Abstract Conductivity of fluids along fractures in all rocks is reduced by increasing normal stress. For sandstones and other hard rocks the onset of shear failure along planar cracks is thought to enhance fluid flow owing to a small amount of dilatancy, yet such effects are poorly quantified. Here we determine experimentally how independently increasing normal and shear stress affects fluid flow along fractures in shale. Gas flow along bedding-parallel planar interfaces was measured for flow parallel and normal to the shear direction. Increasing shear stress causes accelerating reduction of conductivity, even before the onset of macroscopic slip. Such reduction in fluid flow rate is non-recoverable, and the combined effects of normal and shear stress can reduce fracture conductivity by more than 3 orders of magnitude over the range of shale reservoir conditions. Bedding plane-parallel slip is common in shales; it can result in a large enhancement of permeability anisotropy, because flow across bedding planes becomes inhibited. This can impact upon the geometry of developing hydraulic fractures, encouraging complexity and favouring lateral relative to vertical growth. The results will facilitate modelling of fluid flow through fracture networks. Supplementary material: A CSV file containing all experimental conditions and tabulations of results is available at https://doi.org/10.6084/m9.figshare.c.3721831 .

Abstract Specimens of Solnhofen limestone were deformed under conditions where calcite deforms plastically using four experimental configurations: extension, torsion, direct shear and axisymmetric shortening. All experiments were run on dry specimens at the same temperature (600 °C), confining pressure (200 MPa) and comparable strain rates ( c. 10 −4 s −1 ). The different experimental settings and the heterogeneity of deformation within some of the specimens provided a large range of strain geometries. They allowed locally imposed strain geometries to be related to the crystallographic preferred orientation (CPO) patterns of calcite and the orientation of the shape fabric of calcite grains. CPO in calcite was measured using electron back-scattered diffraction (EBSD) in scanning electron microscopy. The development of CPO during deformation under the dominance of intracrystalline plasticity contains information about the strain geometry accumulated in rocks in 3D, although in nature the strain geometry can be modified by dynamic recrystallization that was not seen in the experiments. The different CPO patterns have a significant effect on the velocity structure of the deformed aggregates. Seismic properties inferred from CPO show that the orientation of the fastest V p wave aligns with principal strain directions that are not equivalent in different strain geometries.

Abstract This special publication of the Geological Society of London presents recent advances in the study of deformation mechanisms and rheology and their application to tectonics. We have subdivided the papers into two themed sections. The inference of deformation processes, conditions and rheology at depth in active tectonic settings is of fundamental importance to a quantitative geodynamic understanding of deformation in the Earth. The papers in the section on Lattice Preferred Orientations and Anisotropy are extremely important as they underpin our ability to make such geodynamic interpretations from global seismic data. These papers reflect the growing emphasis on the determination of elastic properties from microstructures, from which acoustic properties can be computed for comparison with in situ seismic measurements. The component of the microstructure that receives most attention is the lattice preferred orientation (LPO), otherwise known as the crystallographic preferred orientation (CPO) or the texture (the term used in material science and metallurgy). The papers include new LPO measurements (made almost exclusively by the relatively new technique of electron backscatter diffraction or EBSD), exploration of the significance of these data for seismic properties of both the crust and the mantle and modelling of LPO generation. An invited contribution from Mainprice and colleagues introduces a computational toolbox to help researchers calculate anisotropic physical properties from their LPO data. Rock microstructures evolve during deformation and rock physical properties, including both elastic properties and creep rheology, evolve with the microstructures as a function of strain and time. The section on Microstructures, Mechanisms and Rheology

Abstract For the past two decades geodetic measurements have quantified surface displacement fields for the continents, illustrating a general complexity. However, the linkage of geodetically defined displacements in the continents to mantle flow and plate tectonics demands understanding of ductile deformations in the middle and lower continental crust. Advances in seismic anisotropy studies are beginning to allow such work, especially in the Himalaya and Tibet, using passive seismological experiments (e.g. teleseismic receiver functions and records from local earthquakes). Although there is general agreement that measured seismic anisotropy in the middle and lower crust reflects bulk mineral alignment (i.e. crystallographic preferred orientation, CPO), there is a need to calibrate the seismic response to deformation structures and their kinematics. Here, we take on this challenge by deducing the seismic properties of typical mid- and lower-crustal rocks that have experienced ductile deformation through quantitative measures of CPO in samples from appropriate outcrops. The effective database of CPO and hence seismic properties can be expanded by a modelling approach that utilizes ‘rock recipes’ derived from the as-measured individual mineral CPOs combined in varying modal proportions. In addition, different deformation fabrics may be diagnostic of specific deformation kinematics that can serve to constrain interpretations of seismic anisotropy data from the continental crust. Thus, the use of ‘fabric recipes’ based on subsets of individual rock fabric CPO allows the effect of different fabrics (e.g. foliations) to be investigated and interpreted from their seismic response. A key issue is the possible discrimination between continental crustal deformation models with strongly localized simple-shear (ductile fault) fabrics from more distributed (‘pure-shear’) crustal flow. The results of our combined rock and fabric-recipe modelling suggest that the seismic properties of the middle and lower crust depend on deformation state and orientation as well as composition, while reliable interpretation of seismic survey data should incorporate as many seismic properties as possible.

