On the high scientific quality of early research on strain and deformation fabrics (1835–1908)

High-quality research developed during the 19th century established the foundations of rock strain investigations. Careful observation and description of rock fabrics and deformed objects in rocks allowed early researchers to obtain mathematical expressions that are still used today to quantify strain. Thus, in a span of a few decades, and applying basic scientific methodology, these researchers developed the concept of the strain ellipsoid, defined mathematically the difference between constant-volume and volume-loss deformation, constructed the basic equations that define pure and simple shear deformation, and discovered the mechanism of pressure–solution deformation. These advances were fundamental to seminal works on strain analysis and deformation fabrics in the mid-20th century. However, they are rarely addressed in modern studies, which suggests a lack of awareness among current researchers. In order to bring attention to these landmarks of strain research, I provide a historical review of the high standards of analysis that led to the definition of the fundamental equations and concepts on strain during the 19th century.

Insights into a dextral transtensional shear zone in NW Anatolia, Turkey: Preliminary results from the three dimensional strain and kinematic analyses of the Marmara Granitoid.

<p>Marmara Granitoid (MG) is an E-W trending sill-like magmatic body exposed in the center of the Marmara Island, NW Anatolia, Turkey. MG is lower Eocene in age and was concordantly emplaced into metamorphic basement rocks of Saraylar Marble and Erdek Complex. It is represented by a deformed granodiorite which widely displays protomylonitic-mylonitic textures with prominent foliation and lineation. Foliation planes display a mean dip direction-angle of 335/29 and mineral stretching lineations show mean trend-plunge of 286/34. Mica-fishes, rotated porphyroclasts and micro-faults are commonly observed and serve as shear gauges pointing out to a dextral movement. Mineral deformation thermometers such as myrmekite development, chessboard extinction, grain boundary migration (GBM), sub-grain rotation recrystallization (SGR), and bulging recrystallization (BLG) in quartz crystals indicate that solid-state deformation of the MG has experienced a high-temperature ductile deformation and superimposed ductile to brittle deformation.</p><p>Three-dimensional strain ellipsoid measurements are investigated on the MG in order to determine the relative amounts of pure shear and simple shear deformation and the mean kinematic vorticity number (W<sub>m</sub>). The image processing of quartz grains is used as strain markers to obtain the three-dimensional best-fit ellipsoids. The results show that, Lode’s ratio (ν) of the samples change between -0.010 and -0.650 and Flinn’s k-values range from 1.026 to 11.157 indicating to a general constrictional (prolate) deformation. The calculated kinematic vorticity numbers change between 0.429 and 0.958 which show that shear deformation of MG is mostly dominated by simple shear. All of these micro and meso structural properties and three-dimensional strain and kinematic analyses collectively suggest that MG has experienced a dextral transtensional deformation.</p>

XtalCAMP: a comprehensive program for the analysis and visualization of scanning Laue X-ray micro-/nanodiffraction data

XtalCAMP is a software package based on the MATLAB platform, which is suitable for, but not limited to, the analysis and visualization of scanning Laue X-ray micro-/nanodiffraction data. The main objective of the software is to provide complementary functionalities to the Laue indexing software packages used at several synchrotron beamlines. The graphical user interfaces allow the easy analysis of characteristic microstructure features, including real-time intensity mapping for a quick examination of phase, grain and defect distribution, 2D color-coded mapping of microstructural properties from the output of other Laue indexing software, crystal orientation visualization, grain boundary characterization based on orientation/misorientation calculation, principal strain/stress analysis, and strain ellipsoid representation, as well as a series of additional toolkits. As an example, XtalCAMP is applied to the microstructural investigation of a solution-heat-treated Ni-based superalloy manufactured using a laser 3D-printing technique, and a deformed natural quartzite from Val Bregaglia in the Central Alps.

Supplemental Material: Quantifying shortening across the central Appalachian fold-thrust belt, Virginia and West Virginia, USA: Reconciling grain-, outcrop-, and map-scale shortening

Supplemental Data Table S1 contains axial ratios for the best-fit vacancy field (with statistics) of grain-scale bulk finite strain from the three mutually perpendicular cuts. Supplemental Data Table S2 contains orientations of the best-fit strain ellipsoid (with statistics) and ellipticity ratios and orientations on the bedding plane.

