Panels b, c and d are measured misorientation axes for YZ, XZ and XY sections respectively for all angles between 0°–120°. The axes for all phase transform misorientation relationships have been marked by a number (1 to 4) and their crystallographic directions in the olivine reference frame, except for No.4 where the direction in the − − antigorite frame is also indicated. Panel e shows the MDF section at an angle of 93° used to confirm the rotation about [594] in olivine and [1144] in antigorite. The black outline on this figure is the boundary of the minimum misorientation angle used to determine the limit of the fundamental region of the olivine-antigorite orientation relationship. Panel f are antigorite − pole figures for XY section illustrating the orientation of the [1144] axes in relation to the other pole figures in sample coordinates. All contours in x uniform.

Table 2 3.4. Seismic properties Parallel planes and directions in the olivine to antigorite phase transformation for Burger orientation relationships No.1, No.2, No.3 and No.4. Our initial modeling was done using the Voigt, Reuss, Hill and

No. Olivine parent Antigorite daughter [Axis]/angle geometric mean methods, which only take into consideration the vo- lume fractions and the single-crystal elastic tensors and crystal or- 1 (100) (001) [12 −6 10]/119.33° ientations in the sections measured by EBSD. We made plots of Vp and − a [001] [010] [ 12 6 10]/120.67° Vs in the three sections YZ, XZ and XY planes. For each plot we also 2 (010) (001) [−100]/90.01° [001] [010] Nonea marked the velocities measured by Kern et al. (2015) and given in their 3b (100) (010) [−12 6 10]/119.33° Table 2 for sample Cube A #755 block measured at 600 MPa, with a [001] [100] [12 6 10]/120.67°a black square and velocity label. We used the average composition given b 4 (010) (210) [−594]/93.00° by the EBSD data on three orthogonal sections with Antigorite 78% and – a [100] [001] [5 94]/94.13° Olivine 22%, ignoring the minor phases and crack porosity as done by

[Axis]/angle pairs are given in the olivine reference frame. Kern et al. (2015). a Equivalent by symmetry for orthorhombic-monoclinic symmetry of olivine to anti- The Vp calculated for sections YZ and XZ have pronounced max- gorite phase transition. imum and minimum values due to the dominant fiber texture of the b Not previously reported by Boudier et al. (2010). antigorite (Fig. 12a–b). On the other hand, Vp in the foliation plane XY is nearly constant with changing propagation direction X to Y, as

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Fig. 8. The antigorite-antigorite phase boundary misorientation angles and axes. Panels a–c show the misorientation angle histograms for YZ, XZ and XY sections, where the red bars show the misorientation between neighbor grains (correlated distribution), the blue line shows the misorientation of non-neighbor pairs (uncorrelated distribution) and the green line shows the theoretical misorientation distribution in the case of a random crystallographic orientation. Panels d–f are MDF fundamental region sections at ω = 5° for YZ, XZ and XY sections, respectively. The fundamental region is half of the upper hemisphere. Panels g–i are MDF sections at ω = 60° for YZ, XZ and XY sections, respectively. Panels j–l are MDF sections at ω = 120° for YZ, XZ and XY sections, respectively. Panels m–o are MDF sections at ω = 180° for YZ, XZ and XY sections, respectively. All contours in x uniform. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) expected for the antigorite fiber texture with axial symmetry along Z// for transverse isotropic macroscopic sample symmetry. Vp propagation to (001) of antigorite, leading to a transverse isotropic macroscopic direction Y is very close to the Reuss average velocity, where as Vp in X sample symmetry (Fig. 12c). However, the difference between the direction is close the Hill average (Fig. 12c) as seen in XZ-plane. modeled and measured Vp along the Z direction is about 0.3 km/s, In the Fig. 12(d–f) the results for S-waves are more complex as the lower than Reuss lower bound velocity, whereas the Vp in Y direction is results are shown as Vs1 > Vs2. The convention of Kern et al. (2015) close to the Reuss average (Fig. 12a). In the XZ plane the Vp along Z for S-waves is VsYX where the first index (Y) is the orthogonal transverse direction is 0.3 km/s slower than Reuss lower bound velocity, and the direction defining the polarization plane and second index (X) is the velocity of in the X direction is very close to the Hill average (Fig. 12b). propagation direction. Therefore there are two polarization directions In the foliation XY plane the P-velocities are nearly constant as expected for the three propagation directions, resulting in six possibilities

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Fig. 9. Antigorite misorientations along the [001] at angles 60° and 120° in the XY section and along the (001)/180° and the [001]/180° in the YZ section. Figure (a) is the [001]/60° misorientation shown as red lines, (b) is the [001]/120° misorientation shown as magenta lines, (c) is the (001)/180° misorientation shown as yellow lines, while (d) the [001]/180° misorientation shown as cyan lines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

propagating along X,Y and Z: (VsYX,VsZX), (VsXY,VsZY) and (VsYZVsXZ). the three Vp velocities in X,Y, and Z directions and six S-wave velocities In section YZ plane (Fig. 12d), as the propagation direction changes and polarizations. The only good matches we obtained are VpX from Z to Y, there is a change in S-wave polarization from VsXZ along Z (7.68 km/s), and VsYX (4.46 km/s), both with propagation along the X to VsXY along Y at 55° from Z, causing the high and low velocities in the direction, and VsXY (4.55 km/s) with direction Y. middle of plot. A similar situation occurs in the plane XZ, (Fig. 12e) as In Kern et al. (2015) they used a composition of Antigorite 95% and the propagation direction changes from Z to X at 60° from Z, where Olivine 5% as determined by X-rays and Neutron diffraction. We have polarization VsYZ changes to VsYX. In the YZ and XY planes the VsXY and reproduced this using the Voigt, Reuss, Hill and geometric mean VsYX are well matched by the Hill average and geometric mean. The methods. The associated figure in given the Supplementary Material measured velocities VsXZ and VsYZ are ~0.3 km/s below the Reuss (Fig. S2). The match of Vp along X,Y and Z directions are very good for lower bound for Vs2. In the XY plane the measured VsZX and VsXZ are Hill average and the almost as good for geometric mean. The match for both lower than Reuss lower bound for Vs2 by 0.3 km/s. VsXZ,VsXY,VsXZ,VsYZ and VsXY are excellent for geometric mean. For The match between measured and modeled velocities is poor. A the XY plane the VsZX and VsZY are good match to Vs2 with the geo- good match would be when the Hill average and geometric mean match metric mean. Although there is a good agreement between measured

104 L.F.G. Morales et al. Tectonophysics 724–725 (2018) 93–115 and modeled seismic properties assuming 95% olivine and 5% anti- 4. Discussion gorite, this composition is rather different from the ones reported by earlier papers on the same sample (e.g. Kern, 1993; Kern et al., 1997), 4.1. Antigorite CPO which are more similar to the composition measured here by EBSD. As mentioned above, Kern et al. (2015) reported a crack volume of The microstructures and crystallographic orientations of the olivine- 1.63% at 600 MPa. Can the inclusion of cracks reconcile the differences antigorite schist studied here provide strong evidence of deformation between the Kern et al. (2015) and the composition measured by EBSD localization during the breakdown of olivine to antigorite in a sub- here? To guide our crack model we examined the main failures of the duction zone environment in Val Malenco, related to subduction and VRH and geometric mean for composition of Antigorite 78% and Oli- related magmatism (e.g. Trommsdorff et al., 1993; Ulmer and vine 22% (Fig. 13). As the most important indicators, we have used the Trommsdorff, 1995). The initial breakdown of olivine to antigorite due Vp values in the X, Y and Z directions, because P-waves are more to hydration probably started in a static environment under relatively sensitive to cracks than S-waves (e.g. Anderson et al., 1974). In YZ and high temperatures, as supported by (i) the presence of bands of anti- XZ planes the velocities are much higher for Vp-Z and also significantly gorite with interpenetration texture (Wicks and Whittaker, 1977; high for Vp-Y. In the XY plane the value of Vp-X is well matched by the Hirauchi et al., 2010 - Fig. 1a, d); (ii) the relatively coarse-grain size of Hill average, suggesting no crack plane normal in this direction. Svitek antigorite in these regions (Fig. 1c–d) and the presence of olivine in et al. (2017) also report that in the lineation direction (X), which has lenses without any evidence of orientation relationship (Fig. 1c). The the highest velocity direction of the sample, increases in quasi-linear static hydration of olivine and development of antigorite seems to be trend with increasing pressure, which indicates that there are no crack relatively common in the replacement of olivine by antigorite (Hirauchi plane normal to the X direction. Hence we constructed three self-con- et al., 2010; Morales et al., 2013). The transformation of olivine to sistent models; (i) SC1, using the antigorite 78% and olivine 22% or- antigorite is topotactically controlled, as demonstrated by Boudier et al. ientations with spherical grain shapes; (ii) SC2, using SC1 as the (2010) and Plümper et al. (2012) and by the presence of several Burgers background medium that hosts one crack plane normal to the Z axis. misorientation relationships between olivine and antigorite (Fig. 7, The crack shape in specimen coordinates of X:Y:Z = 5:5:1 is aligned Table 2). with foliation plane and (iii) SC3, using SC1 as the background medium From the microstructures, it is not possible to define the relative hosting two cracks, one normal to Z axis and another normal to Y axis, timing between the beginning of olivine replacement and the de- with shapes X:Y:Z = 10:10:1 and X:Y:Z = 10:1:10 respectively. In both formation, and most probably both processes occurred together for SC2 and SC3, the crack porosity is 1.63%. some time. The transformation starts by the growth of antigorite crys- The P-wave values calculated for SC2 and SC3 matched the ex- tals with blade-like forms often along olivine sub-grain boundaries that perimental values (Fig. 13, suggesting that a range of crack shapes is dissect the olivine grains e.g. Boudier et al. (2010) and Brownlee et al. present. The experimentally determined S-wave values are either mat- (2013). The olivine grains that are reduced in size by dissection and the ched by SC1 or SC3, which illustrates that S-waves are not sensitive to antigorite grains that are newly grown are mechanically weaker than cracks when matched by SC1 or quite sensitive to cracks when matched olivine at transformation temperatures. Hence the deformation loca- by SC3. The SC models suggest that cracks play a significant role in lizes in the regions where the mechanically weaker antigorite has reducing Vp and Vs velocities in this sample. This simple crack model started to form and the olivine grain size has been reduced. The two matches the experimental data, but it is probable that there are several processes operate sequentially, first with the olivine hydration and solutions to match the experimental values as only three orthogonal transformation to antigorite and then deformation localization. This is directions were used for measurements. indicated by the lack of olivine in the more deformed bands, which The modeled compressional (Vp) and fast shear wave (Vs1) velo- suggests that deformation was initially localized in the undeformed cities vary slightly in the different sections with similar compositions mixture of antigorite and olivine. With progressive deformation, olivine (Fig. 14a,b) and all the values given here are the maximum values grains are consumed more efficiently in these bands until their com-

