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Et-Taoui, Boumediene. "Quaternionic equiangular lines." Advances in Geometry 20, no. 2 (April 28, 2020): 273–84. http://dx.doi.org/10.1515/advgeom-2019-0021.
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AbstractLet 𝔽 = ℝ, ℂ or ℍ. A p-set of equi-isoclinic n-planes with parameter λ in 𝔽r is a set of pn-planes spanning 𝔽r each pair of which has the same non-zero angle arccos $\begin{array}{} \sqrt{\lambda} \end{array}$. It is known that via a complex matrix representation, a pair of isoclinic n-planes in ℍr with angle arccos $\begin{array}{} \sqrt{\lambda} \end{array}$ yields a pair of isoclinic 2n-planes in ℂ2r with angle arccos $\begin{array}{} \sqrt{\lambda} \end{array}$. In this article we characterize all the p-tuples of equi-isoclinic planes in ℂ2r which come via our complex representation from p-tuples of equiangular lines in ℍr. We then construct all the p-tuples of equi-isoclinic planes in ℂ4 and derive all the p-tuples of equiangular lines in ℍ2. Among other things it turns out that the quadruples of equiangular lines in ℍ2 are all regular, i.e. their symmetry groups are isomorphic to the symmetric group S4.
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Yang, Jian Hui, Rong Ling Sun, Zheng Hao Yang, Xin Yang Lin, and Hai Cheng Niu. "Constitutive Relations of Concrete under Plane Stresses Based on Generalized Octahedral Theory." Applied Mechanics and Materials 71-78 (July 2011): 342–52. http://dx.doi.org/10.4028/www.scientific.net/amm.71-78.342.
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Continuous (or generalized) octahedral element bodies can be obtained by intercepting a cube with three groups of failure (or yield) planes successively under true triaxial stress state, on which the stresses are twin stresses. Among the resulting polyhedral characteristic element bodies, isoclinal octahedron and orthogonal octahedron are of particular importance. Strength models of continuous octahedrons are then derived by stress analysis to arbitrary inclined sections in three dimensional stress space, and strain models by the principle of strain analysis, so the plane constitutive relations of concrete can be understood by plane problems transformed by stress-strain space according to the symmetry of an orthogonal octahedral octahedron where an arbitrary oblique plane is parallel to one of three rectangular coordinate axes.
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Et-Taoui, B. "Equi-isoclinic planes of Euclidean spaces." Indagationes Mathematicae 17, no. 2 (June 2006): 205–19. http://dx.doi.org/10.1016/s0019-3577(06)80016-9.
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Pinit, Pichet, Tobita Susumu, and Eisaku Umezaki. "Determination of Principal-Stress Directions by Three-Step Color Phase Shifting Technique." Key Engineering Materials 321-323 (October 2006): 1284–87. http://dx.doi.org/10.4028/www.scientific.net/kem.321-323.1284.
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A three-step phase shifting approach for automatic determination of the isoclinic parameter in photoelasticity is presented. Unreliable isoclinic values affected by the isochromatic parameter are solved using the white light. The method uses three fringe images digitally captured by a digital camera for three different configurations of the dark-field plane polariscope. For a circular disk under compression, results show the method permits the isoclinic parameter in the range -π/2 to π/2 with almost free of the isochromatic parameter and comparable with theory.
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Aghajani, A., and A. Moradifam. "Intersection with the vertical isocline in the Liénard plane." Nonlinear Analysis: Theory, Methods & Applications 68, no. 11 (June 2008): 3475–84. http://dx.doi.org/10.1016/j.na.2007.03.040.
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SRIVASTAVA, DEEPAK C. "Geometrical similarity in successively developed folds and sheath folds in the basement rocks of the northwestern Indian Shield." Geological Magazine 148, no. 1 (August 20, 2010): 171–82. http://dx.doi.org/10.1017/s0016756810000610.
