Corrigendum to “ A database of plagioclase crystal preferred orientations ( CPO ) and microstructures – implications for CPO origin , strength , symmetry and seismic anisotropy in gabbroic rocks ” published in Solid Earth , 4 , 511 – 542 , 2013

T. Satsukawa1,2,*, B. Ildefonse2, D. Mainprice2, L. F. G. Morales3, K. Michibayashi1,4, and F. Barou2 1Graduate School of Science and Technology, Shizuoka University, Ohya 836, Shizuoka 422-8529, Japan 2Géosciences Montpellier, Université Montpellier 2 and CNRS, CC 060, 34095 Montpellier cedex 5, France 3Helmholtz Zentrum Potsdam, Deutsches GeoForschungsZentrum (GFZ), Telegrafenberg, 14473 Potsdam, Germany 4Institute of Geosciences, Shizuoka University, Ohya 836, Shizuoka 422-8529, Japan * present address: ARC Center of Excellence for Core to Crust Fluid Systems (CCFS) and GEMOC National Key Centre, Department of Earth and Planetary Sciences, Macquarie University, Sydney, NSW 2109, Australia

Abstract.This study presents a unique database of 172 plagioclase Crystallographic Preferred Orientations (CPO) of variously deformed gabbroic rocks.The CPO characteristics as a function of the deformation regime (magmatic or crystal-plastic) are outlined and discussed.The studied samples are dominantly from slow-and fast-spread present-day ocean crust, as well as from the Oman ophiolite.Plagioclase is the dominant mineral phase in the studied samples.Plagioclase CPOs are grouped into three main categories: Axial-B, a strong point alignment of (010) with a girdle distribution of [100]; Axial-A, a strong point maximum concentration of [100] with parallel girdle distributions of ( 010) and (001); and P-type, point maxima of [100], (010), and (001).A majority of CPO patterns are Axial-B and P-type, in samples showing either magmatic or crystal-plastic deformation textures.Axial-A CPOs are less common; they represent 21 % of the samples deformed by crystal-plastic flow.Although fabric strength (ODF J index) does not show any consistent variation as a function of the CPO patterns, there is a significant difference in the relationship between the ODF and pole figures J indices; the magmatic type microstructures have high (010) pole figures J indices, which increase linearly with ODF J index, whereas the high [100] pole figures J indices of plastically deformed samples vary in a more scattered manner with ODF J index.The multistage nature of plastic deformation superposed on a magmatic struc-ture compared with magmatic flow, and the large number of possible slip-systems in plagioclase probably account for these differences.Calculated seismic properties (P wave and S wave velocities and anisotropies) of plagioclase aggregates show that anisotropy (up to 12 % for P wave and 14 % for S wave) tends to increase as a function of ODF J index.In comparison with the olivine 1998 CPO database, the magnitude of P wave anisotropy for a given J index is much less than olivine, whereas it is similar for S wave anisotropy.Despite a large variation of fabric patterns and geodynamic setting, seismic properties of plagioclase-rich rocks have similar magnitudes of anisotropy.There is a small difference in the aggregate elastic symmetry, with magmatic microstructures having higher orthorhombic and hexagonal components, whereas plastic deformation microstructures have a slightly higher monoclinic component, possibly correlated with predominant monoclinic simple shear flow in plastically deformed samples.Overall, plots for CPO strength (ODF J index), pole figure strength, CPO symmetry and seismic anisotropy show significant scattering.This could be related to sampling statistics, although our database is a factor of ten higher than the olivine database of 1998, or it could be related to the low symmetry (triclinic) structure of plagioclase resulting in the addition of degrees of freedom in the processes creating the CPOs.

Introduction
The study of the crystallographic preferred orientations (CPO) of naturally and experimentally deformed materials provides crucial insight into geodynamic processes (e.g., Nicolas and Christensen, 1987;Karato, 2008).They are a key component of our understanding of the material processes, mechanical behavior and deformation strain history, from the crustal levels to the deep mantle.The CPOs also induces anisotropic behavior of certain physical properties commonly measured in rocks, such as seismic velocity (e.g., Ben Ismaïl and Mainprice, 1998;Jung and Karato, 2001;Tommasi et al., 2008;Lloyd et al., 2009), thermal diffusivity (e.g., Tommasi et al., 2001;Gibert and Mainprice, 2009) and chemical diffusivity (e.g., Mackwell and Kohlstedt, 1990).
Although not yet quantified, dissolution processes during metamorphic reactions can be attributed to plagioclase deformation (e.g.Imon et al., 2002), and might also result in the development of crystallographic preferred orientations.
One of the main difficulties when dealing with crystallographic preferred orientation of plagioclase is that the CPOs resulting from magmatic flow and dislocation creep are generally similar to each other.In dislocation creep, the main slip systems in plagioclase are [001](010), [100](001) and 110 (001) (Marshal and McLaren, 1997;Montardi and Mainprice, 1987;Stünitz et al., 2003).On the other hand, the crystallographic planes (010), and less commonly (001) tend to align and form a foliation in magmatic flow.The [100] axes (or less commonly [001]) are usually parallel to the magma flow direction.This relates to the shape of plagioclase grains in a magma, with the normal to (010) that tends to be short.Therefore, the coupling between optical and electron-optical microstructures with CPO data is necessary for a complete understanding of the origin of plagioclase crystallographic orientation.
The effect of plagioclase on the seismic properties is also not yet well documented when compared to olivine.Seront et al. (1993) demonstrated that maximum V p (7.8 km s −1 ) is normal to the foliation (with the direction normal to (010) being the fast direction for plagioclase), and S waves are polarized parallel to the foliation or parallel to the lineation in foliated anorthosites.
A database that jointly document plagioclase microstructures, crystallographic orientations and CPO-derived seismic properties is described and discussed herein, with the aim to provide an overview of plagioclase CPO characteristics as a function of the deformation regime (magmatic flow or crystal-plastic flow), and of the implications on seismic properties of plagioclase-bearing rocks.This is the first attempt to develop such a database because in contrast with olivine CPOs in peridotites (e.g., Ben Ismaïl and Mainprice, 1998;Tommasi et al., 2000), the plagioclase preferred orientation is much more complex to measure by optical methods due to its low crystallographic symmetry (e.g.Benn and Mainprice, 1989).However, the growing use of the EBSD (electron backscattered diffraction) technique over the last ∼ 15 yr allowed the complete fabric characterization of virtually any type of mineral, regardless of its crystal symmetry.Problems to indexing albite have been reported (Prior and Wheeler, 1999;Jiang et al., 2000).For plagioclase with high anorthite contents (≥ An 50) as measured herein, we did not encountered difficulties indexing the diffraction patterns.The structure reference file usually used is that of bytownite (developed in Montpellier), which gives excellent results.Here we present a large (172 samples) database of plagioclase CPOs that documents various geodynamic settings and deformation conditions.The samples have been measured using the EBSD facilities at Géosciences Montpellier.