(Vpmax., Vs1max.). We have plotted the line for Vp and Vs based on plete disappearance. These bands are characterized by almost pure experimental measurements of isotropic antigorite aggregates given by antigorite with small grain sizes, strong CPOs and small grain orienta- Christensen (2004) at a pressure of 1 GPa and temperature of 500 °C. tion spread (Figs. 1b, 5), clearly indicating strong localized deforma- For low antigorite content, the XY section has the highest Vp, followed tion. In the coarse-grained antigorite, intracrystalline microstructures by the XZ and YZ sections, whereas for Vs1, XY and XZ have similar such as undulose extinction and low misorientation boundaries are also values. For both Vp and Vs1, the velocity decreases with increasing observed (Figs. 1h, 5). The presence of subgrains is confirmed in the amount of antigorite (Fig. 14a, b). The Vpmax varies between 8.9 km/s TEM images (Fig. 10a). in the olivine-rich aggregate of the XY section to 7.7 km/s with 100% of The antigorite CPO is very strong and has approximately orthor- antigorite in the XY section (Fig. 14a). The Vs1max varies between hombic sample symmetry, different from the pattern produced by the 5.0 km/s in the XY section in the olivine-rich aggregates, to 4.3 km/s expected [hk0] (001) slip in sheet silicates (Fig. 3), and suggests strong when antigorite is the dominant phase in the XY section. The maximum activation of dislocation glide. The strong alignment of (001) planes difference between Vs1 and Vs2 (dVs) varies between 0.2 km/s in the parallel to the foliation and poles to (100) parallel to the lineation YZ section when only olivine CPO is considered, to 1.3 km/s in the XZ suggests that the main active “macroscopic” slip system in the studied section, considering 100% of antigorite. The results of our differential sample was (001)[100] with the lineation X||[100] and the poles of effective media composite model (Fig. 14 - DEM) show that the shape of (001) parallel to Z. The “macroscopic” slip system has been previously the antigorite crystals has little effect on the seismic velocities, and a reported in many other studies (Katayama et al., 2009; Van de Moortele slightly stronger effect on dVs values, particularly for intermediate et al., 2010; Padrón-Navarta et al., 2012), but differs from the work of antigorite volumes (30–80%). Jung (2011), Hirauchi et al. (2010), Nagaya et al. (2014), Brownlee The Vs1 propagation is complex when olivine is the main phase, but et al. (2013) and Soda and Wenk (2014), who reported lineation the polarization direction tends to be parallel to the foliation (Fig. 15). X||[010] and pole to foliation Z||⊥(001). The samples VM1 and VM2 of The addition of antigorite leads to the development of a plane of Jung (2011) are particularly interesting because they also come from transverse isotropy parallel to the foliation, and the main Vs1 polar- Val Malenco, the same area as our sample. In this region, a wide variety ization direction stays parallel to the antigorite foliation, which is also of antigorite-rich rocks occur, with large variations in compositions and parallel to the polarization direction observed in the olivine-rich ag- microstructures affected by regional and local contact metamorphism gregates (Fig. 15). (Mellini et al., 1987). The variation in CPO possibly results from the structural differences in antigorite with metamorphic grade as shown

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and olivine with typical mean values of 0.5°. The CPO strength in the studied samples varies with grain size, with high values for grain sizes ~5 μm, followed by a reduction for larger grain sizes ~10 μm, and then an increase to grain sizes up to 25 μm (maximum value where we had at least 200 grains for the calculations). The Boot strapping method with ± 95% confidence intervals (Fig.4) suggest that the variation of CPO strength with grain size is a robust result and shows that strong CPO for fine-grained antigorite is an im- portant feature of microstructure. The trends for J-indexes are similar when using all grains, random statistical sampling of 200 grains sam- ples or mean orientation per grain with no area (Fig. 4). In this sample we have almost all GOS with values of < 0.5°, meaning that the mean orientation is very representative of the grain orientations, which could explain the similar trends in Fig. 4. The small antigorite grains probably formed in single large olivine grains, which would explain the strong orientation control, even if several orientation relationships were active (e.g. Fig. 1b, h). Such an effect contradicts the observations of Soda and Wenk (2014), who suggests that EBSD detects individual, well-crystal- lized antigorite crystals, and does not index the fine, randomly oriented antigorite grains. For this reason, they suggest that X-ray goniometry gives a true, but weaker texture (e.g. Kern et al., 2015). As demon- strated in the orientation maps, we have measured orientations in an- tigorite in both fine and coarse-grained material, and the fine-grained material has also a very strong CPO. Although there is a small differ- ence on the real values (< 1 x uniform) between the two methods of CPO strength calculations presented here, it is clear that the number of grains does not have a major effect on the CPO strength quantification based on the ODF for the whole aggregate. A potential problem in the EBSD measurements of Soda and Wenk (2014) is the poor indexation of antigorite (~30% in one sample) that might be due to the antigorite structure of their sample. It is more difficult to index antigorite with long a-axis lengths (typical low-grade metamorphism) than short a-axis, which are typical of high-grade metamorphism in the sample studied here. Although the orientations of olivine are relatively easy to measure with EBSD, antigorite is a very complex phase, because the a-axis in the unit cell varies from 33 to 81 Å. This variation has a very strong effect on the Kikuchi band angles. In addition, the structure file for indexation needs Kikuchi bands with hkl indices up to 25, which makes its auto- matic indexation very difficult. Amiguet et al. (2014) reported the grain size reduction and other brittle processes in all their experiments, and interpreted their ob- servations as the result of ineffi cient intra-crystalline deformation to Fig. 10. Plot of long (a), intermediate (b) and short (c) antigorite axes in the antigorite accommodate the imposed strain at relatively fast experimental strain crystal reference frame, for the section XZ. The long and intermediate axes of antigorite rates. These features were not observed in our samples, nor in any other are predominantly parallel to the poles of (310) and (410), while the short axes are naturally deformed antigorite aggregates studied so far. The authors dominantly parallel to the pole of basal (001) planes. All contours in x uniform. argued that dissolution-precipitation is likely to occur as a form of ac- commodation mechanism, which cannot be discarded in our samples by Mellini et al. (1987). Some caution however should be taken when and in a number of antigorite occurrences e.g. Wassmann et al. (2011). using the CPO to define the “macroscopic” slip system. For example, a Evidence for such a mechanism in the studied sample are unclear be- TEM study by Amiguet et al. (2014) reported conjugated slip systems cause the foliation in our samples is very strong and not affected by − [101](101) in experimentally deformed antigorite, giving a “macro- later cleavages, with no concentration of precipitated material in the scopic” slip system similar to [100](001). This is because the cross fold hinges or fluid inclusions as described by Wassmann et al. (2011). − product between the slip direction [101] and slip plane (101) gives Nevertheless in high-resolution TEM, the interface between antigorite misorientation axis [010], which is associated to dislocation tilt and olivine is very wavy (Fig. 10c), contrary to what was observed in − boundaries composed of pure edge dislocation for [101](101) slip. Fur- Boudier et al. (2010) and Plümper et al. (2012). Our TEM images thermore if we take the cross product of the two known Burgers vectors suggest that these are corroded boundaries caused by partial dissolution − [101] and [101], we also have the misorientation axis [010] for the of olivine and transformation to antigorite e.g. Bukowska et al. (2015). dislocation twist boundary composed of pure screws dislocations. These Another possibility is that after a certain point in the transformation of observations suggest that antigorite deformed by a complex combina- olivine to antigorite, the topotactic relationships are reduced or com- tion of dislocation creep, dynamic recrystallization and phase trans- pletely eliminated, as the olivine fraction and olivine-antigorite inter- formation, leading to intense grain size reduction, strong CPO devel- faces are greatly reduced and many new antigorite-antigorite interfaces opment and deformation localized in bands. It is also well established develop. fi that there is thermal annealing related to regional and contact meta- In contrast to what we have described in our pole gures (Fig. 3), morphism in the Val Malenco area (Mellini et al., 1987; Trommsdorff Brownlee et al. (2013) shows that the poles to (001) planes of antigorite fi et al., 1993), which may explain the very low GOS values in antigorite may also be distributed as incomplete girdles in the pole gures. Ac- cording to the authors, this pattern possibly result from antigorite