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AbstractAn intensely deformed gneiss–migmatite terrane and a relatively undeformed granulite–granitoid terrane constitute the bulk of Precambrian basement in the northwestern Indian Shield. This article traces the structural evolution in the gneiss–migmatite terrane, where traditional methods of structural analysis are difficult to apply, and shows how successively developed folds can assume identical geometry and orientation at an advanced stage of progressive ductile shearing. The gneiss–migmatite terrane exemplifies a regional-scale ductile shear zone that preserves the history of polyphase folding and sheath folding. Geometrical similarity between individual/domain-scale sheath folds and mesoscopic/regional-scale folds implies that sheath folding is common at all scales in the gneiss–migmatite terrane. As the mylonite foliation that traces successive folds is curviplanar, the successively initiated hinge lines were curvilinear from their inception in the shear zone. At the advanced stage of ductile shearing, the hinge line curvatures were accentuated due to their rotation towards subvertically directed maximum stretching (X), and variably oriented fold axial planes were brought into approximate parallelism with the upright principal plane (XY) of the bulk strain ellipsoid. Eventually all the folds, irrespective of their relative order of development, became strongly non-cylindrical, extremely tight, isoclinal and approximately co-planar with respect to each other. It is due to the above geometrical modifications during ductile shearing that folds, irrespective of their order of development, now appear identical with respect to isoclinal geometry, axial plane orientation and hinge line curvilinearity. Evidence from the fold orientations, the deformed lineation patterns and the sheath fold geometry suggest that the shearing occurred in a general shear type of bulk strain, and NNW–SSE-directed subhorizontal compression resulted in subvertically directed stretching in the gneiss–migmatite terrane.
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Aghajani, Asadollah, Mohsen Mirafzal, and Donald O’Regan. "Conditions for approaching the origin without intersecting the x-axis in the Liénard plane." Filomat 31, no. 12 (2017): 3761–70. http://dx.doi.org/10.2298/fil1712761a.
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We consider the Li?nard system in the plane and present general assumptions to obtain some new explicit conditions under which this system has or fails to have a positive orbit which starts at a point on the vertical isocline and approaches the origin without intersecting the x-axis. This arises naturally in the existence of homoclinic orbits and oscillatory solutions. Our investigation is based on the notion of orthogonal trajectories of orbits of the system.
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Hara, Tadayuki, and Jitsuro Sugie. "When all trajectories in the Li�nard plane cross the vertical isocline?" Nonlinear Differential Equations and Applications NoDEA 2, no. 4 (December 1995): 527–51. http://dx.doi.org/10.1007/bf01210622.
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Blokhuis, Aart, Ulrich Brehm, and Boumediene Et-Taoui. "Complex conference matrices and equi-isoclinic planes in Euclidean spaces." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 59, no. 3 (December 19, 2017): 491–500. http://dx.doi.org/10.1007/s13366-017-0374-2.
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Aghajani, Asadollah, and Amir Moradifam. "Some sufficient conditions for the intersection with the vertical isocline in the Liénard plane." Applied Mathematics Letters 19, no. 5 (May 2006): 491–97. http://dx.doi.org/10.1016/j.aml.2005.07.005.
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Rodrigues, Rodrigo Antonio de Freitas, Juliana Pertille, Fernanda Gervasoni, Paola Bruno Arab, Thales Sebben Petry, Marina Luiza Jordão Martins, Áquila Ferreira Mesquita, Jorge Henrique Laux, Breno Souza Martins, and Lívia Brochi Nascimento. "Tonian Continental Arc Magmatism of the Porongos Complex, Dom Feliciano Belt, Southern Brazil." Geologia USP. Série Científica 23, no. 3 (August 17, 2023): 19–45. http://dx.doi.org/10.11606/issn.2316-9095.v23-208078.
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This study provides new information on the deformation, metamorphism, and tectonic setting of the metavolcanic rocks of the southern portion of the Porongos Complex, southern Brazil. The structural analysis enabled the identification of three deformational phases, formed under ductile to semi-ductile conditions. D1 progressed through deformation partitioning, comprising closed to isoclinal folds and an axial plane foliation. Then, simple shear prevailed, resulting in isoclinal folds, sigma-type porphyroclasts, foliation transposition, and mylonitic rocks. D2 comprises open to gentle folds and an axial plane cleavage. The formation of shear bands is ascribed to the semi-ductile D3. The mineral assemblage represented by phengite + chlorite + clinozoisite-epidote + actinolite + albite + quartz associated with the temperatures obtained through the chlorite geothermometer (316°C) indicates greenschist facies conditions. The protoliths of these metavolcanic rocks are geochemically discriminated as calc-alkaline, dacite-to-rhyodacite, with peraluminous compositions. The bulk trace element compositions show enrichment in large-ion lithophile elements and light rare-earth elements and depletion in heavy rare-earth elements. Also, negative Nb, P, Ti, and Ta anomalies are observed in the multielement diagram. All these geochemical features are typical of rocks formed in continental magmatic arcs. Geochemical comparison with other pre-collisional Tonian orthometamorphic rocks from the Dom Feliciano Belt demonstrates strong similarities, which corroborates the prior interpretation of a continental arc setting for the origin of these Tonian rocks.