Sample locations and Geological Background
Table 1 lists the 172 gabbro samples compiled in this study, which represent various geodynamic settings.References to published data are also given in Table 1.A majority of samples comes from present-day ocean crust (54 %), or former ocean crust in the Oman ophiolite (25 %).

Fast-spread ocean crust samples
Most of the samples presented here (54 %) are from gabbroic rocks formed in fast-spreading environments, collected in the Oman ophiolite, and in present-day ocean crust in the Hess Deep rift valley and in ODP Hole 1256D.Although the precise initial geodynamic setting of the Oman ophiolite is still a matter of debate, the nearly continuous ocean crust present in this ophiolite makes it a classical analogue for present-day fast-spreading systems (e.g., Nicolas et al., 2000;MacLeod and Yaouancq, 2000).Hess Deep (2 • 14 N; 101 • 33 W; Hey et al., 1972;Francheteau et al., 1990) is the deepest part of a westward-propagating rift valley that is opening up in the eastern flank of the equatorial East Pacific Rise (EPR), in advance of the westward-propagating Cocos-Nazca spreading (1) Ildefonse et al. (1999).Some of the data are unpublished.
center (e.g., Schouten et al., 2008;Smith et al., 2011).The samples used here were collected on the intra-rift ridge during ODP Leg 147 (Gillis et al., 1993), and with the UK ROV ISIS during the RSS James Cook JC21 Cruise in January-February 2008(MacLeod et al., 2011;Harris et al., 2012;Lissenberg et al., 2013).ODP Hole 1256D (6 • 44.2 N; 91 • 56.1 W) is located in an area of the Cocos plate crust that was formed 15 million years ago on the eastern flank of the EPR at a superfast spreading rate (∼ 220 mm yr −1 ; Wilson, 1996).It is situated on a ridge segment of at least 400 km in length, located ∼ 100 km north of the triple ridge junction between the Cocos, Pacific, and Nazca plates.All samples from Hole 1256D come from the petrologically complex sheeted dike -gabbro transition zone (Wilson et al., 2006;France et al., 2009;Koepke et al., 2008Koepke et al., , 2011)).

Slow-spread ocean crust samples
Overall, 25 % of the samples come from slow-spreading oceanic crust environments.A majority was collected in ODP Hole 735B, at the Southwest Indian ridge.The ODP Site 735 is located on the Atlantis Bank, a 11 m.y.old shallow oceanic core complex located 18 km east of the Atlantis II Transform Fault (Dick et al., 2000).Hole 735B was drilled to the depth of 1503 m below seafloor, over two ODP Legs (118 and 176;Robinson et al., 1989;Dick et al., 1999Dick et al., , 2000)).Recovered samples are predominantly medium to coarse-grained crystalline gabbroic rocks from a tectonically exposed lower crustal section.Additional samples come from ODP Holes 1270B, 1275B and 1275D, drilled during ODP Leg 209 at the Mid-Atlantic Ridge in the 15 • 20 N fracture zone area (Kelemen et al., 2004).

Other samples
The remaining samples compiled herein (21 %) come from various locations and represent a variety of gabbroic rocks (sensu lato) from different geodynamic settings.They include gabbros and charnockites from igneous intrusions in the Itabuna belt, in the São Francisco craton, Bahia, Brazil, granulites from the Neoproterozoic Ribeira belt, southeastern Brazil (Egydio-Silva et al., 2002), layered gabbros from La Réunion (Piton des Neiges volcano, Cirque de Salazie), one foliated anorthosite sample from the Precambrian Grenvillian basement in Oklahoma, USA (Seront et al., 1993), and basaltic lava flow samples from Saint Thibéry, southern France (Bascou et al., 2005

Crystallographic preferred orientation measurements
To evaluate the plagioclase fabric characteristics, crystallographic orientation measurements were obtained by electron backscatter diffraction (EBSD) in a scanning electron microscope (SEM).For that, we have used the JEOL JSM 5600 and the CamScan X500FE Crystal Probe SEMs, both equipped with Oxford/Nordlys EBSD detectors and the Channel 5 ® suite of programs, installed at Géosciences Montpellier (CNRS and Université Montpellier 2).Details about the EBSD technique are given in Engler and Randle (2009) and Prior et al. (2009).
For most measured samples, we have made extensive use of the automated crystallographic orientation mapping of whole thin sections (usually 35 mm long and 20 mm wide).The resolution of individual maps was variable, depending on the mean grain size or individual samples; on average the used step sizes ranged from 30 to 35 µm.The indexing rates in the raw maps range from 50 % to 80 %.Post-acquisition data processing included the extrapolation of well-indexed neighboring points to non-indexed points, and removal of grains (as defined by continuous domains characterized by an internal misorientation < 10 • ) smaller than 5 pixels in average diameter.Pole figures were calculated using processed map data (herein called gridded data), and, in order to avoid the overrepresentation of coarse grains in individual sample, using one point per grain (herein called 1 point-per-grain data, or 1 ppg data).The oldest crystallographic orientation data sets measured more than 10 yr ago, when the automatic mapping was not yet fully functional in our system, were obtained manually, in an interactive mode (i.e., the user can select the appropriate indexation pattern for each measured point) with a one-point-per-grain data strategy.Hence 1 ppg data allows us a homogenous presentation of the older and more recent data.The 1 ppg data are used below to plot the CPO pole figures and calculate their strength and symmetry; gridded data are used to calculate seismic properties when available.