Abstract The lattice preferred orientation (LPO) of both muscovite and biotite were measured by electron backscatter diffraction (EBSD) and these data, together with the LPOs of the other main constituent minerals, were used to produce models of the seismic velocity anisotropy of the Alpine Fault Zone. Numerical experiments examine the effects of varying modal percentages of mica within the fault rocks. These models suggest that when the mica modal proportions approach 20% in quartzofeldspathic mylonites the intrinsic seismic anisotropy of the studied fault zone is dominated by mica, with the direction of the fastest P and S wave velocities strongly dependent on the mica LPOs. The LPOs show that micas produce three distinct patterns within mylonitic fault zones: C-fabric, S-fabric and a composite S–C fabric. The asymmetry of the LPOs can be used as kinematic indicators for the deformation within mylonites. Kinematic data from the micas matches the kinematic interpretation of quartz LPOs and field data. The modelling of velocities and velocity anisotropies from sample LPOs is consistent with geophysical data from the crust under the Southern Alps. The Alpine Fault mylonites and parallel Alpine schists have intrinsic P-wave velocity anisotropies of 12% and S-wave anisotropies of 10%.

Abstract The Nanga Parbat Massif (NPM), Pakistan Himalaya, is an exhumed tract of Indian continental crust and represents an area of active crustal thickening and exhumation. While the most effective way to study the NPM at depth is through seismic imaging, interpretation depends upon knowledge of the seismic properties of the rocks. Gneissic, ‘mylonitic’ and cataclastic rocks emplaced at the surface were sampled as proxies for lithologies and fabrics currently accommodating deformation at depth. Mineral crystallographic preferred orientations (CPO) were measured via scanning electron microscope (SEM)/electron backscatter diffraction (EBSD), from which three-dimensional (3D) elastic constants, seismic velocities and anisotropies were predicted. Micas make the main contribution to sample anisotropy. Background gneisses have highest anisotropy (up to 10.4% shear-wave splitting, AVs) compared with samples exhibiting localized deformations (e.g. ‘mylonite’, 4.7% AVs; cataclasite, 1% AVs). Thus, mylonitic shear zones may be characterized by regions of low anisotropy compared to their wall rocks. CPO-derived sample elastic constants were used to construct seismic models of NPM tectonics, through which P-, S- and converted waves were ray-traced. Foliation orientation has dramatic effects on these waves. The seismic models suggest dominantly pure-shear tectonics for the NPM involving horizontal compression and vertical stretching, modified by localized ductile and brittle (‘simple’) shear deformations.

Abstract Samples of the Acebuches metabasites (SW Spain), deformed under low-pressure/medium-to-high temperature metamorphic conditions, have been analysed via electron backscattered diffraction (EBSD) to obtain their plagioclase crystal lattice preferred orientations (LPO). Plagioclases from the highest temperature amphibolites show moderate LPO and a good correlation between 180° misorientation angles and both the crystal and the kinematic coordinate systems, which is attributed to dislocation glide accommodated by mechanical albite+pericline twinning. Plagioclases from medium-temperature amphibolites exhibit well-developed LPO, suggesting that dislocation creep was active during plagioclase deformation. Plagioclases from the more intensively deformed mafic schists exhibit weak LPO, indicating the activity of LPO-destroying deformation mechanisms. Evidence points to grain-boundary sliding accompanied by limited fracturing. The observed LPO are characterized by the alignment of [100] parallel to the kinematic X -direction. This association suggests that [100] was the preferential slip direction during dislocation creep of plagioclase, with (010) and/or (001) appearing to have acted as the dominant slip planes. The observed plagioclase LPO is combined with hornblende LPO to define the seismic fabric of the Acebuches metabasites. In samples with strong plagioclase LPO, the resulting seismic fabrics are highly influenced by this phase.