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Maliakov, Yordan. "Structural observations on the type sections of Kondolovo and Lipačka Formations, SE Strandzha Mountains." Geologica Balcanica 22, no. 5 (October 30, 1992): 71–86. http://dx.doi.org/10.52321/geolbalc.22.5.71.
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Structural observations along the type sections of Kondolovo and Lipačka Formation, introduced as formal lithostratigraphic units by ČataIov, reveal three fold generations: isoclinal to tight synfolial B1 folds with axial-plane slaty cleavage S1 and intersection lineation L1 between bedding and S1; kinkand chevron-type B2 folds as minor folds on the limbs of a B2 conical antiform; open upright B3 folds with gently dipping limbs. These structural data and additional geological studies show that the original descriptions of the type sections are in some respects incorrect. The sections were measured at right angle to surfaces of tectonic origin rather than to primary bedding. For this reason the section do not demonstrate the normal stratigraphic sequence. Since isoclinal folds and the resulting repetitions in the sequence were not recognized, one and the same rock unit was described as different units with different stratigraphic positions. There are also some problems concerning the age and stratigraphic position of Kondolovo Formation. On the basis of structural and paleontological evidence it is suggested that Kondolovo-type limestones occur as packets within the rocks of Lipacka Formation. If this is correct, Kondolovo Formation should be rejected as a formal lithostratigraphic unit.
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Vasconcelos, Bruno Rodrigo, Amarildo Salina Ruiz, and João Batista de Matos. "Polyphase deformation and metamorphism of the Cuiabá group in the Poconé region (MT), Paraguay Fold and Thrust Belt: kinematic and tectonic implications." Brazilian Journal of Geology 45, no. 1 (March 2015): 51–63. http://dx.doi.org/10.1590/23174889201500010004.
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Several deformation models have been proposed for the Paraguay Belt, which primarily differ in the number of phases of deformation, direction of vergence and tectonic style. Structural features presented in this work indicate that the tectonics was dominated by low dip thrust sheets in an initial phase, followed by two progressive deformation phases. The first phase of deformation is characterized by a slate cleavage and axial plane of isoclinal recumbent folds with a NE axial direction, with a recrystallization of the minerals in the greenschist facies associated with horizontal shear zones with a top-to-the-SE sense of movement. The second stage shows vergence towards the NW, characterized by crenulation cleavage axial plane to F2 open folds over S0 and S1, locally associated with reverse faults. The third phase of deformation is characterized by subvertical faults and fractures with a NW direction showing sinistral movement, which are commonly filled by quartz veins. The collection of tectonic structures and metamorphic paragenesis described indicate that the most intense deformation at the deeper crustal level, greenschistfacies, occurred during F1, which accommodated significant crustal shortening through isoclinal recumbent folds and shear zones with low dip angles and hangwall movement to the SE, in a thin-skinned tectonic regime. The F2 deformation phase was less intense and had a brittle to ductile behavior that accommodated a slight shortening through normal open subvertical folds, and reverse faults developed in shallower crustal level, with vergence towards the Amazonian Craton. The third phase was less pervasive, and the shortening was accommodated by relief subvertical sinistral faults.
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Wong, Yung-Chow, and Kam-Ping Mok. "Normally related n-planes and isoclinic n-planes in R2n and strongly linearly independent matrices of order n." Linear Algebra and its Applications 139 (October 1990): 31–52. http://dx.doi.org/10.1016/0024-3795(90)90386-q.
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Salyamova, K. D. "Dynamic calculation of a plane “Earth Dam-Base” system under seismic impact." E3S Web of Conferences 401 (2023): 05086. http://dx.doi.org/10.1051/e3sconf/202340105086.
