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A simple calculation of the components of the total slip vector ( D ) on a fault plane allows the relationships between the magnitudes of the three slip components of D , the lateral horizontal displacement ( L ), the transversal horizontal displacement ( T ) and the vertical offset ( V ), to be determined. The contribution of each slip component to the total slip can be plotted jointly in a ternary diagram, assuming a unit length of the vector modulus and a suitable normalization for D . Each component equals the magnitude of D at the vertices of the diagram, hence it is possible to estimate the percentage contribution of each slip component to the total movement of a fault or a set of faults. The dip of the fault surface and the rake of the slickenlines are the input data required for displaying L , T and V relationships in these diagrams. This information may be useful in the analysis of movement geometry for different fault populations and in the determination of D by measuring just one of the fault-slip components, such as vertical slip associated with a fault scarp.

Oblique convergence and subsequent transpression kinematics can be considered as the general situation in most convergent and strike-slip tectonic boundaries. To better understand such settings, progressively more complex kinematic models have been proposed, which need to be tested against natural shear zones using standardized procedures that minimise subjectivism. In this work, a protocol to test a general triclinic transpression model is applied to the Torcal de Antequera massif (TAM), an essentially brittle shear zone. Our results, given as kinematic parameters of the transpressive flow (transpression obliquity, ϕ; extrusion obliquity, υ; and kinematic vorticity number, Wk), suggest that the bulk triclinic transpressive flow imposed on the TAM was partitioned into two different flow fields, following a general partitioning type. As such, one flow field produced narrow structural domains located at the limits of the TAM, where mainly dextral strike-slip simple-shear-dominated transpression took place (Outer domains, ODs). In contrast, the remaining part of the bulk flow produced pure-shear-dominated dextral triclinic transpression at the inner part of the TAM (Inner domain, ID). A graphical method relating internal (ϕ, Wk) to far-field (dip of the shear zone boundary, δ; angle of oblique convergence, α) transpression parameters is proposed to obtain the theoretical horizontal velocity vector ( V → ), which in the case of the TAM, ranges between 099 and 118. These results support the applicability of kinematic models of triclinic transpression to brittle-ductile shear zones and the potential utility of the proposed protocol.

The potential of using sigmoidal tension gashes as strain markers for assessing strain localisation in shear zones is discussed. The appropriate analytical methods for this purpose depend on the assumed mechanism of tension gash formation. Two such models are considered. The first is one in which the curvature of the gash is produced by passive rotation of different segments of the gash in response shear strain gradients across the shear zone. The other model is one in which the curvature of the gashes is governed by the folding of the competent rock bridges between adjacent gashes. In the latter case, the tension gashes progressively grow within spaces created by the buckling bridges and therefore lead to a bulk dilatation of the shear zone. However, for the folded bridge mechanism to continue to operate beyond shear strains greater than unity requires a significant volume loss which in turn may signal the increase of the shear strength of the zone. The geometrical characteristics of gash arrays resulting from these two mechanisms are described and criteria given for the recognition of the two types of gash arrays. A new graphical method is proposed for the analysis of deformation in shear zones containing folded-bridge tension gashes. Tension gash arrays from Marloes, West Wales are used as examples of the procedures for shear zone analysis.

Folds with different values of viscosity contrast and anisotropy have been simulated using the finite-difference code FLAC™. The kinematical analysis of these folds has enabled conclusions to be reached about strain accommodation mechanisms. The sequence of strain patterns in all the folds analysed only differs in the intensities of the different mechanisms involved, which depend on the mechanical properties of the folds. The order of the different strain patterns in the sequence is the same, regardless of the anisotropy and viscosity contrast. Strain accommodation in folds follows the patterns of tangential longitudinal strain, flexural flow and layer shortening. Nevertheless, no combination of these strain patterns can explain the shape of the folded layer at the inflection point and the high strain intensity values in the inner arc. These problems can only be solved by considering a variant of longitudinal tangential strain that is less intense than has classically been thought and combined with a heterogeneous distribution of flexural flow and layer shortening across the layer. The dependence of the different folding mechanisms on the mechanical properties has been used to devise a graphical method for estimating viscosity contrast and anisotropy from the intensities of the strain patterns in the sequence.