Abstract The relationships between elastic wave velocities and petrofabrics were studied in two antigorite-bearing serpentinite mylonites. Rock samples with antigorite content of 37 and 80 vol% were collected from the Happo ultramafic complex, Central Japan. Compressional and shear-wave velocities were measured by the pulse transmission technique at room temperature and confining pressures of up to 180 MPa. Petrofabrics were examined by optical microscopy and scanning electron microscopy with electron backscattered diffraction (SEM-EBSD). Olivine a - and c -axes are weakly oriented perpendicular to the foliation and parallel to the lineation, respectively. Antigorite b - and c -axes are distinctly oriented parallel to the lineation and perpendicular to the foliation, respectively. Both samples show strong anisotropy of velocity. The compressional wave velocity is fastest in the direction parallel to the lineation, and slowest in the direction perpendicular to the foliation. The shear wave oscillating parallel to the foliation has higher velocity than that oscillating perpendicular to the foliation. As the antigorite content increases, the mean velocity decreases but both azimuthal and polarization anisotropies are enhanced. Measured velocities were compared with velocities calculated from petrofabric data by using Voigt, Reuss and Voight-Reuss-Hill (VRH) averaging schemes. All averaging schemes show velocity anisotropy qualitatively similar to measurements. There are large velocity differences between Voigt and Reuss averages (0.7–1.0 km/s), reflecting the strong elastic anisotropy of antigorite. Measured velocities are found between Reuss and VRH averages. We suggest that the relatively low velocity is due to the platy shape of antigorite grains, the well-developed shape fabric and their strong elastic anisotropy. The configuration of grains should be an important factor for calculating seismic velocities in an aggregate composed of strongly anisotropic materials, such as sheet silicates.

Abstract Large parts of the mantle wedge near subduction boundaries are likely to be hydrated and contain antigorite. This mineral is acoustically highly anisotropic and potentially has a strong influence on seismic properties of the wedge. The Higashi–Akaishi body of SW Japan is an exhumed sliver of partially serpentinized forearc mantle, ideal for studying the effects of antigorite on the development of tectonic fabrics in the mantle. Samples with less than 1% antigorite show strong B-type olivine crystallographic preferred orientation (CPO) patterns. In contrast, samples with >10% antigorite deformed during the same tectonic event show much weaker olivine CPO patterns lacking the flow-normal a -axis concentration. These microstructural data suggest that the development of antigorite during deformation weakens olivine CPO due to phase boundary slip and associated rigid-body rotation of olivine grains. Antigorite and similar sheet silicates are likely to be present to some extent in the mantle wedge of all convergent margins. Our results suggest that even if this amount is only a few percent, strong olivine CPO is unlikely to develop and any pre-existing CPO is likely to be destroyed. Under these conditions, olivine CPO is unlikely to contribute significantly to seismic anisotropy in the mantle wedge.

Abstract Serpentinite is widely assumed to constitute weak material in subduction zones and to play an essential role for the development of a subduction channel. Information on deformation mechanisms and appropriate rheological models to describe these large-scale flow processes can only be obtained from natural serpentinites exhumed from ancient subduction zones. We examine the microstructural record of HP-metamorphic ( P c. 2±0.5 GPa, T c. 550±50 °C) serpentinites exposed in the Zermatt–Saas zone, Western Alps, using optical and scanning electron microscopy with electron backscatter diffraction (EBSD). The schistose and compositionally layered rocks show pervasive small-scale folding. There is no evidence for any significant deformation by dislocation creep. Instead, the microfabrics including strain shadows and crenulation cleavage indicate that high strain is accumulated by dissolution precipitation creep. In terms of rheology, this suggests Newtonian behaviour and a low viscosity for the long-term flow of serpentinites in deeper levels of subduction zones. This does not preclude dislocation creep and a power law rheology at higher stress levels, as realized at local sites of stress concentration and transient episodes of post-seismic creep.

Abstract We have applied transmission electron microscopy (TEM) analyses coupled with viscoplastic self-consistent (VPSC) numerical modelling to identify the active slip systems and to better understand the crystal preferred orientation (CPO) development of the Torridon quartz mylonite (NW Scotland). TEM analyses showed evidence of activation of 1/3〈 a 〉{π′}, 1/3〈 a 〉{ z } and possible 〈 a 〉( c ) slip systems, as well as dislocation climb and dynamic recrystallization. All the CPOs generated by VPSC models share common characteristics with the Torridon quartz mylonite, but only Models 2 and 3 reproduce the [ c ]-axes maxima at low angle (<20°) to the foliation pole along the YZ plane, as observed in the mylonite. In Model 2, this concentration only occurs at γ≥2.6, whereas in Model 3 this maxima occurs at lower shear strains. The models that start with a previous preferred orientation acquire very strong CPOs after small-imposed strains, followed by the rapid rotation of the fabric in relation to the new imposed finite strain axes. The combined activation of 〈 a 〉{π′}, 〈 a 〉{ z } and possibly 〈 a 〉( c ) slip systems, as demonstrated by TEM analyses, suggests that the VPSC model that best predicts CPO development in the Torridon quartz mylonite is Model 2, where the critical resolved shear stress (CRSS) of 〈 a 〉{π/π′} is assumed to be slightly stronger than 〈 a 〉( c ).