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Design, construction, as well as reliable and safe operation of earthen hydraulic structures (earth dams) in the Republic of Uzbekistan, located in a seismically hazardous zone, require constant improvement of load calculation methods, as required by building codes, including constant loads (static - gravity, hydrostatic) and temporary dynamic loads (seismic). The current normative method does not take into account the non-one-dimensional behavior and piecewise heterogeneity of the soil characteristics of the structure and foundation. It does not allow determining the stress-strain state (SSS) of an earthen dam, which is especially important for reliable and safe operation in seismic areas. A mathematical formulation of the dynamic problem of an earthen dam in a flat elastic formulation is given. The problem is solved numerically by the finite element method. The eigenfrequencies and modes of vibrations of the flat system “structure-foundation” are determined taking into account the piecewise inhomogeneous characteristics of the foundation soil. Based on the results of these parameters, an appropriate behavior analysis is performed. The SSS of the “dam-foundation” system was studied at the calculated natural frequencies. The result of the calculation was the isocline of equal displacements, normal and shear stresses in the “dam-foundation” system.
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Marquis, Robert, and Normand Goulet. "Essai de corrélation stratigraphique et structurale à l'est de Val-d'Or: implication pour la prospection aurifère du secteur." Canadian Journal of Earth Sciences 24, no. 12 (December 1, 1987): 2412–21. http://dx.doi.org/10.1139/e87-227.
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Stratigraphic and structural relationships show that the Trivio and Garden Island sedimentary groups could be lateral equivalents. The ubiquitous presence of shear zones between the sedimentary (Trivio and Garden Island) and volcanic (Kinojévis and Malartic) groups indicates that these contacts are tectonic and not stratigraphic. Moreover, the shearing along the Malartic–Trivio contact is located along the extension of the Larder Lake – Cadillac fault zone and could be its equivalent east of Val-d'Or, Quebec.Three major periods of deformation have been recognized in the field. The main east–west deformation, D2, has produced isoclinal folds inclined to the southwest and plunging 60° to the northeast. The axial-plane schistosity associated with D2 is responsible for the regional tectonic grain. Its orientation, 290°/70°, closely parallels the shearing direction along the major volcanic–sedimentary contacts. At Chimo mine, on a mesoscopic scale, the isoclinal D2 folds refold D1 structures, producing interference patterns intermediate between types 2 and 3. On a regional scale the D1 folds do not affect the lithologic pattern.A late deformation, D3, becomes progressively more noticeable toward the Grenville Front. Folds related to this third phase are inclined toward the northwest and plunge to the northeast. The orientation of the fracture cleavage associated with this deformation is 040°/60°. The proximity of the Grenville Front, north of Lake Matchi-Manitou, is shown by strike faults oriented northeast–southwest. The sinistral movement of these faults was determined using a banded iron formation as marker horizon.All gold exploration criteria suggest that the study area is a favourable target for gold exploration.
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Morley, C. K., S. Jitmahantakul, C. von Hagke, J. Warren, and F. Linares. "Development of an intra-carbonate detachment during thrusting: The variable influence of pressure solution on deformation style, Khao Khwang Fold and Thrust Belt, Thailand." Geosphere 17, no. 2 (January 21, 2021): 602–25. http://dx.doi.org/10.1130/ges02267.1.
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Abstract Classic detachment zones in fold and thrust belts are generally defined by a weak lithology (typically salt or shale), often accompanied by high over-pressures. This study describes an atypical detachment that occurs entirely within a relatively strong Permian carbonate lithology, deformed during the Triassic Indosinian orogeny in Thailand under late diagenetic-anchimetamorphic conditions. The key differences between stratigraphic members that led to development of a detachment zone are bedding spacing and clay content. The lower, older, unit is the Khao Yai Member (KYM), which is a dark-gray to black, well-bedded, clay-rich limestone. The upper unit, the Na Phra Lan Member (NPM), comprises more massive, medium- to light-gray, commonly recrystallized limestones and marble. The KYM displays much tighter to even isoclinal, shorter-wavelength folds than the NPM. Pressure solution played a dominant role throughout the structural development—first forming early diagenetic bedding; later tectonic pressure solution preferentially followed this bedding instead of forming axial planar cleavage. The detachment zone between the two members is transitional over tens of meters. Moving up-section, tight to isoclinal folds with steeply inclined axial surfaces are replaced by folds with low-angle axial planes, thrusts, and thrust wedging, bed-parallel shearing, and by pressure solution along bedding-parallel seams (that reduce fold amplitude). In outcrops 100–300 m long, reduction of line-length shortening on folds from >50% to <10% shortening upwards indicates that deformation in the NPM is being accommodated differently from the KYM, probably predominantly by shortening on longer wavelength and/or spacing folds and thrusts, given the low amount of strain observed within the NPM, which excludes widespread layer-parallel thickening.