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Fig. 11. (a) TEM bright field image of two antigorite crystals of different orientations, showing glide planes in the crystal on the left, together with possible thin kink-bands (marked by arrow), and the antigorite basal planes in the crystal on the right; (b) some crystals with closely spaced glide planes may have some low angle grain boundaries, marked by the arrows. At HRTEM, the antigorite-olivine interface is wavy, and the contrast “patchy” on the antigorite side is due to beam damage. On the inset we present the FTT pattern across the whole image.

growth in veins, with (001)atg planes and [010]atg directions normal to belong to different crystallographic symmetries. More importantly, the vein walls. Similar (001)atg girdles were described by Hirauchi et al. through this approach we can study orientation relationships in sta- (2010) for their “transitional-type” serpentine (their Figs. 6 and 7), as tistically representative areas (e.g. an EBSD map), allowing the com- well as by Soda and Takagi (2010) and Soda and Wenk (2014). parison with very local observations from TEM analysis. The YZ and XZ sections have correlated distributions similar to the uncorrelated and 4.2. Olivine CPO uniform distribution lines, indicating that these sections are close to the uniform distribution with weak preferred orientations between the two The lack of crystal plastic microstructures such as subgrain bound- phases. There is a small peak above the uniform distribution in the XZ aries in the relic olivine, and the random distribution of low angle at ~90°, which could be assigned to No.2 or No.4 Burgers phase mis- misorientation axes in olivine may hinder the correct determination of orientation based only on the angles (Table 2). The correlated mis- the original olivine mantle flow plane and direction e.g. Morales et al. orientation angles between olivine and antigorite in the XY (foliation) ff (2013). When all the orientation data collected in individual maps is section were very di erent from the calculated uncorrelated and uni- added together and rotated to antigorite XZ reference, the olivine CPO form distribution lines (Fig. 6). Two major peaks above the uniform has a weak fiber texture, with the [100] point maximum parallel to Z, distribution occur at ~90° and ~120° misorientation angles. These two – – [001] of olivine is distributed along a girdle parallel to the antigorite peaks could be assigned to No.2 or No.4 90° and No.1 or No.4 120° foliation, with the maximum aligned with X, and [010] is distributed based only on the angles (Table 2). As the misorientation angle alone is ffi along a broad crossed girdle with secondary maxima parallel to X, Y insu cient to identify the complete misorientation, the misorientation and Z. In our case, however, it is difficult to know if the CPO still re- axes are plotted in Fig. 7. It is important to note that uniform dis- flects the mantle deformation (e.g. Wallis et al., 2011; Morales et al., tribution of the axes of olivine-antigorite has 4 peaks nearly coincident 2013), or if it was partially erased due to the intense sectioning of the with axes for No.1 and No.3 and their symmetrical equivalents. In olivine grains during the transformation to antigorite and meta- theory the equivalents (marked with circles in Fig. 7a) are just outside morphism in the Val Malenco area. The pole figures of total datasets the fundamental space, with angles of 120° and maxima of 1.6 x uni- give the most complete statistical description of the CPO available for form. The No.1 and No.3 symmetrical equivalents axes have mis- olivine (Fig. 3, bottom line). The olivine direction with the highest pole orientation angles of 120.6°. However, when the misorientation axes for – figure density of 5 x uniform is the [100], followed by [001] with angles between 0 and 120° are plotted for all 3 sections (Fig. 7b d), maximum density of 3.7 x uniform, and finally [010] is the poorly or- weak peaks are observed for YZ and XZ sections for No.1 and No.3 ientated with a maximum density of 2.6 x uniform. The total of the 3 misorientations, with a maximum value of ~2.5 x uniform in YZ sec- sections olivine CPO is of the D-type, also called axial-[100] or [100] tion. Parts of these peaks are related to the uniform distribution fiber geometry because the [010] and [001] both form girdles normal (Fig. 7a), so the orientation relationship signal is indeed very weak. The ff to [100]. The D-type is typical of low to high stress and (0kl)[100] slip situation for the XY section (Fig. 7d) is very di erent because the – systems in dry olivine (e.g. Tommasi et al., 2000; Le Roux et al., 2008). maxima range from ~0.5 x for No.2, ~2 x for No.3, ~10 12 x No.1 and The olivine CPO is less coherent when looking at 3 sections than the ~17 x uniform No.4. Until now only relations No.1 and No.2 have been antigorite. Olivine has the maxima of 7–6 x uniform in the individual recognized by Boudier et al. (2010) and Plümper et al. (2012), and sections reduced to 5 x uniform in the total CPO, whereas antigorite relations No.3 and No.4 have not been reported before. In Fig. 7d the maintains a value of 12 x uniform in the total CPO, compared to 11–14 No.2 and the newly discovered No.4 relationship are in fact between 10 x uniform of the individual. Such an effect is probably caused by the and 17 x uniform, and hence the best preserved in this deformed low olivine modal content in the sections, particularly in the XY section sample. The No.4 misorientation phase boundaries are shown on XY parallel to the antigorite foliation. section map in the Fig. 6. Here there are occasional straight segments and dense clusters of boundary as the olivine-antigorite boundary is discontinuous. The amount of preserved olivine-antigorite boundary is 4.3. Phase boundary misorientation quite small, with No.4 misorientation representing 16.3% of the oli- vine-antigorite boundary length (Table 3) in the XY section. In addition, Phase boundary misorientation analysis between olivine and anti- the No.4 relation is different from the others, with (010) ||(210) and gorite was performed in all 3 studied sections (Figs. 6, 7, 8). We de- ol atg [100] ||[001] , when defined in terms of Burgers orientation re- monstrate that phase boundary misorientation is a useful tool to study ol atg lationships. The parallel planes includes the {210} family of planes, orientation relationships between different phases even when they

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Fig. 12. Predicted seismic velocity models for composition of antigorite 78% and Olivine 22% in planes (a)YZ, (b)XZ and (c)XY for Vp and planes (d)YZ, (e)XZ and (f)XY for Vs using the Voigt, Reuss, Hill averages and geometric mean. Black squares indicated experimental velocities measured by Kern et al. (2015), the numbers next to the black squares are in km/s. Each plane covers propagation directions from a specific sample direction (Z 0°) to (Y 90°) for example in (a)YZ and in similar way for all sections. See text for further details.

−−−− −− − which have a multiplicity of 4 with (210), (210), (210)and (210).Ifwe No.1. If we now substitute antigorite (210)for (210) such a rotation will define the olivine (010) parallel to antigorite (210) as position No.1, be of 124.4° clockwise about the c-axis, relative to position No.2. Fi- − −−− and when we substitute antigorite (210) for (210), this will be equiva- nally if we substitute antigorite (210)for (210) we have again a clockwise lent to a clockwise rotation of 55.6° about the c-axis relative to position rotation of 55.6° about the c-axis relative to the position No.3. These

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Fig. 13. Predicted seismic velocity models for composition of antigorite 78% and Olivine 22% in planes (a)YZ, (b)XZ and (c)XY for Vp and planes (d)YZ, (e)XZ and (f)XY for Vs using the Self-consistent (SC) models. Black squares indicated experimental velocities measured by Kern et al. (2015), the numbers next to the black squares are in km/s. Each plane covers propagation directions from a specific sample direction (Z 0°) to (Y 90°) for example in (a)YZ and in similar way for all sections. Model SC1 is no porosity crack free model using the orientations of antigorite and olivine. Model SC2 has MC1 as background medium with 1.63% crack porosity with crack shape X:Y:Z = 5:5:1⊥Z. Model SC3 has MC1 as background medium with 1.63% crack porosity with crack shape X:Y:Z = 10:10:1⊥Z & X:Y:Z = 10:1:10⊥Y. See text for further details.