CPO strength
We determined the fabric strength and distribution density of the principal crystallographic axes by calculating the J index of the orientation distribution function (ODF), simply called "J index" here, and J index of pole figures called "pfJ index" (e.g.Bunge 1982, Mainprice andSilver, 1993).The rotation matrix between crystal and sample co-ordinates is used to describe the orientation g of a crystal in sample coordinates.In practice, it is convenient to describe the rotation by a triplet of Euler angles (ϕ 1 , , ϕ 2 ; Bunge, 1982).The ODF f (g) is defined as the volume fraction of orientations with an orientation in the interval between g and g + dg in a space containing all possible orientations given by (1) In this equation, V /V is the volume fraction of crystals with orientation g, dg = 1/8π 2 sin dϕ 1 d dϕ 2 is the fractional volume of integration in orientation space.To quantify the strength of CPOs, Mainprice and Silver (1993) used the J index of the ODF, defined by Bunge (1982) as (2) The J index ranges from 1 for a random distribution to infinity for a single crystal.In a similar manner, the strength of a pole figure can be analytically defined by the pfJ index as where α and β are the spherical co-ordinates of the considered direction in the pole figure, P 2 hkl (α, β) is the density squared in that direction for a given crystallographic pole defined by hkl and dω = 1/2π sin αdαdβ is the fractional volume of integration.The index has a value of 1 for a random distribution and infinity for a single crystal.The recent MTEX MatLab toolbox (Hielscher and Schaeben, 2008) now allows one to calculate J for aggregates of triclinic minerals using the de la Vallée Poussin kernel that is exactly defined in Fourier coefficients (Schaeben, 1999); we used half-width of 10 • , which corresponds exactly to a series expansion of 28.
The analysis of the pole figure symmetry was carried out through the evaluation of the parameters P (point), G (girdle) and R (random) fabric indexes.These indexes are calculated from the eigenvalues (λ 1 ≥ λ 2 ≥ λ 3 , with λ 1 + λ 2 + λ 3 = 1) of the normalized orientation matrices for the principal crystallographic axes and can be described as P = λ 1 − λ 3 (P has a high value when λ 1 >λ 2 ≈ λ 3 ), G = 2(λ 2 − λ 3 ) (G has a high value when λ 1 ≈ λ 2 > λ 3 ) and R = 3λ 3 (R has a high value when λ 1 ≈ λ 2 ≈ λ 3 ) (Woodcock, 1977;Vollmer, 1990).These indices range from 0 to 1, and P +G+R = 1.P and G are the values for a given crystallographic pole figure, which represents a set of vectors of pole to planes ⊥ (hkl) or directions [uvw] used for eigenvalue calculations.The notation ⊥ (hkl) is simplified to (hkl) below.P and G are used in the eigenvalue analysis (Sects.5 and 7) when introducing the BA-index.

Calculation of elastic symmetry
We have calculated the elastic symmetry of hypothetical 100 % plagioclase aggregates to further characterize the symmetry aspect associated with CPOs.The analysis of elastic symmetry of minerals and mineral aggregates has been previously applied to mantle samples by Harder (1988) and Mainprice and Silver (1993).More recently Browaeys and Chevrot (2004) have re-formulated the problem in terms of an Euclidean norm for an elastic tensor of arbitrary symmetry.The elastic constants are transformed into an eigentensor representation and stored as a vector X, the Euclidean norm is simply given as √ (X •X).The Euclidean norm gives the measure of the distances between the different elastic symmetry solutions and their relative proportions in the initial arbitrary elastic tensor being analyzed.We have applied the method using the holohedral symmetry classes trigonal, monoclinic, orthorhombic, tetragonal, and hexagonal plus isotropic, which always represents the major fraction.To use this method the Voigt average elastic constants were calculated, as Euclidean norm is only valid for this average.

Calculation of seismic properties
Seismic properties of the polycrystalline aggregates were computed by averaging individual grain elastic-constant tensors as a function of the CPO and modal composition of a sample (e.g.Mainprice, 1990) through the Voigt-Reuss-Hill averaging scheme.Whenever available, the gridded data were used to calculate the seismic properties of the samples, and the modal compositions were derived from these maps as seismic properties dependent on the fractional volume or in present case the fractional area.This method enables the calculation of the three-dimensional distribution of seismic velocities in an anisotropic polycrystalline aggregate (Mainprice and Humbert, 1994).We have used the following elastic constants experimentally determined at ambient conditions (plagioclase: Aleksandrov et al., 1974;clinopyroxene: Collins and Brown, 1998;orthopyroxene: Chai et al., 1997;olivine: Abramson et al., 1997;amphibole: Aleksandrov and Ryzhova, 1961).Anisotropy of seismic velocities (AV p and AV s ) is defined (in percent) as 200 (V max − V min )/(V max + V min ).