Abstract This paper presents the background for the calculation of physical properties of an aggregate from constituent crystal properties and the texture of the aggregate in a coherent manner. Emphasis is placed on the important tensor properties of 2nd and 4th rank with applications in rock deformation, structural geology, geodynamics and geophysics. We cover texture information that comes from pole figure diffraction and single orientation measurements (electron backscattered diffraction or EBSD, electron channelling pattern, Laue pattern, optical microscope universal-stage). In particular, we provide explicit formulae for the calculation of the averaged tensor from individual orientations or from an orientation distribution function (ODF). For the latter we consider numerical integration and an approach based on the expansion into spherical harmonics. This paper also serves as a reference paper for the mathematical tensor capabilities of the texture analysis software MTEX, which is a comprehensive, freely available MatLab toolbox that covers a wide range of problems in quantitative texture analysis, for example, ODF modelling, pole figure to ODF inversion, EBSD data analysis and grain detection. MTEX offers a programming interface which allows the processing of involved research problems as well as highly customizable visualization capabilities; MTEX is therefore ideal for presentations, publications and teaching demonstrations.

Abstract Evidence of localized strain is ubiquitous in deformed lithospheric rocks. Recent advances in laboratory deformation techniques, including the use of torsion experiments, have enabled the coupling of microstructural and rheological evolution to be investigated in experiments run to strains approaching those reached in many natural shear zones. Further, the increased use of electron backscatter diffraction to quantify crystallographic preferred orientation (CPO) has significantly increased understanding of CPO formation and evolution. Combined, these laboratory and field observations support the assertion that a rock's microstructure is strongly linked to its rheology. However, complete quantification of the coupling between microstructure and rheology is complicated by the fact that rocks have inherently complex microstructures. This paper reviews recent work focused on quantifying the rates of microstructural evolution and the attainment of steady state for two key microstructural parameters: grain size and crystallographic preferred orientation. Theoretical considerations, laboratory measurements and field observations suggest that a full description of all relevant microstructural parameters, and the appropriate evolution equations for these parameters, may be needed to link microstructural and rheological evolution and therefore to quantify the bulk rheology of the lithosphere.

Abstract Large strain deformation experiments in torsion were conducted on a coarse-grained natural dunite with a pre-existing lattice preferred orientation (LPO). Experiments were conducted at conditions where deformation by diffusion creep is initially negligible. Microstructural evolution was studied as a function of strain. We observe that the pre-existing LPO persists to a shear strain of at least 0.5. At larger strains, this LPO is transformed. Relict deformed grains exhibit LPO with [100] crystallographic axes at high angles to the shear plane. Unlike previous experimental studies, these axes do not readily rotate into the shear plane with increasing strain. Partial dynamic recrystallization occurs in samples deformed to moderate strains ( γ >0.5). Recrystallized material forms bands that mostly transect grain interiors. The negligible rate of diffusion creep along relict grain boundaries, as well as the limited nature of dynamic recrystallization, may account for the relatively large strains required to observe evolution of microstructures. Our data support hypotheses based on natural samples that microstructures may preserve evidence of complex deformation histories. Relationships between LPO, seismic anisotropy and deformation kinematics may not always be straightforward.

Abstract A slip-system analysis was performed on two synthetic compressively deformed olivine aggregates, derived from experimental solution–gelation (sol–gel) and natural San Carlos precursors to determine how dislocation density relates to Schmid factor for slip in olivine. Individual grain orientations were measured with electron backscatter diffraction. Using decorated dislocations, grain populations were separated into subsets of high versus low dislocation density. Analysis of preferred orientations and distributions of Schmid factors suggests that there is only weak correlation between Schmid factor and dislocation density, slip on (010)[100] in San Carlos grains but (001)[100] in sol–gel material, with multiple slip or stress heterogeneity in both.