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Fig. 14. Seismic wave velocities of maximum compressional (Vp max) and maximum fast shear wave (Vs1 max), and the absolute difference between dVs max = |Vs1 − Vs2| in a given plane (XZ, XY or YZ) for Voigt-Reuss-Hill averages, resulting from the fabric recipe modeling, from 100% olivine to 100% antigorite, calculated for the three different sections. The colored region near 80% is the range of antigorite content of the sample 987. The differential effective medium (DEM) values are maxima in this 3D estimate of Vp, Vs1 and dVs are indicated by the black lines. The DEM antigorite inclusions have axial ratios of X:Y:Z = 10:10:1 with the shortest axis normal to the foliation. The experimentally determined relationships given by Christensen (2004) using isotropic end members of olivine and antigorite aggregates are shown as dark green lines only for Vp and Vs, as Vs1 = Vs2 in an isotropic aggregate. The red, light green, dark blue lines are Voigt-Reuss-Hill values for Vp max, Vs1 max and dVs max for the sections XZ, XY and YZ sections, respectively. The anisotropic values for the DEM and Voigt-Reuss-Hill models show non-linear relationships between Vp, Vs1 and dVs and antigorite content. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) rotation angles vary between 55.6° and 124.4° for antigorite with a-axis relationship, a potential rotation about the c-axis may exist, depending length of 35.02 Å. As 55.6° + 124.4° = 180° it is possible the rotations on the chosen {210} plane. Note that the two parallel directions in the about the antigorite c-axis of 56°, 124.4° and 180° could be generated orientation relationship misorientation No.4 are two directions that are by the multiplicity of {210} (see Supplemental Material Fig. S1). In the most highly aligned, [100] of olivine and [001] of antigorite (see case of the No.4 relationship, which is the most frequent orientation Fig. 3). It is also true that for the No.1 relationship, the most highly

Fig. 15. Variations in the propagation and polarization direction of the fast shear wave (Vs1) resulting from the fabric recipe, from 100% olivine to 100% antigorite, calculated for the orientation maps obtained in three orthogonal sections. Note the polarization of Vs1 parallel to the foliation XY plane with increasing with antigorite content. The calculations were carried after the data was rotated to the common tectonic reference plane XZ (YZ to XZ and XY to XZ). Seismic properties calculated via the Voigt-Reuss-Hill averaging scheme using the elastic constants of olivine (Abramson et al., 1997) and antigorite (Bezacier et al., 2010). All plots have the same reference frame as Fig. 3.

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Table 3 even if there is a slight difference in densities and their distributions. Olivine-antigorite boundary total lengths and percentages of boundary lengths for having The 180° in the YZ section is typically interpreted as twinning, but in XZ Burger orientation relationships No.1, No.2, No.3 and No.4 in thin sections YZ, XZ and and XY sections the 180° is interpreted as an indexing error. XY. To understand the MDF sections at 180°, we have chosen the YZ No. ⊥X section YZ ⊥Y section XZ ⊥Z section XY section because it has the highest peak at 180° in the misorientation angle histogram (Fig. 8a). The boundaries with misorientations of μ μ μ 1 Length 105 m Length 394 m Length 7629 m (100)/180° and [100]/180° in the YZ (Fig. 9c–d) generate identical Percent 0.12 Percent 0.19 Percent 7.36 2 Length 180 μm Length 161 μm Length 196 μm plots, showing that the boundaries are the same. The XY section has Percent 0.20 Percent 0.08 Percent 0.19 very high misorientation peaks at 60° and 120° (Fig. 9a–b), but the 3 Length 303 μm Length 606 μm Length 434 μm boundaries have very different morphologies. The [001]/60° bound- Percent 0.33 Percent 0.30 Percent 0.42 aries have quite long straight segments often parallel the long axis of 4 Length 609 μm Length 1993 μm Length 16,857 μm grains, whereas the [001]/120° have more complex clusters. The Percent 0.67 Percent 0.94 Percent 16.26 Total Length 1198 μm Length 3095 μm Length 25,117.0 μm [001]/60° boundaries look more like twin morphologies than the 1,2,3 & 4 Percent 1.32 Percent 1.51 Percent 24.23 [001]/120°, which looks more like a complex indexing error. As the antigorite orientation is controlled by the olivine parent grain or- Highest values highlighted by bold characters for Burger misorientation relationships for ientation, it is possible that we have an additional orientation re- given section and total scores for 1, 2, & 3. lationship (No.4 orientation relationship), with some of the ~60° and

~120° misorientations due to the multiplicity of {210}atg in the basal aligned planes are (100) and (001) in both phases. Hence the fre- ol atg plane as mention above. Clearly more detailed studies are needed to quency of No.1 and No.4 are directly related to the highly aligned understand the significance of 60° and 120° misorientation in anti- crystallographic directions in specimen coordinates as shown in the gorite. pole figures of Fig. 3. Only in section XY (foliation) these phase rela- tions are clearly seen, showing the particularity of this section for mi- crostructural analysis. Another feature clearly seen in Fig. 7f is the 4.5. Considerations of orientation relationships and antigorite − misorientations antigorite [1144] direction parallel to the No.4 misorientation axis, which is statistically centered on the [010] in sample coordinates in The Fig. 7d shows all the most significant features of phase transi- Fig. 7f. tion in the XY section, with the relative importance given by their density x uniform values. The contours give the orientation spread of 4.4. Antigorite boundary misorientation ~10° about calculated axes for the orientation relationship: − − −− − [12610], [100], [12610]and [594], all the axes in the olivine reference Here we investigated the misorientation of antigorite to better un- − ° derstand its plasticity and phase transformation. The correlated mis- frame and the symmetrical equivalents. Except for No.2 [100]/90 , all the other misorientations lie on planes normal to directions to orientation angle histograms in the YZ, XZ and XY planes in Fig. 8a–c − − give the first information. The three planes have very different corre- [504]or [504], where these directions are 6.3° from [101]or [101] re- lated angle histograms, with YZ having a very strong peak at 180°, XZ a spectively. In Fig. 7d the [010] direction of olivine is parallel to [010] very strong peak at very low angles and secondary peak at 120° and direction in antigorite. The conjugate glide planes and directions for ⟨ ⟩ finally the XY (foliation) plane has peaks at low-angles, 60° and 120°. antigorite 101 {101} system reported by Amiguet et al. [2014] share − To interpret the histograms we need to refer to the MDF sections at the the same zone [010]ol||[010]atg axis in Fig. 7d, as the olivine [ 504] − angles where the histogram peaks occur. [504] [101] and [ 101]. von Mises (1928) stated that for grains to fi For the peaks at low angles we have plotted the sections at 5° and all undergo an arbitrary plastic strain, ve independent slip systems are ⟨ ⟩ three section look very similar, with a high density parallel to [010], required. The antigorite 101 {101}slip system is however limited to which is the misorientation axis associated with slip system ⟨101⟩ plastic strains in the (010) plane and therefore other mechanisms are {101} determined by Amiguet et al. (2014). There is a slight variation required to accommodate deformation. Amiguet et al. (2014) also re- ported kinking, which could provide another misorientation me- in the maximum density 2.2 (YZ) to 4.0 (XY) to 6.0 (XZ) x uniform. One − would expect the XZ section to have the highest value, as the Y direc- chanism. We should point out that in antigorite, [101] and [101] slip − tion is normal to this section and the total pole figure for [010] has a directions are only 11° from the [100], and poles to (101) and (101) slip − high value (5.1 x uniform) in this direction (Figs. 3, 7). planes are only 10° from [001] and [001] directions in this phase. We also observed misorientation angle peaks at 60° and 120° in Fig. 8d–f shows that the [010] axis is the preferred misorientation for Fig. 8a–c, to which we calculate the MDF sections plotted in Fig. 8g–l. angles of 5°, typically associated with plasticity for all 3 sections. In the For both misorientation angles the densities are very high (~20 x − sample reference frame, the [010] antigorite axes are concentrated uniform), with maxima at poles (100) and (100). In the XZ and XY planes along Y in the foliation plane and normal to the lineation (Fig. 3). The − the densities are higher, around 80 x uniform for XZ and 150 x uniform [1144]atg of No.4 orientation relationship is aligned closely with [010]atg for XY. The main characteristic of the YZ section is that there are no (Fig. 7f). All together, these observations suggest that the dominant fi signi cant peaks at 60 and 120° and hence the lower MDF section misorientation axis in antigorite is [010]atg, aligned with the structural densities. The only significant misorientation is normal to (100) planes. Y axis. In addition, it seems clear that the No.4 orientation relationship In comparison, the XZ and XY sections have a high peak at 60° and 120° is more favored during the subsequent deformation process than the parallel to [001] axis, but no other significant axes. Some authors have second most frequent misorientation No.1. As observed in the Fig. 7d, assigned the 60° and 120° rotations about the [001] axis to EBSD mis- there is a clear relationship between the concentration of misorienta- indexing (e.g. Padrón-Navarta et al., 2012), which is certainly the tion axes parallel to a certain crystal direction and the angular distance simplest interpretation. Finally there is the case of the 180° rotations to [010] (the closer to [010], the higher is the orientation density in x about the [001] axes (Fig. 8m–o). The highest misorientation in all 3 − uniform). We speculate that this almost linear relationship gives some sections are (100), [001] and (100). In this section the interpretation is indication of the coupling between the antigorite deformation and complicated by the fact that (100)/180° is equivalent to [001]/180° due olivine hydration. While the No.4 represents 16.26% of the boundary to the presence of the orthogonal antigorite crystal symmetry axis of length, the No.1 relationship represents 7.36%, whereas No.2 and No.3 [010]/180°. This creates an orthorhombic type symmetry with 3 per- represent < 0.5% of boundary length in the section XY (Table 4). The pendicular two-fold axes, and hence all the plots at 180° look the same, data are rather limited, but the trend can be described as the highest

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Table 4 Parallel planes and directions in the olivine to antigorite phase transformation No.1, No.2, No.3 and No.4 angles from [010] and maximum densities in XY plane.

