褶皱复杂程度的分形分类

本文根据褶皱的白相似性特征,引用分形概念,分析褶皱的分形分布特性,并利用MichaelBamsley（1986）的分形插值理论首次模拟褶皱的复杂形态,主要利用插值点（x、y）和褶皱扰动系数d模拟各种褶皱,在此基础上,提出褶皱复杂程度的分形分类方案。这种新的分类方案即褶皱形态的传统分类名称附缀分形分类名称,解决了传统分类方法不能区分褶皱复杂性的难题。这种方法使褶皱的形态分析达到较精确的定量描述和分类,分形分类方法是对褶雏形态分类的一个补充。     

Transmission of Elastic P-waves across Single Fractures with a Nonlinear Normal Deformational Behavior

Summary This paper presents a theoretical study on normally incident elastic P-wave transmission across single dry fractures with a nonlinear normal deformational behavior. The effects of nonlinear fracture normal behavior on P-wave transmission are examined without the mixture of fracture shear behavior. The linear displacement discontinuity model for wave propagation across fractures is extended to a nonlinear model – the hyperbolic elastic model (BB model). Numeric solutions of magnitudes of transmission (|T _non|) and reflection (|R _non|) coefficients, for normally incident P-wave transmission across the nonlinear deformable fractures, are obtained and related to the closure behavior of fractures. Parametric studies are conducted to acquire an insight into the effects of the nonlinear fracture normal deformation on P-wave transmission, in terms of initial normal stiffness and the ratio of current maximum closure to maximum allowable closure of the fractures, as well as the incident wave amplitude and frequency. Comparisons between the linear and nonlinear models are presented. It is shown that, |T _lin| and |R _lin| for the linear model are special solutions of |T _non| and |R _non| for the nonlinear model, when the incident wave amplitude is so low that the current maximum closure of fracture incurred during the wave transmission is much smaller, relative to the maximum allowable closure. In addition, the nonlinear fracture behavior gives rise to a phenomenon of higher harmonics during the wave transmission across the fracture. The higher harmonics contribute to the increase of |T _non| from |T _lin|.     

Layer shortening and fold-shape development in the buckling of single layers

The progressive development of folds by buckling in single isolated viscous layers compressed parallel to the layering and embedded in a less viscous host is examined in several ways; by use of experiments, an analogue model to simulate simultaneous buckling and flattening and by an application of finite-element analysis.The appearance of folds with a characteristic wavelength in an initially flat layer occurs in the experiments for viscosity ratios (μ_layer/μ_host = μ₁/μ₂) of between 11 and 100; progressive fold development after the initial folds have appeared is similar in the experiments and in the finite-element models. Except for the finite-element model for μ₁/μ₂ = 1,000 layer-parallel shortening occurs in the early stages of folding and a stage is reached where little further changes in arc length occur. The amount of layer-parallel shortening increases with decreasing viscosity contrast, and becomes relatively unimportant after the folds have attained limb dips of about 15°–25°.Thickness variations with dip are only significant here for the finite-element model with μ₁/μ₂ = 10, and in experiments for μ₁/μ₂ = 5 where the layer is initially in the form of a moderate-amplitude sine wave. The variations range from a parallel to a near-similar fold geometry, and in general depend on the viscosity contrast, the degree of shortening and the initial wavelength/thickness ratio. They are very similar to the variations predicted by the analogue model of combined buckling and flattening. The difference between the thickness/dip variations in a fold produced by buckling at low viscosity contrast and one produced by flattening a parallel fold is marked at high limb dips and very slight at low limb dips.Many natural folds in isolated rock layers or veins show thickness/dip relationships expected for a flattened parallel fold, and some show relationships expected for buckling at low viscosity contrasts. Studies of the wavelength/thickness ratios in natural folds have suggested that competence contrast is often low. Many folds in isolated rock layers or veins whose geometry may vary between parallel and almost similar, and may be indistinguishable from those of flattened parallel folds, have probably developed by a process of buckling at low viscosity contrasts.     