Supplemental Material: Quantifying shortening across the central Appalachian fold-thrust belt, Virginia and West Virginia, USA: Reconciling grain-, outcrop-, and map-scale shortening

Supplemental Data Table S1 contains axial ratios for the best-fit vacancy field (with statistics) of grain-scale bulk finite strain from the three mutually perpendicular cuts. Supplemental Data Table S2 contains orientations of the best-fit strain ellipsoid (with statistics) and ellipticity ratios and orientations on the bedding plane.

Strain

A discussion of the continuum approximation is followed by the definition of deformation as a transformation involving changes in separation between points within a continuum. This leads to the mathematical definition of the deformation tensor. The introduction of the displacement vector and its gradient leads to the definition of the strain tensor. The linear elastic strain tensor involves an approximation in which gradients of the displacement vector are assumed to be small. The deformation tensor can be written as the sum of syymetric and antisymmetric parts, the former being the strain tensor. Normal and shear strains are distinguished. Problems set 1 introduces the strain ellipsoid, the invariance of the trace of the strain tensor, proof that the strain tensor satisfies the transformation law of second rank tensors and a general expression for the change in separation of points within a continuum subjected to a homogeneous strain.

Extreme values of fold-related shortening in the hinterland structure of the Shilbilisaj section in the Talas Ridge (Tien Shan)

<p>Talas Ridge forms the western part of the Tien Shan Caledonian structure. The sedimentary cover shows a thickness of about 10 km and consists of carbonate flysch and para-platform deposits metamorphosed under greenschist and lesser grade. This structure relates to the "hinterland" tectonic type, characterized by the abundance of many small and moderate-sized folds of the "similar" morphological type. Conventional cross-section balancing techniques developed for "foreland" structures, with large "parallel" folds cannot be applied correctly to such complicated structures. Thus, a special method based on the "geometry of folded domains" was developed for balancing of "hinterland" structures. To test the proposed method, we choose the westernmost Shilbilisaj profile of the Talas Ridge that consists of a large number of folds.</p><p>The proposed approach is based on the hierarchical system of hinterland fold structures, and on the accordance of the “folded domain” deformation to the strain ellipsoid, as described in detail in F. Yakovlev [2017]. On the first step the detailed structural profile is divided into a number of domains, 0.5-1 km wide; each domain consists of several folds of almost the same morphology. Consequently, a number of morphological parameters are measured, together with the axial surface dip angle and the interlimb angle that allow the construction of a strain ellipsoid for each domain. The core of the reconstruction method consists of three consecutive kinematic operations: 1) rotation, 2) horizontal simple shearing, and 3) horizontal stretching. As a result, a pre-folded form of a domain is produced, characterized by length and tilting of a domain segment that differ from the current profile parameter values. Sequential aggregation of all pre-folded domains leads to a complete pre-folded profile that allows the calculation of its shortening value. In the next step a few "structural cells" with a length approximately equal to the sedimentary cover thickness, are selected that combine several pre-folded domains. Taking into account the pre-folded and current lengths of such cells, their shortening values are determined. In the system of hierarchy of folded structures, folded domains and structural cells (and its strain parameters) belong to the third and fourth levels, respectively.</p><p>The first three project participants restored the structure of the section independently, starting with the domain selection procedure. The preliminary estimates of the shortening of the entire profile obtained by participants were close to each other and very high (K=L0/L1, where K – shortening value, L0, and L1 – pre-folded and current length in km, respectively): 4.49=118.5/26.4; 4.29=114.0/26.6; 4.67=119.1/25.5. The first participant allocated 63 domains and 12 structural cells, based on the thickness of the sedimentary cover. The shortening values for these cells varied along the profile from high in the southern cells to relatively small in the center and again to high in the northern parts (K=5.20, 4.47, 4.27, 3.79, 3.86, 3.93, 4.24, 4.91, 4.74, 5.53, 4.84, 4.9).</p><p>Yakovlev F.L. 2017. Reconstruction of folded and faulted structures in zones of the linear folding using structural cross-sections. Moscow, Published in IPE RAS, 60 p.</p>