No. Olivine parent Antigorite daughter [Axis]/angle Percent length in XY plane [Axis] from [010] in XY plane Max. density x uniform

1 ***(100) ***(001) [12 −6 10]/119.33° 7.36% 126.53° (53.47°)+ ∼11 [001] [010] *[−12 6 10]/120.67° 53.47° 2 (010) (001) [−100]/90.01° 0.19% 90.00° ∼0.5 [001] [010] *None 3 (100) (010) [−12 −6 10]/119.33° 0.42% 126.53° (53.47°)+ ∼2 [001] [100] *[12 6 10]/120.67° 53.47° 4 (010) (210) [−594]/93.00° 16.26% 20.16° ∼17 ***[100] [***001] *[5–94]/94.13° 159.84° (20.16°)+

+ angle from [0–10]. *** directions with highest degree of alignment in olivine and antigorite.

~17 x uniform value at the lowest angle (20.16°) to [010], and the attenuation anisotropy, with the Q-factor varying significantly in lowest ~0.5 x uniform value at highest angle (90°) to [010]. The or- magnitude and orientation. The variations are probably caused by the ientation relationship creates a new antigorite orientation from olivine closing of micro-cracks due to action of increasing hydrostatic pressure, only once, with misorientation ranging from 90° to 120° (Table 2), with being most important in direction normal to the foliation (Z), but also in the most active No.4 orientation relationship having an angle of 93° and other directions. Although there is some doubt about the sample com- the No.1, 120°. Both No.4 and No.1 (Table 4) have directions and planes position, it is clear that microcracks are present (Svitek et al., 2017). with highest degree of alignment in olivine [100]ol (100)ol and [001]atg Given the number of composition measurements of the studied (001)atg. However, in the first step (i.e. time = 0) of the olivine-anti- sample, we assume that any value between 75 and 80% of antigorite gorite transformation, there was no antigorite. Therefore the strong and 20–25% of olivine is acceptable, with the measured crack porosity orientation of the [001]atg (001)atg antigorite has been somehow of 1.63% to be characteristic of Cube A #755, block measured at maintained during deformation. This involved misorientations No.4 600 MPa. Hence it is justified to use EBSD measured 78% antigorite and and No.1 and presumably misorientation axis [010]atg associated to the 22% olivine with crack porosity of 1.63% for our self-consistent model plasticity of antigorite. Localization of the initial transformation along to explain the experimental measurements. However, it does not ne- low (100)ol tilt boundaries (rather common in olivine) and dissection cessarily imply that this crack porosity is present in conditions in sub- along these boundaries to form antigorite have been reported by duction zones as typical pressures and temperatures are 500 to 600 °C Boudier et al. (2010), Plümper et al. (2012), Brownlee et al. (2013) and and pressures of 3 to 5 GPa (e.g. Iwamori, 2007). The remnant porosity/ others. In this case, a similar argument may hold for antigorite, as the crack is probably related to grain boundary porosity that is not elimi- activation of ⟨101⟩{101} slip system may generate tilt and twist nated until pressures of 10 kbar (1 GPa) in some cases (Christensen, boundaries with {101} planes only 11° from antigorite basal plane. 1974). It is well known from theoretical studies that small spherical pores are difficult to close even at very high pressure (e.g. Walsh, 1965). 4.6. A comparison between calculated and measured seismic properties The velocities of P- and S-waves are compatible with many other determinations of these properties in antigorite-rich aggregates (e.g. The comparison between the Voigt, Reuss, Hill and Geometric mean Hirauchi et al., 2010; Jung, 2011; Watanabe et al., 2014; Soda and for the composition given in the EBSD data (antigorite 78%, olivine Wenk, 2014; Kern et al., 2015). The small difference of Vp and Vs1 for 22%) is given in the Fig. 14. The good matches are VpX (7.68 km/s), the different sections (Fig. 14, see also Supplemental Material Fig. S2) is and VsYX (4.46 km/s), where both are propagation along the X direc- most probably the result of differences in the CPO strength of olivine tion, and VsXY (4.55 km/s) in the direction Y. Hence only 1/3 of pro- and antigorite. In addition, the CPO of olivine is different in each sec- pagation directions have a good match to the experimental measure- tion, which may also induce variations in the seismic velocities. The ments at a pressure of 600 MPa. Kern et al. (2015) reported a measured seismic velocities predicted through the DEM modeling (considering crack porosity of 1.63% at 600 MPa. Kern et al. (2015) used a compo- the shape of antigorite grains), are similar to the velocities calculated sition of antigorite 95% and olivine 5% measured by X-ray and Neutron assuming only variations in modal composition using Voigt-Reuss-Hill ff di raction to predict the velocities using the geometric mean and ig- averages. Nevertheless, the absolute difference between fast and slow nored the minor phases and the crack porosity. We have shown in the shear wave velocities is higher when considering the grain shapes, supporting material using antigorite 95% and olivine 5% and the geo- particularly in the compositional interval between 30 and 80% of an- metric mean gives a good match to the experimental data. However the tigorite ((Fig. 14), see Supplemental Material, Figs. S3 and S4). This is question remains what is correct composition and what is the impact of in agreement with the observations of Vasin et al. (2013), who showed the crack porosity on the experimental and modeled velocities. that aggregates with high axial ratio grains had higher elastic aniso- The antigorite and olivine fractions given by Kern (1993) using thin tropy than aggregates with same compositions and low axial ratio section point counting antigorite 75% and olivine 20% and further grains. analysis by Kern et al. (1997) report antigorite 74.9% and olivine The non-linear relationship between increasing modal content of 20.3%. Professor Kurt Mengel (University of Clausthal) kindly provided antigorite and decreasing seismic velocities results from the presence of a chemical analysis (H. Kern personal communication) that has been CPO in our sample, as also observed in similar studies published in the converted to volume fractions with antigorite 78.3% olivine 18.1% plus last few years (Katayama et al., 2009; Hirauchi et al., 2010; Jung, 2011; some minor phases. More recently Svitek et al. (2017) in detailed 3D Morales et al., 2013; Soda and Wenk, 2014). For comparison, we have distribution of P-wave velocity in 132 directions at 400 MPa and added the isotropic Vp and Vs velocities experimentally measured by measured anisotropy, which is consistent with volume fraction of an- Christensen (2004) at 1 GPa and 500 °C for isotropic olivine and anti- tigorite of ~75% antigorite. Hence there is some doubt about the gorite aggregates. In this case, the seismic velocities decrease linearly sample composition, however EBSD, thin section point counting, che- with increasing antigorite content and support the idea that the non- mical analysis and detailed P-wave measurements seem to converge to linear relationship observed in our sample is a consequence of the ∼ ∼ a composition of 78% antigorite and 22% olivine. presence of CPO in our anisotropic sample. Svitek et al. (2017), working on the same sample, also reported the

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Table 5 properties in antigorite-rich rocks and seismic data might not be as Compressional (P) wave seismic velocities determined experimentally and calculated straightforward as previously thought. This is because the CPO-derived ff from crystallographic preferred orientation with di erent methods. Data marked with (*) velocities are overestimated, particularly when the propagation direc- from Kern et al. (2015) for Cube A (#755). tion is normal to the antigorite foliation, when crack porosity is present Methods X (km/s) Y (km/s) Z (km/s) in the foliation.