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Beura, D., S. K. Nanda, A. Parida, and L. Pattanayak. "Deformation Episodes in Iron Formation of Eastern Province of North Odisha Iron Ore Craton, Eastern India." Journal of Geosciences Research 8, no. 1 (January 1, 2023): 38–42. http://dx.doi.org/10.56153/g19088-022-0090-18.
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Banded Iron Formation (BIF), a bi-component rock of the Precambrian period is exposed along with iron ore in distinct geographical entities encircling the North Odisha Iron Ore Craton (NOIOC) in Odisha – Jharkhand states, eastern India. Iron formation of the eastern province is confined to Badampahar-Gorumahisani-Sulaipat belt. The litho assemblages belonging to this Iron Ore Group comprise of banded cherty quartzite, banded magnetite quartzite, banded magnetite grunerite quartzite, tremolite-actinolite schist and fuchsite quartzite. Deformations in phases affected the BIF members and associated rocks of the area resulting in successive fold structures. The first generation folds (F1) are characteristically tight and isoclinal having NE plunging axes. The second phase fold (F2) structures in the area with reference to first fold are co-axial, upright and tight to open in nature profusely overprinting the F1 folds are parallel to the general trend (NE-SW) of the belt. Axial plane of the third phase folds (F3) are gentle and broad warps having NW-SE trending axial planes and are found to be the last traceable ones in the area. trending in NW-SE direction are found to be the last traceable ones in the area having gentle and broad warps. The co-axial F1 and F2 folds along the general trend (NE-SW) of the belt are superposed by NW-SE trending F3 fold, which exhibits a geometric configuration as F1 // F2 F3. Such type of multiphase deformed terrain has produced many interference fold patterns in minor scale out of superposition i.e. dome and basin structures, hook shaped patterns, eyed fold and S, Z, and M shaped folds. The paper discusses the episodes of structural events and their signatures in the interference fold patterns in the eastern province of the NOIOC. Keywords: Banded Iron Formation, Badampahar-Gorumahisani-Sulaipat Belt, Deformation Episodes, NOIOC
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Et-Taoui, Boumediene. "Infinite family of equi-isoclinic planes in Euclidean odd dimensional spaces and of complex symmetric conference matrices of odd orders." Linear Algebra and its Applications 556 (November 2018): 373–80. http://dx.doi.org/10.1016/j.laa.2018.07.014.
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Borradaile, G., P. Sarvas, R. Dutka, R. Stewart, and M. Stubley. "Transpression in slates along the margin of an Archean gneiss belt, northern Ontario—magnetic fabrics and petrofabrics." Canadian Journal of Earth Sciences 25, no. 7 (July 1, 1988): 1069–77. http://dx.doi.org/10.1139/e88-104.
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Archean slates along the northern boundary of the Quetico subprovince of the Superior Province show marked variations of the structural facing direction within coplanar primary cleavage surfaces. These are interpreted as being due to sheath folds near the faulted east–west boundary of the slates with the metavolcanic Wabigoon Belt. Sheath folds with axial traces nearly parallel to the belt boundary are macroscopic, primary, and isoclinal and are believed to result from pervasive dextral transpression of the northern margin of the Quetico subprovince. Magnetic fabrics confirm the presence of a single penetrative flattening tectonic microfabric and considerable north–south shortening on the scale of hand specimens and outcrops. The magnetic fabric is due to the alignment of metamorphic sheet silicates, with a subordinate contribution due to the preferred dimensional orientation of detrital magnetite grains. In some low-strain environments at the hinges of sheath folds and at the sandy bases of graded beds relict sedimentary magnetic fabrics are preserved. However, a tectonic magnetic fabric is usual, with flat susceptibility ellipsoids parallel to axial planes and with variably oriented maximum susceptibility directions. To the south, farther into the interior of the Quetico subprovince, the primary folds become more homoaxial and the metamorphic grade rises rather steeply, and still farther south, small-scale polyphase deformation becomes evident especially where the rocks are remobilized.