The structural evolution of sheath folds: A case study from Cap de Creus

It has long been recognised that within zones of intense non-coaxial deformation, fold hinges may rotate progressively towards the transport direction ultimately resulting in highly curvilinear sheath folds. However, there is a surprising lack of detailed and systematic field analysis of such “evolving” sheath folds. This case study therefore focuses on the sequential development of cm-scale curvilinear folds in the greenschist-facies El Llimac shear zone, Cap de Creus, Spain. This simple shear-dominated dextral shear zone displays superb three dimensional exposures of sheath folds defined by mylonitic quartz bands within phyllonite. Increasing amounts of fold hinge curvature (δ) are marked by hinge segments rotating into sub-parallelism with the mineral lineation (Lm), whilst the acute angle between the axial-planar hinge girdle and foliation (ω) also displays a sequential reduction. Although Lm bisects the noses of sheath folds, it is also clearly folded and wrapped-around the sheath hinges. Lm typically preserves a larger angle (θ) with the fold hinge on the lower limb (L) compared to the upper (U) limb (θL > θU), suggesting that Lm failed to achieve a steady orientation on the lower limb. Adjacent sheath fold hinges forming fold pairs may display the same sense of hinge arcing to define synthetic curvature, or alternatively opposing directions of antithetic curvature. Such patterns reflect original buckle fold geometries coupled with the direction of shearing. The ratio of long/short fold limbs decreases with increasing hinge curvilinearity, indicating sheath folds developed via stretching of the short limb, rather than migrating or rolling hinge models. This study unequivocally demonstrates that both hinges of fold pairs become curvilinear with sheaths closing in the transport direction recording greater hinge-line curvilinearity compared to adjacent return hinges. This may provide a useful guide to bulk shear sense.     

Response of unconfined turbidity current to deep‐water fold and thrust belt topography: Orthogonal incidence on solitary and segmented folds

Sea‐floor topography of deep‐water folds is widely considered to have a major impact on turbidity currents and their depositional systems, but understanding the flow response to such features was limited mainly to conceptual notions inspired by small‐scale laboratory experiments. High‐resolution three‐dimensional numerical experiments can compensate for the lack of natural‐scale flow observations. The present study combines numerical modelling of thrusts with fault‐propagation folds by Trishear3D software with computational fluid dynamics simulations of a natural‐scale unconfined turbidity current by MassFlow‐3D? software. The study reveals the hydraulic and depositional responses of a turbidity current (ca 50 m thick) to typical topographic features that it might encounter in an orthogonal incidence on a sea‐floor deep‐water fold and thrust belt. The supercritical current (ca 10 m sec^?1) decelerated and thickened due to the hydraulic jump on the fold backlimb counter‐slope, where a reverse overflow formed through current self‐reflection and a reverse underflow was issued by backward squeezing of a dense near‐bed sediment load. The reverse flows were re‐feeding sediment to the parental current, reducing its waning rate and extending its runout. The low‐efficiency current, carrying sand and silt, outran a downslope distance of >17 km with only modest deposition (<0·2 m) beyond the fold. Most of the flow volume diverted sideways along the backlimb to surround the fold and spread further downslope, with some overspill across the fold and another hydraulic jump at the forelimb toe. In the case of a segmented fold, a large part of the flow went downslope through the segment boundary. Preferential deposition (0·2 to 1·8 m) occurred on the fold backlimb and directly upslope, and on the forelimb slope in the case of a smaller fold. The spatial patterns of sand entrapment revealed by the study may serve as guidelines for assessing the influence of substrate folds on turbiditic sedimentation in a basin.     

分形褶皱复杂性的流变因素研究

根据Ramberg的纵弯褶皱粘性力学实验,在褶皱形态的分形分析基础上,利用分形理论和褶皱的流变学理论导出了褶皱的分数维(D)与岩层厚度(h)和粘度(μ)间的关系式,并探讨了褶皱复杂性对褶皱分数维的影响,从中获得有关复杂褶皱的流变学信息。影响分形褶皱复杂程度的因素很多,主要因素包括岩层的厚度和粘度。因此,对褶皱的分形测量和岩层厚度及粘度的分析,可以定量分析分形褶皱形成的流变机理。这一研究是褶皱的非线性流变学理论研究的一个尝试。     

On the Equivalence of the Cokriging and Kriging Systems

Simple cokriging of components of a p-dimensional second-order stationary random process is considered. Necessary and sufficient conditions under which simple cokriging is equivalent to simple kriging are given. Essentially this condition requires that it should be possible to express the cross-covariance at any lag series h using the cross-covariance at |h|=0 and the auto-covariance at lag series h. The mosaic model, multicolocated kriging and the linear model of coregionalization are examined in this context. A data analytic method to examine whether simple kriging of components of a multivariate random process is equivalent to its cokriging is given     

Conical folds and apparent rotations in paleomagnetism (a case study in the Southern Pyrenees)