Exp. cube (100 MPa)* 7.62 7.25 5.62 5. Conclusions Exp. cube (600 MPa)* 7.68 7.34 6.20 X-Ray* (95% atg, 5% ol) CPO modeling 7.26 7.10 6.16 geometric mean Three-dimensional microstructural analyses coupled with CPO-de- Neutron* (95% atg, 5% ol) CPO modeling 7.50 6.96 6.15 rived seismic properties of the antigorite-olivine serpentinites pre- geometric mean viously studied by ultrasonic methods by Kern et al. (1997, 2015) al- EBSD (95% atg, 5% ol) CPO modeling 7.97 7.88 6.13 lowed us to make the following conclusions: geometric mean EBSD (78% atg, 22% ol) geometric mean 8.03 7.97 6.72 EBSD (78% atg, 22% ol) hill average 7.78 7.75 6.72 (i) In rocks exhibiting micro-inhomogeneity and shape preferred EBSD (78% atg, 22% ol) self-consistent 1 no 7.83 7.78 6.40 orientation (SPO) of platy minerals, the analysis of three ortho- porosity gonal sections related to the structural reference frame (foliation, EBSD (78% atg, 22% ol) self-consistent 2 crack 7.81 7.77 6.21 porosity of 1.63% and shape X:Y:Z = 5:5:1 lineation) are needed to correctly estimate the crystallographic ⊥Z preferred orientation (CPO) and volume fractions of major mi- EBSD (78% atg, 22% ol) self-consistent 3 crack 7.28 7.66 5.99 nerals by means of EBSD and image analysis, respectively. porosity of 1.63% and shape (ii) The strong alignment of (001) planes parallel to the antigorite ⊥ X:Y:Z = 10:10:1 Z and foliation and the direction [100] parallel to the lineation suggests X:Y:Z = 10;1;10⊥Z that deformation was predominantly accommodated by disloca- tion glide due to ⟨101⟩{101} slip system, but this slip system only Table 5 (see also Supplemental Material, Fig. S5) compare the CPO- provides plastic strain directions in the (010) plane and is not based calculated P wave velocities derived from the EBSD measure- enough for strain compatibility. The olivine [100] fiber texture, ments of the three structural directions X, Y, and Z with experimental assuming that the mantle foliation lies at 90° to the antigorite and calculated data reported by Kern et al. (1997, 2015). The velocities foliation, suggests deformation under high temperature and low based on the CPOs of the EBSD measurements refer to calculations stress, with predominant [100](0kl) slip. Nevertheless, as the based on 78% antigorite and 22% of olivine. Experimental (low and olivine area fraction is lower (0.22) than antigorite (0.78) and the high pressure) as well as calculated P- and S-wave velocities are pre- olivine grains might have been rotated during subsequent anti- sented for the three structural directions, X, Y, and Z, along with the gorite controlled deformation (e.g. Wallis et al., 2011), these corresponding polarization planes of the two orthogonal shear waves. patterns might not indicate the olivine mantle flow conditions for The average P-wave velocities determined via numerical approach are the formation of this CPO. virtually the same as the ones determined by Kern et al. (1997, 2015) (iii) Antigorite CPO strength measured by the texture index J tends to and also by Ji et al. (2013) and Shao et al. (2014) with velocities increase with increasing grain size. Contrary to previous ob- varying between about 7.2 and 7.7 km/s in the Y and X directions. On servations, it is possible to determine the crystal orientation of the other hand, the differences between the calculated and measured fine-grained antigorite with EBSD, which in our case also shows slowest P-wave velocities vary between 1.5 km/s to 0.5 km/s, con- strong CPOs. sidering the experiments conducted at low and high pressure, respec- (iv) Olivine-antigorite orientation relationships are detected using tively (Table 5). phase boundary misorientation analyses. Our analysis reveals that there are 4 possible orientation relationships misorientations

present in this sample. No.1 (100)ol||(001)atg & [001]ol||[010]atg 4.7. Implications for the dynamics of subduction and No.2 (010)ol||(001)atg & [001]ol||[010]atg relationships were previously described by Boudier et al. (2010). In addition, we

The mantle wedge of active subduction zones is likely to be partially have found two new relationships, named No.3 (100)ol||(010)atg hydrated, triggering the hydration of olivine and formation of anti- & [001]ol||[100]atg and No.4 (010)ol||(210)atg & gorite. This process can be controlled by the orientation of olivine, and [100]ol||[001]atg. We have found that No.4 and No.1 are most as demonstrated here, there are at least 4 topotactic orientation re- frequent orientation relationships preserved in our sample, and lationships (two described for the first time). The progressive con- are favored because both involve the [100]ol and [001]atg, the sumption of olivine and crystallization of antigorite in a dynamic en- two directions with strongest alignment between the two phases. vironment leads to deformation localization in the antigorite and The misorientation angles of No.1 to No.4 are about 90° to 120°. development of strong crystallographic preferred orientations of this Small angle variations of the expected misorientation axes are phase. In addition, as the modal proportion of antigorite increases and most probably caused by subsequent plastic deformation of an- the olivine decreases, the original olivine CPO is progressively dis- tigorite. rupted, because the grains start to rotate mechanically along the anti- (v) Fabric recipes between two end-members of olivine and anti- gorite rich bands. As the antigorite is elastically more anisotropic and gorite respectively show that seismic velocities decrease and an- develops stronger CPOs than olivine during the hydration and de- isotropy increases with increasing antigorite content; grain shape formation of the mantle wedge, even a limited amount of this phase in has minor effect on the seismic velocities but contributes to in- the mantle wedge induces a substantial decrease in the seismic velo- creasing the anisotropy, particularly for antigorite fractions be- cities and increase in the seismic anisotropy of P and S waves. tween 30 and 80%. Furthermore, it has the potential to change the polarization direction of (vi) There is a good agreement between the CPO-derived seismic ve- the fastest shear wave from normal to parallel to the subduction zone locities and the velocities measured by ultrasonic methods at trench, as previously demonstrated by many authors (e.g. Katayama 600 MPa Kern et al. (1997, 2015) for the EBSD measured com- et al., 2009; Jung, 2011; Morales et al., 2013; Brownlee et al., 2013; position of antigorite 78% and olivine 22% only when the crack Soda and Wenk, 2014; Nagaya et al., 2016). It is important to notice porosity of 1.63% is taken into account using self-consistent however that the direct comparison between CPO-derived seismic modeling. The cracks with planes normal to Y and Z sample

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Serpentine in active subduction zones. Lithos 178, 171–185. 391, 24–35. Scambelluri, M., Philippot, P., 2001. Deep fluids in subduction zones. Lithos 55, 213–227. Wicks, F.J., Whittaker, E.J.W., 1977. Serpentine textures and serpentinization. Can. Schwartz, S., Guillot, S., Reynard, B., Lafay, R., Nicollet, C., Debret, B., Auzende, A.L., Mineral. 15, 459–488. 2013. Pressure–temperature estimates of the lizardite/antigorite transition in high- Willis, J.R., 1977. Bounds and self-consistent estimates for the overall properties of ani- pressure serpentinites. Lithos 178, 197–210. sotropic composites. J. Mech. Phys. Solids 25 (3), 185–202.

115 Tectonophysics

Supporting Information for

Olivine-antigorite orientation relationships: microstructures, phase boundary misorientations and the effect of cracks in the seismic properties of serpentinites

Luiz F.G. Morales1, David Mainprice2, Hartmut Kern3

1 – Scientific Center for Optical and Electron Microscopy (ScopeM), ETH Zürich. Auguste-Piccard-Hof 1, HPT D9, 8093, Zürich, Switzerland. 2 – Géosciences Montpellier and Université Montpellier 2. Place Eugène Bataillon, Batîment 22, 34095, Montpellier, France. 3- Institut für Geowissenschaften, Universität Kiel, 24098 Kiel, Germany

Contents of this file

Figures S1, S2, S3, & S4 Tables S1, S2 & S3 and elastic stiffness tensors, A, B, C and D used for seismic calculations.

Introduction

Figure S1 shows the orientation relationships between olivine (010) and antigorite {210}.

Figure S2 is complimentary material associated with Figure 12 Predicted seismic velocity Voigt, Reuss, Hill averages and geometric mean models for composition of antigorite 79% and olivine 21%. Figure S2 is the predicted seismic velocity Voigt, Reuss, Hill averages and geometric mean models for composition of antigorite 95% and olivine 5% used by Kern et al. (2015).

Figure S3 presents the differential effective media (DEM) model for 3D propagation of Vp compressional waves with different amounts of antigorite and olivine.

Figure S4 presents the DEM model the absolute difference between the fast and slow shear waves, also considering different amounts of these phases. These DEM figures are complementary to the Figure 14.

Table S1 gives the number of grains per section, Table S2 gives the indexed orientations per section and Table S3 gives the elastic tensor assuming 78% of antigorite and 22% of olivine, as used in our calculations

A) Single crystal of antigorite used here is slightly modified version Bezacier et al (2010). Details and references given below with full stiffness tensor.

B) Voigt, Reuss and Hill averages and geometric mean elastic stiffness tensors for a composition of antigorite 78% and olivine 22% used in this study. Full stiffness tensors given below.

C) Voigt, Reuss and Hill averages and geometric mean elastic stiffness tensors for a composition of antigorite 95% and olivine 5% used by Kern et al. 2015. Full stiffness tensors given below.

D) Self-consistent elastic stiffness tensors for a composition of antigorite 78% and olivine 22% used in this study as a background medium to host cracks. Full stiffness tensors given below.