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Mohd Nor, Mohd Khir, Rade Vignjevic, and James Campbell. "Modelling of Shockwave Propagation in Orthotropic Materials." Applied Mechanics and Materials 315 (April 2013): 557–61. http://dx.doi.org/10.4028/www.scientific.net/amm.315.557.
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Modelling of shockwave propagation in orthotropic materials requires an appropriate description of material behaviour within elastic and plastic regimes. To deal with this issues, a finite strain constitutive model for orthotropic materials was developed within a consistent thermodynamic framework of irreversible process in this paper. The important features of this material model are the multiplicative decomposition of the deformation gradient and a Mandel stress tensor combined with the new stress tensor decomposition generalised for orthotropic materials. The elastic free energy function and the yield function are defined within an invariant theory by means of the introduction of the structural tensors. The plastic behaviour is characterised within the associative plasticity framework using the Hills yield criterion. The complexity was further extended by coupling the formulation with the equation of state (EOS) to control the response of the material to shock loading. This material model which was developed and integrated in the isoclinic configuration provides a unique treatment for elastic and plastic anisotropy. The effects of elastic anisotropy are taken into account through the stress tensor decomposition and plastic anisotropy through yield surface defined in the generalized deviatoric plane perpendicular to the generalised pressure. To test its ability to describe shockwave propagation, the new material model was implemented into the LLNL-DYNA3D code. The results generated by the proposed material model were compared against the experimental Plate Impact test data of Aluminium Alloy 7010. A good agreement between experimental and simulation was obtained for two principal directions of material orthotropy.
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Alexander, Richard R. "Functional significance of variations in the central fold of shells of late Ordovician through Devonian biconvex brachiopod genera." Paleontological Society Special Publications 6 (1992): 2. http://dx.doi.org/10.1017/s2475262200005621.
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Flume experiments with models of Mid-Paleozoic atrypids, orthids, rhynchonellids, and spiriferids indicate that the central fold functions efficiently to separate lateral-margin incurrents from the anterior-medial margin excurrent in five of nine possible life orientations of the shell relative to the current direction and substrate. Anterior-medial incurrents and lateral excurrents are effectively separated in four of the nine orientations used with models of spiriferids and atrypids, but nonpediculate brachiopods drawing in water anterior-medially could not take advantage of reversing tidal currents to feed. The risk of refiltration of medial excurrent water is reduced with increasing relief of the central fold above the commissural plane. Downcurrent turbulance increases with increasing relief of the central fold. Eddies with a large radius of curvature are generated by large chevron-shaped central folds at low current velocities (5 cm/sec) and boomerang against the downcurrent lateral margin of models. Flume experiments on models also reveal that a well-developed sinus accelerated erosion of the supporting sediment around the weight-bearing posterior of the valves. Shells with high relief in the sinus destabilized comparatively quickly from valves-erect orientations when subjected to moderate current velocities (25 cm/sec).Morphospace (ternary) diagrams of sinus shape for Late Ordovician (Caradocian) through Devonian (Famennian) genera show the realized field among the potential morphotypic extremes, namely, 1) rectimarginate (no fold), 2) isoclinal, chevron-shaped, and 3) M-shaped anterior commissural outlines. Morphospace plots through successive stages suggest centripetal selection for taxa with moderately developed folds in the atrypids and spiriferids, with occasional evolution of “outlier” genera with chevron-shaped central folds. Orthids display progressive loss of rectimarginate genera through the Devonian. Weak directional selection is suggested by the succcessive stage-level plots of the rhynchonellid genera which expanded toward the extremes of chevron- and M-shaped central folds in potential morphospace during the Devonian.
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Salve, Vinay V., and Durga P. Mohanty. "Structural Analysis and Petrography of High-Grade Gneisses and Associated Mafic / Ultramafic Dikes Around Salem, Southern India." Journal of Geosciences Research 9, no. 1 (January 1, 2024): 1–8. http://dx.doi.org/10.56153/g19088-023-0165-45.