The so-called apparent rotation was defined as the angular deviation between a local paleomagnetic direction (after the standard bedding correction) and their corresponding paleomagnetic reference [J. Geophys. Res. 85 (1980) 3659]. In this paper, we make a theoretical exploration on this concept and we conclude that (depending on the number, sequence, orientation and magnitude of the deformation axes that have affected to the rock volume) the apparent rotation may be the addition of a vertical-axis rotation plus a spurious rotation. The later is an error whose origin is the inappropriate application of the bedding correction during the restoration (which does not fit the reverse sequence of deformations). Then, Apparent rot. (s.l.) (δ)=Spurious rot. (θ)+Vertical-axis rot. (β).Conical folds are complex geometries that cannot be restored by using the bedding correction. However, appearance of apparent and spurious rotations has not been studied even though the presence of this kind of folds is very common in fold and thrust belts. In this paper, we show a way to restore these structures and its associated paleomagnetic data by means of forward modelling on a stereographic projection. The modelling has to be based on a good characterization of the geometry (fold axis orientation) and understanding of the kinematics of the fold. General modelling has also allowed us to predict the apparent rotation in conical synclines. Its magnitude depends on the semiapical angle and on the degree of development of the fold; the sense of the rotation (clockwise or counter-clockwise) will depend on the sense of rotation the fold axis.The western External Sierras provide an excellent case study of apparent rotations due to the presence of a conical fold in the footwall (Ebro foreland basin) of the South Pyrenean sole thrust. In addition, a vertical-axis clockwise rotation up to 47° (32° in average) has been detected in the hagingwall. An apparent rotation up to 28° (20° in average) is observed in the footwall of the structure when a simple bedding correction is used. This deviation does not fit with the expected Ebro basin direction (reference) and is caused by the effect of the Riglos conical syncline, developed by the flexure of the foot wall ramp of the South Pyrenean sole thrust. The forward modelling carried out considering the geometry and kinematics (non significant rotations in the autochthonous foot wall) of this structure predicts very well the paleomagnetic observations in the field (geographic coordinates) with angular departures of only 5° (in average). The only application of the bedding correction would introduce errors (spurious rotations up to 21°, 12 in average) related to the conical geometry that would not allow the differentiation of these distinct structural units.     

Experimental analysis of folding in simple shear

Six experiments of single-layer folding with simple-shear boundary conditions were completed. Using materials of ethyl cellulose, the viscosity ratio of the stiff layer to matrix ranged from 20 to 100. The experiments were monitored by 10–14 photographs taken at equally spaced time intervals. Strain distributions in both the stiff layer and matrix were calculated from the displacements of over 300 ink dots distributed over the surface of each experiment. Both incremental strain (calculated from the relative displacements of the dots between successive photographs) and accumulating strain were determined on the two-dimensional profile of the materials as they folded.Symmetrical fold wavelengths occur and seem to be controlled by the wavelengths of initial perturbations in the stiff layer. If the Biot wavelength was not present initially, it will not occur in the final waveform. Consequently, in a group of natural folds, the mean value of wavelength/thickness ratios apparently reflects the initial perturbations. The mean value should not be confused with the Biot wavelength and should not be used to calculate viscosity ratios in naturally deformed rocks.Substantial layer thickening occurred only with viscosity ratios of 20. The amount of layer thickening also depends on initial perturbations of the stiff layer. If these perturbations are near the Biot wavelength, they are greatly amplified, the folds grow rapidly and layer thickening is small. If the perturbations are not near the Biot wavelength, amplification is small, the folds grow slowly and layer thickening is much greater.Principal elongations of the accumulated strain in the cores of some of the folds are not symmetrically distributed about axial planes and may cut across the axial plane at angles up to 20°. Strain shadows in the matrix, near the convex side of fold hinges, are also prominent. These triangular-shaped regions of low strain are not symmetrically disposed about fold axial planes, in contrast to strain shadows occurring in folds produced under pure-shear boundary conditions.The rotation of accumulating principal elongations in the stiff layer was calculated at fold inflections. Even though the folds themselves are generally symmetrical, these rotations at opposite fold inflections are not. One fold limb exhibits little rotation of principal elongations during folding while the other has rotations up to 70°. In contrast, folds formed in pure-shear boundary conditions have rotations of principal directions on opposite fold limbs equal in magnitude.     