The symmetry relations between olivine (010) and antigorite {210} Position No.2 Position No.1 _ (010) olivine || (210) antigorite (010) olivine || (210) antigorite Rotation 55.6° around [001] with respect to No.1

(010) (010) _ (210) (210) _ (210) (210)

[001] [001]

_ __ (210) (210)

__ _ (210) (210)

Position No.3 Position No.4 __ _ (010) olivine || (210) antigorite (010) olivine || (210) antigorite Rotation 124.4° around [001] with respect to No.2 Rotation 55.6° around [001] with respect to No.3 (010) (010) __ _ (210) (210) _ __ (210) (210)

[001] [001]

_ (210) (210)

_ (210) (210) Upper hemisphere equal angle stereographic projections with 10° net. N.B. For olivine [010] is parallel to the plane normal (010). The combined rotation angles of 55.6° + 124.4° = 180°

Figure S1 – The symmetry relationships between olivine (010) and the antigorite {210} planes, plotted in the upper hemisphere of equal angle stereographic projection. Due to the orthorhombic symmetry of olivine, [010] direction is parallel to the plane normal (010). YZ plane : Antigorite 95% Olivine 5% Vp YZ plane : Antigorite 95% Olivine 5% Vs1 & Vs2 8 4.8 Voigt Voigt Vs1 Hill Hill Vs1 7.8 4.6 Reuss Vs1 Vs Reuss XY 4.55 GM GM Vs1 7.6 4.4 Voigt Vs2 Hill Vs2 Reuss Vs2 7.4 4.2 GM Vs2 Y-Vp 7.34 7.2 4 7 3.8 6.8 3.6 6.6 3.4 S-wave velocity (km/s) P-wave velocity (km/s) Vs 3.18 6.4 3.2 XZ

6.2 Z-Vp 6.20 3 Z Y 6 Z Y 2.8 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 a Angle from normal foliation (Z) to normal to lineation (Y) d Angle from normal foliation (Z) to normal to lineation (Y) XZ plane : Antigorite 95% Olivine 5% Vp XZ plane : Antigorite 95% Olivine 5% Vs1 & Vs2 8 Voigt 4.8 Voigt Vs1 Hill Hill Vs1 7.8 Reuss 4.6 Reuss Vs1 GM X-Vp 7.68 Vs 4.46 GM Vs1 YX 7.6 4.4 Voigt Vs2 Hill Vs2 7.4 Reuss Vs2 4.2 GM Vs2 7.2 4 7 3.8 6.8 3.6

P-wave velocity (km/s) 6.6 3.4 S-wave velocity (km/s) 6.4 3.2 Vs 3.18 YZ 6.2 Z-Vp 6.20 3 Z X Z X 6 2.8 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 b Angle from normal foliation (Z) to lineation (X) e Angle from normal foliation (Z) to lineation (X) XY plane : Antigorite 95% Olivine 5% Vs1 & Vs2 XY plane : Antigorite 95% Olivine 5% Vp 4.8 9 Voigt Vs1 Voigt Hill Vs1 Hill 4.6 Reuss Vs1 Reuss GM Vs1 GM 8.5 4.4 Voigt Vs2 Hill Vs2 Reuss Vs2 4.2 GM Vs2 8 4 X-Vp 7.68 7.5 3.8 Y-Vp 7.34 3.6 7 3.4

S-waves velocity (km/s) Vs 3.22 ZY

P-wave velocity (km/s) 3.2 Vs 3.17 6.5 ZX 3 X Y X Y 6 2.8 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 c Angle from lineation (X) in foliation to (Y) f Angle from lineation (X) in foliation to (Y)

Figure S2 – Predicted seismic velocity models for composition of antigorite 95% and Olivine 5% used by Kern et al.(2015) in planes (a)YZ, (b)XZ and (c)XY for Vp and planes (d)YZ, (e)XZ and (f)XY for Vs using the Voigt, Reuss, Hill averages and geometric mean. Black squares indicated experimental velocities measured by Kern et al. (2015), the numbers next to the black squares are in km/s. Each plane covers propagation directions from a specific sample direction (Z 0°) to (Y 90°) for example in (a)YZ and in similar way for all sections. See text for further details.

Figure S2 - Variations in the propagation direction of compressional waves (Vp) resulting from the fabric recipe, from 100% olivine to 100% antigorite, calculated for the orientation maps obtained in three orthogonal sections. The calculations were carried after the data was rotated to the common tectonic reference plane XZ (YZ to XZ and XY to XZ). Seismic properties calculated via the Voigt-Reuss-Hill averaging scheme using the elastic constants of olivine (Abramson et al., 1997) and antigorite (Bezacier et al., 2010). All plots have the same reference frame of Figure 3.

Figure S3 - Variations in the absolute difference between the fast and slow shear waves (Vs1-Vs2) resulting from the fabric recipe, from 100% olivine to 100% antigorite, calculated for the orientation maps obtained in three orthogonal sections. Note the polarization of Vs1 parallel to the foliation with increasing in antigorite content. The calculations were carried after the data was rotated to the common tectonic reference plane XZ (YZ to XZ and XY to XZ). Seismic properties calculated via the Voigt-Reuss-Hill averaging scheme using the elastic constants of olivine (Abramson et al., 1997) and antigorite (Bezacier et al., 2010). All plots have the same reference frame of Figure 3.

Figure S4 – Variations in propagation direction, anisotropy and polarization of seismic waves calculated via differential effective media (DEM) composite modelling for a mixture of 78% of antigorite and 22% of olivine, assuming a shape aspect ratio of 10:1:10 for antigorite (flattened crystals parallel to the foliation). For the calculations, we have used the elastic constants of olivine (Abramson et al., 1997) and antigorite (Bezacier et al., 2010). All plots have the same reference frame of Figure 3. Vp – compressional waves; Vs1 – fast shear wave; Vs2 – slow shear wave

Section Total Olivine Antigorite 3328 227 3051 Normal Y plane XZ 8393 2313 6080 Normal X plane YZ 3820 2826 994 Total grains for 3 15541 5366 10125 sections Table S1 - grain number per section. All grains contain at 10 or more indexed orientations. Some olivine grains are fragments of grains, dissected by antigorite. All antigorite grains are new grains.

Section Total Olivine Antigorite Normal Z plane XY 222929 19191 203738 Normal Y plane XZ 321483 79703 241780 Normal X plane YZ 205821 140864 64957 Total orientations for 750233 239758 510475 3 sections Table S2 - indexed orientations per section

A) Single crystal of antigorite used here is slightly modified version Bezacier et al (2010).

The correction is that C11 and C22 are interchanged so that C22 > C11, this correction only has a minor impact as the difference between C11 and C22 is only 3.32%. It was shown that the C11=208.10 GPa and C22=201.60 GPa where not in correct order by Marquardt et al. (2015) due to an error in the assignment of the a- and b-axes. It is coincidence that the single-crystal of antigorite used in this study was collected from the central part of the Malenco serpentinite body in northern Italy. The correction is also agreement with C22>C11 predicted by ab initio calculations of Mookherjee and Capitani (2011).

References Bezacier, L., Reynard, B., Bass, J.D., Sanchez-Valle, C., and Van de Moortèle, B. (2010) Elasticity of antigorite, seismic detection of serpentinites, and anisotropy in subduction zones. Earth and Planetary Science Letters, 289, 198–208.

Marquardt,H., Speziale,S., Koch-Müller,M., Marquardt, K., and Capitani, G.C. (2015) Structural insights and elasticity of single-crystal antigorite from high-pressure Raman and Brillouin spectroscopy measured in the (010) plane. American Mineralogist, 100, 1932– 1939.

Mookherjee, M., and Capitani, G.C. (2011) Trench parallel anisotropy and large delay times: Elasticity and anisotropy of antigorite at high pressures. Geophysical Research Letters, 38, L09315.

Corrected stiffness tensor of Bezacier et al. (2010) with X||a, Y||b, Z||c*

[ 201.60 66.40 16.00 0.00 5.50 0.00] [ 66.40 208.10 4.90 0.00 -3.10 0.00] [ 16.00 4.90 96.80 0.00 1.60 0.00] [ 0.00 0.00 0.00 16.90 0.00 -12.10] [ 5.50 -3.10 1.60 0.00 18.40 0.00] [ 0.00 0.00 0.00 -12.10 0.00 65.50]

Antigorite single-crystal density = 2.62 g/cm3

B) Voigt, Reuss and Hill averages and geometric mean elastic stiffness tensors for a composition of antigorite 78% and olivine 22% used in this study.

Voigt, Reuss and Hill averages and geometric mean elastic stiffness tensors for a composition of antigorite 78% and olivine 22%. The composition was determined by EBSD using the average of 3 orthogonal thin sections. To make comparisons with the geometric mean used by Kern et al. 2015 JGR we did not consider minor contributions from magnetite and chromite.