Microstructures
Rock types, modal compositions and microstructural observations are listed in Table 2 for all samples presented here.Some of the modal compositions are shown as 100 % of plagioclase when measurements were done manually.Mineral composition is plagioclase + clinopyroxene ± olivine ± amphibole (± orthopyroxene).Typical plagioclase microstructures in this study are shown in Fig. 1.The samples can be classified into two types, those that have a predominant magmatic microstructure (Fig. 1a to d) and those that have crystal-plastic microstructures (Fig. 1e and f).The magmatic flow textures display straight or curvilinear grain boundaries (Fig. 1a and b).Plagioclase grains are commonly oriented and their shape defines a foliation (Fig. 1a).In some samples grain boundaries have more irregular shapes, and grain size becomes bi-modal with a few recrystallized grains (Fig. 1c and d).These microstructures are characteristics of incipient high temperature plastic deformation, which overprint magmatic flow textures.Samples deformed by significant crystal-plastic flow (Fig. 1e and f) are characterized by the joint occurrence of porphyroclasts and neoblasts.Porphyroclasts consist of plagioclase and clinopyroxene, whereas neoblasts are commonly only plagioclase.Some ultramylonitic samples from Hole 735B also show recrystallized olivine and clinopyroxene.Small-grained size textures (Fig. 1e and f) are from localized shear zones, associated with enhanced strain rate and/or decreasing lithospheric temperature.For all samples in this study, deformation type was defined for each sample (Table 2).More than 60 % of samples have a magmatic flow texture.

Crystallographic preferred orientation of plagioclase
Measured CPOs are presented in equal-area, lowerhemisphere stereographic projections (Figs. 2 and 3, and Supplement Figs. 1 to 7).Pole figures of plagioclase crystal orientations are in the thin section reference frame; the long axis of thin section is parallel to the east-west horizontal direction in the pole figure.The significance of this reference Table 2. Modal composition (%), rock type, deformation type and related references for the gabbros studied here.Mode: modal composition; Pl: plagioclase; Cpx; clinopyroxene; Ol: olivine, Opx: orthopyroxene; Amp: amphibole, respectively.* An contents of plagioclase from the crustal section in the Oman ophiolite are on average in the range 60-90 (e.g., Pallister and Hopson, 1981).** An contents of plagioclase from the sheeted dike/gabbro transition zone in Hole 1256D, from which these samples are from, range from 44 to 76, and are 62 on average (Yamazaki et al., 2009).*** An contents of plagioclase from gabbroic rocks in ODP Hole 894G range from ∼ 43 to 90, and are ∼ 65 on average (Pedersen et al., 1996;Natland and Dick, 1996)    frame differs with the sample provenance.The samples from Oman ophiolite, Brazil and Oklahoma, and the dive samples from Hess Deep were cut in (or close to) the structural XZ plane (parallel to the lineation and normal to the foliation).Samples from ocean drill cores were cut in the core reference frame, with the core vertical direction either parallel or perpendicular to the long axis of thin section.To obtain a representative CPO of the rock, the number of measured crystals must be at least 100 grains (e.g.Ben Ismaïl and Mainprice, 1998); the automated mapping of CPOs allows one to measure many more than this in general (see Table 3).

Fast-spread ocean crust samples
About 43 plagioclase CPOs from gabbros and anorthosites from the Oman ophiolite (Fig. 2b and c, Supplement Fig. 1, and Morales et al., 2011) show relatively high concentrations of (010) poles in a point maximum with a perpendicular girdle concentration of [100] axes.Some samples show CPO patterns with concentration of both ( 010) and ( 001) poles perpendicular to the foliation, and with [100] axes distributed along the foliation plane (e.g., 95OB4, 98OB10g, 90OA77).

Slow-spread ocean crust samples
ODP Hole 735B in slow-spread crust provides the second largest single data set of 40 samples in the database.They display various types of CPO (Supplement Fig. 4).Slip systems cannot be uniquely inferred from the CPO in plastically deformed samples.The majority of samples shows CPO patterns with girdle concentrations of both ( 010) and (001) poles and with [100] axes distributed normal to them (Fig. 2f to h).Another type of pattern shows no girdle concentration, [100] and (010) are both concentrated as point maxima (e.g., 176-735B-130R3-115, 176-735B-189R7-98).
A few samples have the pattern commonly described in fastspread ocean crust, with strong (010) concentration (e.g., 176-735B-165R3-111).The three samples from the Mid-Atlantic Ridge have relatively weak CPOs with no girdle concentration (Supplement Fig. 5).

Other samples
The remainder of the samples compiled herein comes from various locations (Supplement Figs. 5 to 7).Samples of gabbros and charnockites from igneous intrusions in the Itabuna belt (Sao Francisco craton, Bahia, Brazil) and granulites from the Neoproterozoic Ribeira belt (southeastern Brazil) show generally weak plagioclase CPOs and do not show a strong concentration of any particular axis in relation to the specimen reference frame.The CPOs of layered gabbros from La Réunion (Piton des Neiges volcano, Cirque de Salazie; Supplement Fig. 5) show the same common type of CPO as in fast-spread ocean crust; (010) poles are strongly concentrated with girdle concentration of [100] and/or (001).Samples of basaltic lava flow samples from Saint Thibéry (Southern France; Supplement Fig. 7) show plagioclase CPOs with relatively strong (010) maxima.The foliated anorthosite sample from the Precambrian Grenvillian basement in Oklahoma (USA; Seront et al., 1993;Fig. 2d; Supplement Fig. 7) shows a very strong concentration of (010) with clear girdle concentration of [100] and (001).