It is now a conventional technique to determine the optimal stress from fault-slip data by inversion. However, the method is weak when applied to heterogeneous data. A new technique is presented here to visualize the reliability of the solution. It is also shown that the technique allows us to separate stresses from those data. The technique is simple: it is the visualization of the object function of the inversion. The present method is compared with the conventional inverse method and the multi-inverse method using artificial and natural heterogeneous data sets. The conventional method can determine one of the stresses, if the orientation of the faults has a large variation. It is shown that the solutions of the method are non-unique and unstable for some data sets, indicating that they are not reliable. The present graphical method and multi-inverse method are more robust than the conventional one for heterogeneity. The multi-inverse method seems to have better resolution than the present method. However, unlike the multi-inverse method, the time of computation of the present method does not increase with the number of faults, so that the method becomes favorable for processing hundreds of faults.

A simple graphical method is proposed to infer the tectonic regime from a fault and slip data set. An abacus is overlaid on a plot of the rake versus strike of the data. This yields the horizontal principal stress directions and a constraint on the stress tensor aspect ratio, in a manner similar to Breddin’s graph for two-dimensional strain analysis. The main requirement is that one of the principal stress directions is close to the vertical. This method is illustrated on monophase synthetic and natural data, but is also expected to help sort out multiphase data sets.

A new graphical method is developed to determine the direction of the maximum resolved shear stress on a fault plane. It differs from existing graphical methods in using the direction perpendicular to the maximum resolved shear. It is based upon the theory of vector manipulation, making the proposed method more straightforward and more graphical, and, hence, we believe more accessible.

Striations on a pebble are interpreted as resulting from slip due to either a homogeneous stress state or a small homogeneous coaxial deformation in the matrix. In terms of stress, striations are assumed to be parallel to the applied shear stress. In terms of strain, striations are considered to be parallel to the relative tangential displacement between the pebble and adjacent matrix particles. Slip on the surface of a spherical rigid body enclosed in a deformable matrix (brittle or ductile) is theoretically analysed for different stress and strain regimes. The analysis predicts the topology of the resulting striations and singularity distribution on the sphere. Both in terms of stress and strain, the tangential vector field on the sphere's surface derives from a potential function proportional to the magnitude of the normal vector field. Tangential and normal vectors represent either shear and normal stresses, or displacement components (in terms of strain). The plot of continuous curves parallel to striations (integral curves) and of equipotential curves on the sphere, allows simultaneously the magnitude and orientation of the tangential and normal vector fields to be visualized. Close to singular points, the integral curves correspond to power laws and the equipotentials correspond to conic sections. This theoretical analysis allows graphical method for estimating the stress ratio (σ2 − σ3)(σ1 − σ3) from striated faults to be proposed, once the orientations of the principal stress directions are known (i.e. by means of other graphical methods).

A variety of methods devised in the last twelve years for measuring two-dimensional strain ratios have been applied to the same deformed oolitic limestone from southwest Dyfed. Their relative merits are discussed. A graphical method for studying relative locations of marker objects is described and its application to a variety of rocks illustrated. It is shown to have theoretical and practical advantages, while giving values of two-dimensional strain ratios comparable with those of other methods.

Faults and fractures evolve kinematically as Somigliana dislocations. As a result, displacement gradients are always present, with displacements reducing to zero at fault/fracture tips. We present a graphical method for the comparison of displacement gradients from fractures of various magnitudes and types. Displacement efficiency of a fault/fracture is defined as its ability to maximise displacement across its surface.

The Mohr diagram for strain is rarely used in its full form, as a representation of three-dimensional strain. Recent attention has focused on various uses of the Mohr circle to express two-dimensional strain tensors. This contribution redescribes the Mohr diagram for three-dimensional strain and illustrates some new applications. The Mohr diagram for any strain ellipsoid provides an immediate method for ellipsoid shape classification. However, its greatest new potential is considered to be in the representation of strain ellipses as sections of ellipsoids. Any plane section of a strain ellipsoid can be plotted on the ellipsoid's Mohr diagram: it is here called a ‘Mohr locus’ because it is constructed as a locus of points representing the sheaf of lines which can be considered to define the plane. Mohr loci for sectional ellipses have a variety of forms, according to their orientation in the strain ellipsoid. Generally oblique sections are represented by loops bounded by the three principal circles. Their most leftward and rightward points are the plane's principal axes. Any Mohr locus can be transformed into a Mohr circle for the sectional ellipse. Mohr diagrams with Mohr loci have considerable potential as a graphical method of deriving best-fit strain ellipsoids from natural strain data. This is illustrated in three examples.

The estimation of the strain ellipse from data consisting of longitudinal strains measured along different directions is one of the basic problems of strain analysis and one which has recently received renewed attention. A graphical method based on the Mohr circle, described more than 40 years ago by Glenn Murphy but overlooked by geologists, represents the simplest solution of the problem yet devised.