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Southern Granulite Terrane (SGT) of India preserves extensive high-grade granulite facies rocks of Archaean and Proterozoic age. The SGT is divided into number of blocks by several suture/shear zone. Structural investigations on the basement gneisses and younger mafic/ultramafic dikes have been carried out within the Salem block which is part of Northern Granulite Block (NGB), north of the Cauvery Suture Zone (CSZ). The present work emphasizes various scale fold styles and other structural patterns of the area, which includes regionally metamorphosed high-grade rocks as basement for the multiple ultramafic intrusions to the north of Cauvery Suture Zone (CSZ) which highlights the finite strain geometry, complex deformation pattern and high-grade metamorphism. Structural map of the study area is prepared showing two generations of folding, namely F1 whose axial trend is NE-SW, subparallel with general trend of gneissic foliation and are tight isoclinal folds while F2 which are open folds with axial trend NW-SE.E-W structural cross section across the foliation planes, characterizes antiformal and synformal fold patterns of the basement due to varying dip directions which also reflects type-3 interference pattern of folding. Mesoscopic scale shear zones of dextral kinematics in response to E-W collision during Paleo-Meso Archean time, delta type porphyroclasts, S-C fabrics with the dextral movement of CSZ system, Riedel shear, thrust imbricates implying duplex structures, rotation of mafic boudins along shear zones are the most prominent ductile structural features of this area. Brittle structures like different sets of cross cutting joints and faults indicate younger deformation as well. Petrography of major lithologies has classified them into amphibolite gneiss, migmatite gneiss, charnockites, granulites and mylonites as basement rocks to the younger pyroxenite intrusions. Typical textures like, perthite, granulose, reaction rims, sieve textures and microstructures like S-C fabrics, kink bands, rotated porphyroclasts, etc are observed within the basement rocks. Coarse grained textures with fractured porphyroclasts of garnets indicating the water interactions and retrogradations within the granulite facies rocks. Reaction rims observed in charnockites and granulites are indicative of retrogression during shearing. The coarse grained cummulate nature of pyroxenites neither represent deformation nor metamorphism. Keywords: Southern Granulite Terrane, Salem, Structural Analysis, Mafic/Ultramafics, Dikes, Petrography
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ΑΥΓΕΡΙΝΑΣ, Α., Α. ΚΙΛΙΑΣ, Α. ΚΟΡΩΝΑΙΟΣ, Δ. ΜΟΥΝΤΡΑΚΗΣ, W. FRISCH, I. DUNKL, and Τ. MOST. "Cretaceous structural evolution of the Pelagonian crystalline in western Voras Mt (Macedonia, Northern Greece)." Bulletin of the Geological Society of Greece 34, no. 1 (January 1, 2001): 129. http://dx.doi.org/10.12681/bgsg.16952.
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The kinematic of the Cretaceous deformation and the relationship between deformation and metamorphism of the Pelagonian crystalline was studied in Voras Mt (northern Greece). The Pelagonian crystalline in this area has been subdivided into a lower, core part, consisting mainly of gneissic rocks and schists and an upper, cover part, consistine of schists and quartzites with marble intercalations. Intensely deformed granitic rocks of Upper Paleozoic age intrude the Pelagonian crystalline basement. An S j foliation is the oldest fabric recognized in the Pelagonian crystalline. Sj is mainly defined by syn-Sjgarnet(Gr1), biotite(Btj), white mica (Wnij), chloritoid, kyanite and plagioclase in the metapelitic rocks and green amphibole, epidote, plagioclase, and biotiteiBtj) in the amphibolite. Garnet grows also in some cases post-kinematically. Ilmenite and tourmaline are often found in the pelitic rocks as well. S is overprinted by an S2 foliation that developed as a crenulation cleavage. In most places, however, S2 has destroyed all earlier fabrics and a single S2 fabric is present related to, isoclinal or sheath folds intrafolial in places. S2 in the metapelitic rocks is characterized by the syn-S2 development of chlorite, white mica(Wm2) and plagioclase. In the amphibolite S2 is mainly defined by the syn-kinematic development of actinolite, plagioclase, biotite(Bt2), white mica(Wm2) and chlorite. During D2 garnet(Gr1) and biotiteiBtj) are partially replaced by chlorite, while green amphibole is replaced by actinolite and chlorite. Chloritoid remains generally stable along the S2-planes but in some places transforms to chlorite and sericite. Furthermore, D2 was locally followed by a static post-kinematic annealing indicated by polygonal quartz microfabrics with equilibrated grain boundaries and triple