Classification of the plagioclase CPOs
There is a large variability in the plagioclase CPOs in the database and we need to introduce some descriptive methods.We can classify them into three main groups (Fig. 3).The Axial-B fabric is defined by a strong point maximum concentration of (010) and perpendicular girdle distributions of [100] and (001), and it can be also called (010)-fiber pattern or texture.The type-P CPO shows point maxima of the three pole figures [100], ( 010) and ( 001), however the concentration of (001) poles is often weaker than the others.Lastly the Axial-A fabric has a strong point maximum concentra-tion of [100] with perpendicular girdle distributions of ( 010) and ( 001), this is a [100]-fiber pattern or texture.Nearly all of the plagioclase fabrics compiled in this study fall into one of these three groups, as reported in the last column of Table 3.However, some samples are noted in Table 3 as having weak or not identifiable CPOs.

Plagioclase CPO and microstructure
Figure 2 shows typical examples of magmatic flow and crystal-plastic flow textures, with corresponding CPOs.Samples with typical magmatic textures systematically show Axial-B fabric when CPO is developed, with a strong concentration of (010) planes parallel to the magmatic foliation of those samples (Fig. 2a to d).The systematic relationship between plagioclase (010) concentration and magmatic foliation is related to the tabular shape of plagioclase grains, and commonly described in other studies (e.g., Lamoureux et al., 1999;Morales et al., 2011).Sample 176-735B-133R1-35 shows type-P CPO, with [100] being sub-parallel to the foliation, and (010) normal to foliation (Fig. 2e), which is consistent with the classically described (010)[100] slip system (e.g., Montardi and Mainprice, 1987;Rosenberg and Stünitz, 2003).The other plastically deformed samples show Axial-A CPOs that have high concentrations of [100], consistent with the lineation direction, indicating that the activated plagioclase slip system is [100](010) and/or [100](001) (Fig. 2e to f), as described also by Mehl and Hirth (2008) in similar samples from ODP Hole 735B.

Fabric strength
The literature on olivine CPOs is abundant and their relationships with deformation processes and intensity are well documented (e.g., Ben Ismail and Mainprice, 1998;Dijkstra et al., 2002;Tommasi et al., 2004;Linckens et al., 2011).In contrast, because of the inherent difficulty to measure lowsymmetry crystal orientations in pre-EBSD times, the literature on plagioclase CPOs is much less abundant and relationships with deformation processes remain poorly documented (see references in the introduction).The calculated J index of all plagioclase fabrics reported in this study is shown in Figs. 4 and 5, and Table 3.We have removed from further analysis the three files with less than 100 measurements, as J is then abnormally high.The ODF J index ranges from 1.1 to 14.3, with a mean value of 4.1 and a standard deviation of 2.43.The fabric strength of samples with magmatic flow textures is slightly more variable than that of plastically deformed samples (Fig. 5a), both types of textures have dominantly weak J indices (Fig. 5a and d).

Eigenvalue analysis of (010) and [100] pole figure symmetry
To characterize (010) and [100] pole figure symmetry, as it is important to identify the differences between Axial-B type and Axial-A type, we use the BA-index defined by the eigenvalue analysis, which does not depend on contouring methods and is independent on the sample reference frame.This method is based on well-established technique of eigenvalue analysis of pole figures, and is presented in detail by Ulrich and Mainprice (2005), who used a similar index to quantify CPO variations in omphacite.
In the present study, there is a clear variation of the (010) and [100] pole figures from point maxima to girdle distributions, with associated changes in the (001) pole figures.We introduce the BA-index (similar to the LS index used Ulrich and Mainprice (2005) to described variations between the symmetry of ( 010 3, and ranges from 0.09 to 0.85.Samples with magmatic textures show a dominant Axial-B signature (Fig. 6a), consistent with our observation that magmatic sample CPOs are dominated by a strong maximum of (010).BA-indices related to CPOs of plastically deformed samples are more randomly distributed (Fig. 6b).
The variation of the ODF and pole figure J indices as a function of fabric symmetry shows some differences between samples with the magmatic (Fig. 6c) and plastic (Fig. 6d) deformation microstructures.Although ODF J indices have similar ranges in both microstructural types, pole figure J indices are nearly twice as strong for magmatic samples as   for plastic ones.The magmatic flow CPOs are more tightly grouped between Axial-B and P types with a BA-index of 0.1 to 0.6, whereas the plastic deformation CPOs are wildly spread over the full BA-index range.The (001) pole figure J index is the lowest pole figure value in both microstructural types.In the magmatic samples, the (010) pole figure J index is the highest values and the [100] pfJ has an intermediate value, but both decrease as the BA-index increases from 0.1 to about 0.6.In contrast, in the plastically deformed samples the (010) and ( 001) pfJ linear fit are almost constant, whereas the [100] pfJ increases with increasing BAindex, and is the highest pfJ value for BA-indices > 0.3.

Elastic symmetry analysis
Here we use the decomposition of the elastic tensors calculated using plagioclase CPOs (see Sect. 3) as additional information about fabric related symmetry.Both magmatic and plastic deformation microstructural types have very high isotropic components, 95.9 and 96.2 % respectively, and among the anisotropic components triclinic is the highest, 2.1 and 2.3 % respectively (Fig. 7, Table 4).The magmatic type has higher orthorhombic (1.0 %) and hexagonal (0.4 %) components whereas the plastic deformation has a relatively high monoclinic (0.8 %) component.