Sheath fold development in monoclinic shear zones

We use numerical simulations to investigate the evolution of sheath folds around slip surfaces in simple‐shear‐dominated monoclinic shear zones. A variety of sheath fold shapes develops under general shear, including tubular folds with low aspect ratio eye patterns and tongue‐like structures showing bivergent flanking structures in sections normal to the sheath elongation, which may potentially lead to confusing shear sense interpretations. Not all investigated monoclinic flow end‐members lead to the development of sheath folds sensu stricto (folds with apical angle <90°). The aspect ratio of the eye patterns, R_yz, correlates with the ratio between the principal strain in the Y‐direction and the smaller of the principal strains in the X–Z plane, and thus it could be used in strain analysis.     

An analysis of noncylindrical and incongruous fold pattern from the eo-cambrian rocks of söröy, northern Norway: II. The significance of synfold stretching lineation in the evolution of noncylindrical folds

Many folds of both deformation phases on Söröy exhibit a prominent lineation brought out by elongate micas or spindleform-quartz grains. This lineation displays a variety of patterns, depending on ils orientation relative to the fold axis. This dependence confirms the primary nature of the axial noncy lindrism.The lineation is a product of layer-parallel extension and represents the long axis of the sectional strain ellipse (X¹), for the particular attitude of the layering. The formation of the lineation is confined to those layer orientations which cut the extension field of the strain ellipsoid. If the noncylindrical fold axes curve from normal into parallelism with the lineation, the patterns of lineation orientation developed will reveal the attitude of the major extension axis (X) and indicate the nature of the strain.The lineation developed in the earlier stages of fold growth and became a passive marker in later fold modification.The regional pattern of the lineation is similar to that for minor fold axes, and together they are held to identify the XY-plane of the bulk finite strain-field.     

Self-Similar and Self-Affine Properties of Two-Dimensional Fracture Patterns in Rocks

In this paper, we investigate the fractal properties of binary maps of rock fractures at different scales and different geological types, as well as different families of fracture patterns obtained from a two-dimensional Laplacian growth model (LGM). From these analyses we figure out which families of the LGM patterns match the structural properties of the fracture binary maps. The LGM is defined in terms of a nonlinear map that depends on two parameters, λ and \mathfraka\mathfrak{a}, that respectively define the area and shape of the elements of the aggregate that conforms the patterns. The fractal dimension and roughness exponent of the LGM patterns are found to depend on \mathfraka\mathfrak{a}, with 0 < \mathfrak a < 10<\mathfrak {a}<1. From a detailed statistical analysis of these patterns we found that the fractal dimensions of capacity, correlation and information decrease monotonically as \mathfraka\mathfrak{a} increases. We also found that the values of these three fractal dimensions tend to collapse on top of each other as \mathfraka\lessapprox1\mathfrak{a}\lessapprox1. Remarkably, the fractal properties of rock fractures in the scales from millimeters up to a few meters appear to be well represented by the fractal structure of the LGM families of patterns with \mathfraka=0.15\mathfrak{a}=0.15 and 0.30, while the fractal properties of rock fractures in the scale of kilometers seems to be well represented by the LGM family with \mathfraka=0.90\mathfrak{a}=0.90. In addition, the three fractal dimension values of fracture binary maps in the scales from millimeters up to meters were found to be different between them. Nonetheless, for fractures in the scale of kilometers, the values of the three fractal dimensions are very close to each other as an indication of self-similar behavior. Analysis of the corrections to the scaling of the roughness exponent, ζ, suggests that they are negligible for the LGM family of fracture patterns with \mathfraka=0.9\mathfrak{a}=0.9. This finding points to a self-affine structure for this family of patterns. In fact, the calculated roughness exponent results are in the range of values characteristic of rock fractures.     

The sheath folds in the Tananao Group between Tienshiang and Tailuko, east-west cross-island highway, Taiwan

Sheath folds or “eye” folds on decimetric to metric scales are well-developed in the metachert-marble-green rock interlayers of the Changchun Formation and in the marble lens of the Tienhsiang Formation, within the Tananao Group between Tienhsiang and Tailuko, along E-W cross-island highway of Taiwan. Closely associated with the sheath folds are the tight to isoclinal folds with rectilinear axes which are parallel to the hinge line of the “eyes”, and the directions of these folds range from N-S to N30°E with gentle plunges to the north or south.The sheath folds are believed to have been formed during the second phase of deformation in this region. The traces of the earlier folding can generally be found at the hinges or limbs of these sheath folds.The explanation presented here is that the sheath fold might be generated episodically during the F₂ deformational phase throughout the entire history of progressive shearing as a result of episodic instability of the flow with successive refolding of metamorphic fabric, during Plio-Pleistocene deformation of Taiwan.     