Abstract Anhydrite-rich layers within foreland fold and thrust belts are frequently observed to be the weakest horizon of the sequence. Characterizing the microstructure of anhydrite is therefore important for interpreting the larger-scale deformation history of these rocks. Two microstructures from naturally deformed, fine-grained (<15 µm mean grain size) anhydrite samples from the Triassic Evaporites of the Umbria–Marche Apennines, Italy were analysed using electron backscatter diffraction (EBSD). Microstructural observations, misorientation analysis and crystallographic preferred orientation (CPO) determination were carried out on these samples. Both samples have a CPO characterized by alignment of 〈001〉 and distribution of 〈100〉 and 〈010〉 on a great circle normal to this. This anhydrite 〈001〉 ‘fibre texture’ has not been described before. Microstructure A is characterized by a moderate to weak CPO and a weak shape preferred orientation at 55° to 70° from the trace of the 〈001〉 maximum. Low-angle boundaries are revealed by misorientation analysis. A change in grain size from c . 10 to c . 7 µm corresponds to reduction in strength of CPO and reduction in the number of low-angle grain boundaries. Microstructure B is characterized by a very strong CPO. The orientation of the CPO changes between different microstructural domains. The 〈001〉 maximum is always perpendicular to the trace of a strong grain elongation and high-angle grain boundaries have misorientations close to 〈001〉, suggesting that the CPO is geometrically controlled: anhydrite grains are platy with 〈001〉 short axes. The origin of the CPO is therefore unclear but it need not relate to dislocation creep deformation. Whether or not CPO relates to dislocation creep, both samples have a high number of lower-angle grain boundaries and internal grain distortions with 〈010〉 and 〈001〉 misorientation axes. These are indicative of dislocation activity and the data are best explained by slip on either (100)[010] (dominant) and (001)[100] or a combination of these. Neither of these slip systems has been recognized before. Both microstructures are interpreted to have undergone dynamic recrystallization, and the weakening of the CPO with decreasing grain size in microstructure A is suggested to be indicative of a grain-boundary sliding mechanism becoming active. Comparison with experimental data shows that creep mechanisms involving dislocations at the observed grain sizes require the differential stress magnitudes driving deformation to be greater than c . 100 MPa.

Abstract Extreme grain-size reduction due to cataclasis, neocrystallization or phase change results in a switch to diffusion creep and dramatic weakening in deforming rocks. Grain growth increases strength until dislocation creep becomes a significant deformation mechanism. We quantify the ‘lifetime’ of diffusion creep by substituting the normal grain growth law into the diffusion creep flow law to calculate the time taken for dislocation creep to become significant. Stress-temperature and strain-rate-temperature space is outlined where diffusion creep may accommodate significant strain: these regions have an upper temperature limit beyond which grain growth is fast enough to move the rock quickly into the dislocation creep field. For plagioclase the limit lies in the amphibolite facies. Rocks in a mantle upwelling experience grain-size reduction during phase changes. Pressure-dependent grain growth limits the deformation that can be accommodated by diffusion creep. This time limit and associated strain limit is independent of starting grain size with a small dependence on upwelling rate and plume width. In both these tectonic environments, second phases are likely to play a role in the maximum achievable grain size due to grain-boundary pinning. Hence we predict the minimum lifetimes of diffusion-creep-dominated deformation following extreme grain-size reduction.

Abstract The inter-relationships between mineral reactions and deformation are explored with a view to understanding the development of certain mineral foliations and lineations. The following arguments are presented: (i) the processes involved during mineral reactions in deforming metamorphic rocks are described by coupled reaction–diffusion–deformation equations; (ii) these reactions can become unstable producing compositional patterning in both space (metamorphic differentiation) and time (compositional zoning); (iii) the patterns (foliations and mineral lineations) that result from coupled reaction–diffusion–deformation equations are described by surfaces that approximate minimal surfaces (surfaces of zero mean curvature) and an example of such geometry is given; and (iv) the foliations and mineral lineations that form by such processes are controlled by the evolution of the kinematics of the deformation history and not by the finite strain tensor.

Abstract A description of the systematic errors associated with the measurement of the vorticity number from poryhroclasts in natural systems is presented and discussed. We show that strong biases and systematic errors could derive both from some erroneous physical (i.e. no slip across clast/matrix boundary, homogeneity within the matrix) as well as geometrical assumptions (i.e. the radius ratio and angular measurements carried out in two dimensions on outcrop surfaces and thin section). By comparing natural datasets of porphyroclast shape preferred orientation (SPO) with different theoretical curves plots, we suggest that at least one of the Jeffery physical assumptions can be tested when applying vorticity techniques. The comparison of different possible sources of systematic errors indicates that, for medium-to-low vorticity numbers ( W m <0.8), vorticity data are strongly biased and that a minimum systematic error of 0.2 should be taken into account. Finally, we use data from natural shear zones from the Southern Variscan Belt in Sardinia to test and discuss the starting assumptions of the Jeffery model.