Seismic properties
We calculated two versions of the seismic properties, depending on the type of CPO data (1 ppg or gridded data) to show the effect of these parameters on the calculated properties: 1. 1 ppg data considering just the plagioclase CPOs (plagioclase 100 %, Table 5), and 2. gridded data considering just the plagioclase CPOs (plagioclase 100 %, Table 6).
The results for 1 sample are shown in Fig. 8 as an example.Seismic properties are calculated from 1 ppg data (Fig. 8a and c) and gridded data (Fig. 8b and d).P wave propagation is fastest parallel to the highest density of (010) and slowest in the orthogonal direction (Fig. 9a and b).The polarization plane of the fastest S wave (V s 1 ) is dominantly sub-perpendicular to the great circle that defines the preferred alignment of (010) planes.V p ranges from 6.56 to 6.80 km s −1 for the 1 ppg version, and from 6.51 to 6.91 km s −1 for the gridded data version.The differences between 1 ppg and gridded CPO data is the effect of the grain size heterogeneity that is only recorded in the gridded data; this effect is particularly marked in the case of a porphyroclastic texture with large porphyroclast grains as in sample 176-735B-133R1-35 (Fig. 2e).Gridded data in this case also produces higher values of anisotropy for both P wave and S wave, but does not markedly change the anisotropy direction; P wave anisotropy (AV p ) changes from 3.6 % to 5.9 %, and maximum S wave anisotropy (AV s max ) changes from 4.3 % to 7.3 % (Fig. 8).
To calculate seismic properties of the complete CPO database in a consistent way, including oldest data sets that were acquired manually, we have to use the 1 ppg data.This also has the advantage to allow a direct comparison with the other existing CPO database for olivine of Ben Ismaïl and Mainprice (1998).We should point out that 100 % plagioclase aggregates do not realistically represent the seismic properties of polyphased rocks such as gabbro, it does however allow us to quantify the contribution of plagioclase to the anisotropy of crustal rocks.The 100 % plagioclase aggregate P wave velocity varies from 6.38 km s −1 to 7.30 km s −1 , the mean S wave velocity varies from 3.29 km s −1 to 3.56 km s −1 , P wave anisotropy varies from 1.0 % to 11.0 %, and the maximum S wave anisotropy varies from 0.99 % to 13.85 %.The seismic properties of the three CPO symmetry types defined above, Axial-B, P-type and Axial-A, are presented in Fig. 9 for 100 % plagioclase aggregates.The P wave velocity distribution illustrates the changes with CPO symmetry; the Axial-B has a high V p point maximum normal to the foliation, the P-type has similar high velocity normal to the foliation and north-south girdle of high velocity, and the Axial-A has a high velocity girdle normal to the foliation.The evolution of the S wave anisotropy is more complex as Axial-B has two symmetrical girdles of high anisotropy.The P-type has two less symmetrical girdles of high anisotropy.The Axial-A has a large girdle of high anisotropy nearly parallel to the foliation.The V s 1 polarization pattern has no simple relationship to the foliation orientation, but is essentially sub-perpendicular to the foliation in all three types of CPO.

Relationships between seismic anisotropy, fabric strength and symmetry
The effect of plagioclase CPO symmetry on seismic properties is directly illustrated in Fig. 9.In all three types of CPO, the fast velocity direction of the samples is that of the preferred orientation of the normal to planes (010), i.e., perpendicular to the foliation in foliated samples.The Ptype symmetry is clearly a transitional symmetry between the two Axial-B and Axial-A end-members, with fast directions defining a point maximum, and a girdle, respectively.The magnitude of anisotropy does not change greatly between the three CPO symmetries, for both P wave (7.2, 7.7 and 6.4 %) and S wave (6.7, 8.2 and 7.2 %).The variation of the P wave velocities follows a simple pattern, the S wave anisotropy and V s 1 polarization have more complex distributions in all the CPO symmetry types.
In our database, the range of J index for plagioclase CPOs covers a slightly smaller range (1.1 to 14.3; Table 3) than that documented for olivine (2.3 to 16.9) when recalculated here using our MTEX code (Hielscher and Schaeben, 2008;Mainprice et al., 2011) for the data used by Ben Ismaïl and Mainprice (1998).Figure 10 shows the seismic anisotropy as a function of the ODF J index for both P waves (Fig. 10a) and S waves (Fig. 10b), we have also plotted a trend line for the olivine CPO data from Ben Ismaïl and Mainprice (1998).The seismic anisotropy increases as a non-linear function of fabric strength, up to 11 % for P wave and 14 % for S wave.The P wave anisotropy is higher for magmatic than plastic deformation microstructures (Fig. 10a), whereas for S wave anisotropy both microstructures have similar anisotropies.The scatter in anisotropy values for P and S waves for both microstructural types increases with increasing J index (Fig. 10a, b).This is more prominent for S waves, and was not observed for olivine by Ben Ismaïl and Mainprice (1998).The anisotropy of P waves (AV p ) varies between 1.0 and 11.0 %, with a mean value of 4.7 % and a standard deviation of 2.0, whereas the maximum shear wave splitting (AV s max ) varies between 1.0 % and 13.8 %, with a mean value of 4.7 % and a standard deviation of 2.2.AV p is smaller than those reported for olivine aggregates and AV s has similar range (in olivine aggregates, AV p varies between 3.1 % to 19.1% and AV s max varies between 2.5 % to 13.5 %; Ben Ismaïl and Mainprice, 1998).The trend line for AV p of olivine aggregates on Fig. 10a shows a much stronger anisotropy at low to moderate J index than that for plagioclase aggregates.Although seismic anisotropy (for both P and S waves) increases non-linearly as a function of fabric strength for both plagioclase (Fig. 10a and b) and olivine, the non-linearity is stronger for olivine.AV p is significantly higher in olivine, whereas for AV s olivine anisotropy is only slightly higher than that of plagioclase.
The plots of anisotropy as a function of fabric symmetry using the BA-index (Fig. 10c and d) shows similar trends for P and S wave, including high values for Axial-A and P-type for the magmatic microstructures.AV p and AV s do not vary significantly with fabric symmetry for the plastic deformation microstructure.The scatter is more apparent in the symmetry plots than for fabric strength, suggesting that fabric strength is the first-order control of the magnitude of anisotropy.