Elastic behaviour and structural evolution of topaz at high pressure

The elastic behaviour and the high-pressure structural evolution of a natural topaz, Al_2.00Si_1.05O_4.00(OH_0.26F_1.75), have been investigated by means of in situ single-crystal X-ray diffraction up to 10.55(5) GPa. No phase transition has been observed within the pressure range investigated. Unit-cell volume data were fitted with a third-order Birch-Murnaghan Equation of State (III-BM-EoS). The III-BM-EoS parameters, simultaneously refined using the data weighted by the uncertainties in P and V, are: V ₀=345.57(7) ų, K _T0=164(2) GPa and K′=2.9(4). The axial-EoS parameters are: a ₀=4.6634(3) Å, K _T0(a)=152(2) GPa, K′(a)=2.8(4) for the a-axis; b ₀=8.8349(5) Å, K _T0(b)=224(3) GPa, K′(b)=2.6(6) for the b-axis; c ₀=8.3875(7) Å, K _T0(c)=137(2) GPa, K′(c)=2.9(4) for the c-axis. The magnitude and the orientation of the principal Lagrangian unit-strain ellipsoid were determined. At P−P ₀=10.55 GPa, the ratios ε₁:ε₂:ε₃ are 1.00:1.42:1.56 (with ε₁||b, ε₂||a, ε₃||c and |ε₃| > |ε₂| > |ε₁|). Four structural refinements, performed at 0.0001, 3.14(5), 5.79(5) and 8.39(5) GPa describe the structural evolution in terms of polyhedral distortions.     

Deformation history of the Hampden Synform in the Eastern Fold Belt of the Mt Isa terrane

The moderately metamorphosed and deformed rocks exposed in the Hampden Synform, Eastern Fold Belt, in the Mt Isa terrane, underwent complex multiple deformations during the early Mesoproterozoic Isan Orogeny (ca 1590–1500 Ma). The earliest deformation elements preserved in the Hampden Synform are first‐generation tight to isoclinal folds and an associated axial‐planar slaty cleavage. Preservation of recumbent first‐generation folds in the hinge zones of second‐generation folds, and the approximately northeast‐southwest orientation of restored L¹ ₀ intersection lineation suggest recumbent folding occurred during east‐west to northwest‐southeast shortening. First‐generation folds are refolded by north‐south‐oriented upright non‐cylindrical tight to isoclinal second‐generation folds. A differentiated axial‐planar cleavage to the second‐generation fold is the dominant fabric in the study area. This fabric crenulates an earlier fabric in the hinge zones of second‐generation folds, but forms a composite cleavage on the fold limbs. Two weakly developed steeply dipping crenulation cleavages overprint the dominant composite cleavage at a relatively high angle (>45°). These deformations appear to have had little regional effect. The composite cleavage is also overprinted by a subhorizontal crenulation cleavage inferred to have developed during vertical shortening associated with late‐orogenic pluton emplacement. We interpret the sequence of deformation events in the Hampden Synform to reflect the progression from thin‐skinned crustal shortening during the development of first‐generation structures to thick‐skinned crustal shortening during subsequent events. The Hampden Synform is interpreted to occur within a progressively deformed thrust slice located in the hangingwall of the Overhang Shear.     

A distribution-free alternative to least-squares regression and its application to Rb/Sr isochron calculations

A distribution-free estimator of the slope of a regression line is introduced. This estimator is designated S_m and is given by the median of the set of n(n – 1)/2 slope estimators, which may be calculated by inserting pairs of points (X _i, Y_i)and (X _j, Y_j)into the slope formula S _i = (Y _i – Y_j)/(X _i – X_j),1 i < j n Once S _m is determined, outliers may be detected by calculating the residuals given by R_i = Y_i – S_mX_i where 1 i n, and chosing the median R_m. Outliers are defined as points for which |R_i – R_m| > k (median {|R _i – R_m|}). If no outliers are found, the Y-intercept is given by R_m. Confidence limits on R_m and S_m can be found from the sets of R_i and S_i, respectively. The distribution-free estimators are compared with the least-squares estimators now in use by utilizing published data. Differences between the least-squares and distribution-free estimates are discussed, as are the drawbacks of the distribution-free techniques.     