Sample (antigorite 78% and olivine 22%) Voigt average rank: 4 (3 x 3 x 3 x 3) units GPa

tensor in Voigt matrix representation: 130.54 41.35 38.64 0.51 0.45 -0.07 41.35 184.51 61.47 -0.78 -1.05 -6.52 38.64 61.47 188.65 -1.26 -3.22 -3.07 0.51 -0.78 -1.26 62.16 -2.11 -0.5 0.45 -1.05 -3.22 -2.11 45.42 0.39 -0.07 -6.52 -3.07 -0.5 0.39 45.22

Sample (antigorite 78% and olivine 22%) Reuss average rank: 4 (3 x 3 x 3 x 3) units GPa

tensor in Voigt matrix representation: 117.54 45.95 45.35 0.63 0.72 0.64 45.95 147.99 50.73 -0.45 -0.26 -3.84 45.35 50.73 146.83 -1.2 -1.84 -0.79 0.63 -0.45 -1.2 47.76 -1.75 -0.28 0.72 -0.26 -1.84 -1.75 33.12 0.17 0.64 -3.84 -0.79 -0.28 0.17 34.45

Sample (antigorite 78% and olivine 22%) Hill average rank: 4 (3 x 3 x 3 x 3) units GPa

tensor in Voigt matrix representation: 124.04 43.65 42 0.57 0.58 0.28 43.65 166.25 56.1 -0.61 -0.65 -5.18 42 56.1 167.74 -1.23 -2.53 -1.93 0.57 -0.61 -1.23 54.96 -1.93 -0.39 0.58 -0.65 -2.53 -1.93 39.27 0.28 0.28 -5.18 -1.93 -0.39 0.28 39.83

Sample (antigorite 78% and olivine 22%) Geometric mean rank: 4 (3 x 3 x 3 x 3) units GPa

tensor in Voigt matrix representation: 124.2 42.44 39.87 0.87 1.03 1 42.44 175.47 59.7 -0.82 -0.8 -6.85 39.87 59.7 178.75 -1.68 -3.55 -2.54 0.87 -0.82 -1.68 56.78 -2.6 -0.54 1.03 -0.8 -3.55 -2.6 35.93 0.39 1 -6.85 -2.54 -0.54 0.39 37.03

Sample density = 2.7744 g/cm3

C) Voigt, Reuss and Hill averages and geometric mean elastic stiffness tensors for a composition of antigorite 95% and olivine 5% used by Kern et al. 2015.

Reference Kern, H., T. Lokajicek, T. Svitek, and H.-R. Wenk (2015), Seismic anisotropy of serpentinite from Val Malenco, Italy, J. Geophys. Res. Solid Earth, 120, doi:10.1002/2015JB012030.

Quote from page 5 "The percentage of olivine from the Rietveld refinement from both the X-ray and neutron refinement converged to ∼ 5 volume %, which is lower than values of 20% given by Kern et al.(1997) measured by point-counting. For the CPO-based modelling, we did not consider minor contributions from magnetite and chromite."

Sample (antigorite 95% and olivine 5%) Voigt rank: 4 (3 x 3 x 3 x 3) units GPa

tensor in Voigt matrix representation: 106.57 33.94 30.75 0.54 -0.16 -0.79 33.94 174.64 57.98 -0.89 -1.19 -8.28 30.75 57.98 179.66 -1.45 -4.43 -3.68 0.54 -0.89 -1.45 59.1 -2.7 -0.86 -0.16 -1.19 -4.43 -2.7 38.28 0.52 -0.79 -8.28 -3.68 -0.86 0.52 38.28

Sample (antigorite 95% and olivine 5%) Reuss rank: 4 (3 x 3 x 3 x 3) units GPa

tensor in Voigt matrix representation: 93.16 39.81 39.31 0.64 0.35 0.21 39.81 131.96 45.4 -0.56 -0.18 -5.01 39.31 45.4 130.92 -1.48 -2.6 -0.92 0.64 -0.56 -1.48 42.34 -2.26 -0.56 0.35 -0.18 -2.6 -2.26 24.1 0.25 0.21 -5.01 -0.92 -0.56 0.25 25.89

Sample (antigorite 95% and olivine 5%) Hill rank: 4 (3 x 3 x 3 x 3) units GPa

tensor in Voigt matrix representation: 99.87 36.88 35.03 0.59 0.1 -0.29 36.88 153.3 51.69 -0.73 -0.68 -6.64 35.03 51.69 155.29 -1.46 -3.52 -2.3 0.59 -0.73 -1.46 50.72 -2.48 -0.71 0.1 -0.68 -3.52 -2.48 31.19 0.39 -0.29 -6.64 -2.3 -0.71 0.39 32.08

Sample (antigorite 95% and olivine 5%) Geometric mean rank: 4 (3 x 3 x 3 x 3) units GPa

tensor in Voigt matrix representation: 99.7 35.31 32.33 0.94 0.57 0.51 35.31 164.31 55.88 -0.98 -0.85 -8.67 32.33 55.88 168.47 -2 -4.77 -3.02 0.94 -0.98 -2 53 -3.29 -0.89 0.57 -0.85 -4.77 -3.29 27.23 0.52 0.51 -8.67 -3.02 -0.89 0.52 28.8

Sample density = 2.6568 g/cm3

D) Self-consistent elastic stiffness tensors for a composition of antigorite 78% and olivine 22% used in this study as a background medium to host cracks.

Self-consistent models: all use a background medium of antigorite 78% and olivine 22% the average composition based on EBSD measurements on three orthogonal sections .

Reference Kern, H., T. Lokajicek, T. Svitek, and H.-R. Wenk (2015), Seismic anisotropy of serpentinite from Val Malenco, Italy, J. Geophys. Res. Solid Earth, 120, doi:10.1002/2015JB012030.

Quote page 7

"The corresponding volume compaction, representing mainly the crack porosity, is 1.63%, and the bulk density of the aggregate at 600MPa is 2.74 g/cm3 compared to 2.71 g/cm3 at ambient conditions."

A total crack porosity of 1.63% was used in Self-consistent models, which is the same value measured by Kern et al. (2015) at 600 MPa pressure. ************************************************************************ MODEL SC1 - Crack-free model of Antigorite 78% Olivine 22% with spherical grains ************************************************************************

Self-consistent model with spherical grains and zero crack porosity Antigorite 78% Olivine 22% Sample_density = 2.7744 g/cm3

Sample_SC1 = SC1 tensor rank : 4 (3 x 3 x 3 x 3) Units GPa

tensor in Voigt matrix representation: 113.74 38.37 34.16 0.38 0.25 -0.1 38.37 168.13 53.67 -0.48 -0.62 -0.69 34.16 53.67 170.01 -0.85 -2.74 -0.51 0.38 -0.48 -0.85 55.29 -0.34 -0.6 0.25 -0.62 -2.74 -0.34 32.95 0.08 -0.1 -0.69 -0.51 -0.6 0.08 35.34

Sample SC1 density with no porosity = 2.7744 g/cm3

************************************************************************ MODEL SC2 - Crack planes normal to Z sample direction with total crack porosity of 1.63% and crack shape of X:Y:Z =5:5:1 ************************************************************************

Self-consistent model with spherical grains with total crack porosity of 1.63% Cracks are oblate ellipsoids in foliation plane with crack shape X:Y:Z = 5:5:1 Crack plane normal to Z. Orientation of ellipsoid axes (A1 and A3) are defined by Azimuth and Inclination angles in sample reference frame X,Y,Z. So that A1 azimuth of 90° and inclination of 0°, and A3 azimuth of 0° and inclination of 0°, with ellipsoid axis A2 is orthogonal of A1 and A3.

Sample_SC2 = SC2 tensor rank : 4 (3 x 3 x 3 x 3) Units GPa

tensor in Voigt matrix representation: 105.4 36.17 32.25 0.35 0.2 -0.11 36.17 164.62 52.27 -0.48 -0.6 -0.68 32.25 52.27 166.55 -0.85 -2.67 -0.49 0.35 -0.48 -0.85 54.27 -0.33 -0.59 0.2 -0.6 -2.67 -0.33 31.49 0.07 -0.11 -0.68 -0.49 -0.59 0.07 33.78

Sample SC2 density with a total 1.63% crack porosity = 2.7292 g/cm3

************************************************************************ MODEL SC3 - Crack planes normal to Z and Y sample directions with total crack porosity of 1.63% and crack shape of X:Y:Z = 10:10:1 and X:Y:Z = 10:1:10 respectively ************************************************************************

Self-consistent model with spherical grains with total crack porosity of 1.63%. Cracks are oblate ellipsoids in foliation plane with crack shape X:Y:Z = 10:10:1 Crack plane normal to Z. The orientation of the ellipsoidal are defined as in Model SC2. Orientation of ellipsoid axes (A1 and A3) for the crack plane normal to the Y direction are defined by Azimuth and Inclination angles in sample reference frame X,Y,Z. So that A1 azimuth of 90° and inclination of 0°,and A3 azimuth of 90° and inclination of 90°, with ellipsoid axis A2 is orthogonal of A1 and A3.

Sample_SC3 = SC3 tensor rank : 4 (3 x 3 x 3 x 3) Units GPa

tensor in Voigt matrix representation: 97.81 33.28 27.62 0.33 0.2 -0.11 33.28 159.96 45.85 -0.43 -0.49 -0.66 27.62 45.85 144.48 -0.74 -2.26 -0.42 0.33 -0.43 -0.74 50.19 -0.3 -0.55 0.2 -0.49 -2.26 -0.3 28.47 0.07 -0.11 -0.66 -0.42 -0.55 0.07 32.18

Sample SC3 density with a total 1.63% crack porosity = 2.7292 g/cm3