The effect of plastic deformation overprint of a magmatic microstructure on CPO type
In most plastically deformed samples, it is highly likely that crystal-plastic deformation is superposed on pre-existing  magmatic microstructure.This crystal-plastic overprint of magmatic textures is commonly described in slow-spread crust drill cores (e.g., Dick et al., 1999Dick et al., , 2000;;Blackman et al., 2006).In our plagioclase database, the factors that are consistent with such plastic deformation overprint are:    -Differences in the plot of PF J index versus ODF J index (Fig. 5c and d).A stronger linear correlation between PF and ODF J indices is seen for magmatic microstructure, formed by a simple CPO symmetry preserving a process of progressive CPO development.In contrast, plastic deformation microstructure has very poor correlation between PF and ODF J indices, particularly for the likely dominant [100] slip direction, and to lesser extent the likely (010) slip plane.The overprinting plastic deformation is probably developing in any orientation with respect to the pre-existing magmatic structure.If the latter has a strong CPO, it is plastically extremely anisotropic, and hence not necessarily very favorable to enhance (homogeneous) plastic deformation.
-Differences in the relation between fabric strength (ODF and PF J indices) and fabric symmetry (BAindex) (Fig. 6c and d). Figure 5 shows that magmatic samples has stronger fabrics than plastically deformed samples.The fabric symmetries of the magmatic samples are strongly dominated by Axial-B and to a lesser extent by P-type fabrics, i.e., they are strongly foliated, with variably well-defined lineations.In contrast, plastic deformation is not preferentially associated with any particular fabric type; it results in fairly widely distributed BA-index values (Fig. 6).The data suggests that plastic deformation may reduce the fabric strength as it imposes new fabric symmetry.As pointed above, the symmetry of CPO formed by plastic deformation is not systematically well aligned with the magmatic CPO, hence it has a tendency to destroy magmatic crystal alignment and produce a weaker CPO.
-If we refer to the symmetry of the elastic tensors calculated from plagioclase CPOs (Fig. 7), we note there is a difference between plastic deformation microstructure with relatively higher monoclinic symmetry component, with a ratio plastic / magmatic of 0.8 % / 0.4 %, and magmatic microstructure with relatively high orthorhombic and hexagonal, with ratios plastic / magmatic of 0.4 % / 1 % and 0.3 % / 0.4 %, respectively.In case of a superposed plastic deformation the high orthorhombic and hexagonal components of the magmatic microstructure are partly compensated by a relative increase of the monoclinic component (i.e., dominantly simple shear) associated with plastic deformation.

Conclusions
We have selected 169 plagioclase-bearing samples for detailed microstructural and CPO study.All samples had between 100 and 28 367 measured grains, with a total of 194 842 grains that have been measured with an average of 1153 grains per sample.This represents one order of magnitude increase in the number of mineral grains measured per sample compared with the olivine CPO database of Ben Ismaïl and Mainprice (1998).
The large mass of data has allowed the detection of a number of important characteristics of plagioclase CPOs:    010) and ( 001) (high BA-index≈0.7).The transition from Axial-B to Axial-A, through P-type, corresponds to the change from a dominantly foliated fabric, with the foliation marked by the preferred alignment of (010) planes, and no or a weak lineation, to a dominantly linear fabric, with the lineation defined by the preferred alignment of [100] axes.
-The classification of the microstructures in magmatic and plastic deformation allowed the distribution of the CPO symmetry to be defined, with the Axial-B and P-type being more frequent in the magmatic, whereas for plastic deformation the CPO symmetry is more distributed in all three types, with Axial-A being the most characteristic.Axial-A fabrics are particularly expected to develop when crystal-plastic deformation overprints a prominent magmatic foliation and is sub-parallel to it.In this case, the pre-existing foliation allow the grains to be favorably oriented for the [100](010) slip system to be preferentially activated -There is a significant difference in the relationship between the ODF and pole figures J indices.The magmatic microstructures have high (010) pole figures J indices, which vary linearly with ODF J index, where as the high [100] pole figures J indices of plastically deformed samples vary in a more scattered manner with ODF J index.In the magmatic case, the relation is simpler as it is only related to the preferred alignment of plagioclase grains in magmatic flow.The stronger scattering observed for plastic deformation results from the combination of changing CPO symmetry due to the superposition of plastic deformation on pre-existing magmatic CPOs, and of the possible activation of multiple slip systems during dislocation creep in plagioclase (e.g., Montardi and Mainprice, 1987;Stunitz et al., 2003).
-Seismic anisotropy increases as a function of plagioclase CPO strength (ODF J index) for both P and S waves.In comparison with the olivine CPO database of Ben Ismaïl and Mainprice (1998), the magnitude of P wave anisotropy for a given J index is much less than olivine, whereas it similar for S wave anisotropy.There is a weak correlation between seismic anisotropy and fabric symmetry for magmatic microstructures, being more anisotropic for Axial-B; there is no correlation for plastic deformation microstructures.
-The three CPO types are associated with three different distributions of seismic anisotropy.For P wave anisotropy the fast direction is correlated with the point maximum of (010) pole figure in all cases, i.e., normal to the foliation when the rock is foliated.The velocity is higher for the Axial-B, which typically has a stronger CPO.In the Axial-A CPO type, the high V p directions are distributed in a girdle normal to the point maximum of [100] pole figure, i.e., to the lineation.The girdle contains a maximum that is variably strong, depending on the preferred alignment of (010) planes that define a weak mineral foliation.The distribution of the S wave anisotropy also varies with CPO symmetry, but it has a relatively complex relationship to the foliation.