A mathematical model for orientation data from macroscopic cylindrical folds

An asymptotic form of Bingham's distribution on the sphere is applied to orientation data from cylindrical folds. Data from cylindrical folds typically form two clusters, one cluster for each fold limb. A bimodal distribution is obtained by fitting a unimodal distribution to each cluster. One parameter of the distribution gives the fold axis, another parameter is directly related to the curvature of the fold limb. Certain tests of hypotheses based on this distribution are the same as tests based on the Dimroth—Watson (symmetric girdle)distribution. One such is the test of whether two folds have the same fold axis.     

Paleomagnetic dating of Alleghanian orogenesis and mineralisation in the Mascot–Jefferson City zinc district of East Tennessee, USA

The Mascot–Jefferson City (M-JC) Mississippi Valley-type (MVT) deposits are in the Valley and Ridge province of the Appalachian orogen in East Tennessee. They have been a major source of zinc for the USA but their age is uncertain and thus their genesis controversial. About 10 specimens from each of 37 sites have been analysed paleomagnetically using alternating field and thermal step demagnetisation methods and saturation isothermal remanence methods. The sites sample limestones, dolostones, breccia clasts and sphalerite–dolomite MVT mineralisation from mines in the Lower Ordovician Kingsport and Mascot formations of the Knox Group. The characteristic remanent magnetisation (ChRM) is carried by magnetite in the limestones, by both magnetite and pyrrhotite in the dolostones and by pyrrhotite preferentially to magnetite in the mineralisation. Mineralized sites have a more intense ChRM than non-mineralised, indicating that the mineralising and magnetisation event are coeval. Paleomagnetic breccia tests on clasts at the three sites are negative, indicating that their ChRM is post-depositional remagnetisation, and a paleomagnetic fold test is negative, indicating that the ChRM is a remagnetisation, and a post-dates peak Alleghanian deformation. The unit mean ChRM direction for the: (a) limestones gives a paleopole at 129°E, 12°N (d_p=18°, d_m=26°, N=3), indicating diagenesis formed a secondary chemical remanent magnetisation during the Late Ordovician–Early Silurian; (b) dolomitic limestones and dolostone host rocks gives a paleopole at 125.3°E, 31.9°N (d_p=5.3°, d_m=9.4°, N=7), recording regional dolomitisation at 334±14 Ma (1σ); and (c) MVT mineralisation gives a paleopole at 128.7°E, 34.0°N (d_p=2.4°, d_m=4.4°, N=25), showing that it acquired its primary chemical remanence at 316±8 Ma (1σ). The mineralisation is interpreted to have formed from hydrothermal fluid flow, either gravity or tectonically driven, after peak Alleghanian deformation in eastern Tennessee with regional dolomitisation of the host rocks occurring as part of a continuum during the 20 Ma prior to and during peak deformation.     

On the elastic behaviour of zeolite mordenite: a synchrotron powder diffraction study

The high-pressure elastic behaviour of a synthetic zeolite mordenite, Na₆Al_6.02Si_42.02O₉₆·19H₂O [a=18.131(2), b=20.507(2), c=7.5221(5) Å, space group Cmc2₁], has been investigated by means of in situ synchrotron X-ray powder diffraction up to 5.68 GPa. No phase transition has been observed within the pressure range investigated. Axial and volume bulk moduli have been calculated using a truncated second-order Birch–Murnaghan equation-of-state (II-BM-EoS). The refined elastic parameters are: V ₀=2801(11) ų, K _T0= 41(2) GPa for the unit-cell volume; a ₀=18.138(32) Å, K _T0(a)=70(8) GPa for the a-axis; b ₀=20.517(35) Å, K _T0(b)=29(2) GPa for the b-axis and c ₀=7.531(5) Å, K _T0(c)=38(1) GPa for the c-axis [K _T0(a): K _T0(b): K _T0(c)=2.41:1.00:1.31]. Axial and volume Eulerian finite strain versus “normalized stress” plots (fe–Fe plot) show an almost linear trend and the weighted linear regression through the data points yields the following intercept values: Fe(0)=39(4) GPa for V; Fe _a (0)=65(18) GPa for a; Fe _b (0)=28(3) GPa for b; Fe _c (0)=38(2) GPa for c. The magnitudes of the principal Lagrangian unit-strain coefficients, between 0.47 GPa (the lowest HP-data point) and each measured P>0.47 GPa, were calculated. The unit-strain ellipsoid is oriented with ε₁ || b, ε₂ || c, ε₃ || a and |ε₁|> |ε₂|> |ε₃|. Between 0.47 and 5.68 GPa the relationship between the unit-strain coefficient is ε₁: ε₂: ε₃=2.16:1.81:1.00. The reasons of the elastic anisotropy are discussed.An erratum to this article can be found at