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-There is a small difference in the elastic anisotropy, with magmatic microstructures having higher orthorhombic and hexagonal components, whereas plastic deformation microstructures have a slightly higher monoclinic component, possibly correlated with predominant monoclinic simple shear flow in plastically deformed samples.
-There is a lot of scatter in many of the plots for CPO strength, pole figure strength, CPO symmetry and seismic anisotropy.This could be related to sampling statistics, although our database is a factor of ten larger than the olivine database of 1998, or it could be related to the low symmetry (triclinic) structure of plagioclase resulting in the addition of degrees of freedom in the processes creating the CPO.
Finally, the presence of others phases such as olivine, orthopyroxene and/or clinopyroxene will generally, by destructive interference, reduce seismic anisotropy in multi-phase plagioclase rocks, such as gabbros.

Fig. 2 .
Fig. 2. CPOs of plagioclase, and corresponding photomicrographs.(a-d) B-type CPOs of plagioclase of magmatic deformed samples.(a) HD70r14a from Hess Deep, (b) 98OB8B from Oman ophiolite, (c) 86OA20A from Oman ophiolite, (d) 89anok3 from Oklahoma.(e-f) Plastically deformed samples from ODP Hole 735B.(e) Type-P CPO and mylonitic texture deformed at low temperature, (f) Axial-A CPO and mylonitic texture deformed at low temperature, (g) Type-P CPO and porphyroclastic texture deformed at low temperature, (h) Axial-A CPO and medium grained deformed at high temperature.N is the number of measurements, pfJ is an index of pole figure intensity, and MD is the maximum pole figure density in times uniform distribution.Dotted lines and stars represent the trace of the foliation, and the vertical in the drill core, respectively.

Fig. 3 .
Fig. 3. Typical plagioclase Crystallographic preferred orientation (CPO) patterns.Lower hemisphere, equal-area stereographic projections, contours at one multiple of uniform distribution.The foliation plane, as defined by the preferred alignment of (010) is indicated by dashed great circles.N is the number of measurements, pfJ is an index of fabric intensity, and MD is the maximum density.Stars represent the vertical in the drill core, respectively.All plagioclase CPOs are classified within these three main types.Axial-B is defined by a strong point concentration of (010) perpendicular to the foliation and a girdle distribution of [100] parallel to the foliation; it can be also called (010)-fiber.Type P CPO shows point maxima of the three axes, with the (010) maximum perpendicular to the foliation.Type Axial-A has a strong point maximum concentration of [100] parallel to the lineation, and parallel girdle distributions of (010) and (001), perpendicular to the foliation.

Fig. 4 .
Fig. 4. Relationship between the fabric strength (J index) and the number of measured grains.CPOs with less than 100 measurements show abnormally high J values, and are not considered.

Fig. 5 .
Fig. 5. (a, b) Histograms of J index.Data are grouped as a function of deformation type (a) and CPO type (b).See text for further description.(c, d) Relation between ODF and pole figure J indices for magmatic (c) and plastic deformation microstructures (d).The straight lines [100], ⊥(010) and ⊥(001) are linear fits to scattered data for J index of pole figures of the plagioclase CPOs of individual samples.

Fig. 6 .
Fig. 6. (a, b) Histograms of BA-index.Data are grouped as a function of deformation type; (a) magmatic microstructure and (b) plastic deformation microstructure.(c, d) The variation of J index of ODFs and pole figures as a function of symmetry defined by BAindex for magmatic (c) and plastic deformation microstructures (d).The straight lines J , [100], ⊥(010) and ⊥(001) are linear leastsquared fits to scattered data for J index of ODFs and pole figures of the plagioclase CPOs of individual samples.

Fig. 7 .
Fig. 7. Decomposition of elastic symmetry into anisotropic triclinic, monoclinic, orthorhombic, tetragonal and hexagonal components of Voigt averages calculated using plagioclase CPOs.The frequencies are mean values of all samples.N.B. the isotropic symmetry component is not shown here, it represents 95.9 % of magmatic microstructure and 96.2 % of plastic deformation microstructure.

Fig. 8 .
Fig. 8. Seismic properties of sample 176-735B-133R1-35 (ODP Hole 735B oxide gabbro, crystal-plastic microstructure).Plagioclase CPOs plotted from 1 ppg (a) and gridded (b) data (see Secti.3.1 for further explanation).Dotted lines and stars represent the trace of the foliation, and the vertical in the drill core, respectively.Seismic properties are calculated from 1 ppg (c) and gridded (d) data.The differences between 1 ppg data and gridded data reflect the effect of the heterogeneity of grain size.Contours are multiples of uniform density; V p is the threedimensional distribution of the P wave velocity; anisotropy is 100(V p max − V p min )/(V p mean ); AV s is the three-dimensional distribution of the polarization anisotropy of S waves due to S wave splitting; and VS1 is the velocity of the fast S wave (S1); each small segment represents the orientation of the polarization plane at the point at which S1 penetrates the hemisphere.

Fig. 10 .
Fig. 10.Relation between P and S wave anisotropy of 100 % plagioclase aggregates with CPO strength measured by the J index of the ODF (a, b), and CPO symmetry measured by the BA-index for magmatic and plastic deformation microstructures (c, d).Red and blue curves lines in are power-law least-square fits (a, b) and linear least-square fits (c, d) for plagioclase.The green curve is the logarithmic least-square fit to the Ben Ismaïl and Mainprice (1998) data base of olivine CPOs.

Table 1 .
Geodynamic environment, deformation type, CPO type, locality and related references of each sample in this study.B, P and A in the CPO type column are Axial-B, type P and Axial-A, respectively.

Table 3 .
CPO characteristics for the gabbros studied here.I: data from interactive mode; M: data from mapping mode; N: number of measurements; BA: BA index.B, P and A in the CPO type column are Axial-B, type P and Axial-A, respectively; n.i.: not identified.

Table 5 .
Seismic properties (velocity and anisotropy) calculated as plagioclase 100 % using one point per grain data for gabbros studied here.V p : P wave; AV p : P wave anisotropy; AV s : S wave anisotropy, respectively.