points. The overall orientation of S2 is dome shaped with a gentle SW-ward and NE-ward dip in the southwestern and northeastern flanks of the dome respectively. Syn-S2 minerals defined a very well exposed NW-SE trending stretching lineation. Kinematic indicators show a main top to the SE sense of movement. An S3 crenulation cleavage associated with asymmetric NW-SE trending folds is also present in most parts of the core and cover rocks, possibly, related to a constrictional type of deformation. A well developed, S4 shear band cleavage is mainly present in the upper parts of the metamorphic dome and formed under cooler conditions. S4 shear bands are associated with a NW-SE developed stretching lineation defined by elongated and dynamically recrystallized quartz grains and a preferred orientation of white mica and chlorite. Along the S4 shear bands a transformation of garnet, biotite, chloritoid and amphibole into chlorite is always observed. S4 shear bands indicate a main top to the SE sense of movement. The P-T metamorphic conditions were derived from textural equilibria and mineral assemblages, as well as from the spatial distribution of the metamorphic minerals. Syn-Dj metamorphism reached the conditions of the boundaries between greenschist and amphibolite facies. Syn-D2 retrogression took place under greenschist facie conditions. K/Ar radiometric datings on coarse-grained syn-St and younger fine-grained syn-S2 micas define an Early Cretaceous cooling age ('135Ma) for the older event and a Mid- to Late Cretaceous age ('90-80Ma) for the second event. A white mica age of ca. 65Ma correlates with S4 shear band clevage. Furthermore, the intrusion age of a granitic body into the Pelagonian crystalline is dated using the Pb/Pb single zircon evaporation method. The estimated intrusion age of 300±3Ma suggests that the Pelagonian crystalline was affected by a pre-kinematic magmatic activity relative to its Cretaceous deformation.
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Flinch, Joan, Antonio Olaiz, Promod Painuly, Riccardo Rocca, Virginia Alonso de Linaje, Begoña Amigo, Monica Armellini, et al. "Geological cross-section through the Garhwall Himalaya, NW India." Boletín de la Real Sociedad Española de Historia Natural 115 (2021): 219–33. http://dx.doi.org/10.29077/bol.115.v02.flinch.
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In early October 2018, a group of oil exploration geologists carried out a geological expedition through the Himalayas, in the Garhwall region, near the Indian state of Uttarakhand. The objective of this paper is to describe a regional geological cross section, from the Gangetic plain to the High Himalayan mountains of the Nanda Devi National Park in the border with Tíbet, today part of China. Close to the city of Dehradun the Main Boundary Thrust is croping out, it represents a major contact between Neo-Proterozoic schists and Eocene gravels of the Siwalik unit, the molasses type deposits that record the flexure of the Indian Plate. Further north is located the Lesser Himalaya, made up by imbricates of Neoproterozoic limestones, quartzites and metabasites of the Krol Group, all exposed along the Ganges river Valley, where the Tons Thrust can be observed. Further north, in the Helang area, the Main Central Thrust acts as a major crustal detachment. In this paper the structure associated to this wide kilometric scale contractional shear zone is described. In fact, two major thrusts define these deformation zones the lower Munsiari Thrust and the upper Vaikrita Thrust that bring mid crustal rocks in contact with upper crustal units of the Lesser Himalayan Sequence. The high strain area is defined by C-S fabrics, mylonites and penetrative isoclinal folding. Moving north some extensional structures, extensional shear zones and normal faults are observed. Further north, near the small village of Malari, close to the Tíbetan border a major extensional detachment knows as the South Tíbetan Detachment (STD), puts into contact high grade metamorphic rocks mostly migmatitesintruded by tourmaline-rich leucogranites of the Higher Himalayan crystallines with low grade to non-metamorphic Neoproterozoic and Paleozoic units of the Tethys Himalayan sequences. Integration of new collected field data with previous works may suggest that during Early Miocene time thrusting along the MCT is coeval with extension through the STD, afterwards the contractional activity continues in the MCT while ductile extensional shear in the STD ceases at Middle Miocene time, syn-orogenic extensional collapse is from that time onwards assume by fragile normal faults. A principios de octubre de 2018, un grupo de geólogos de exploración petrolera realizó una expedición geológica por el Himalaya, en la denominada región de Garhwall, en el estado indio de Uttarakhand. El objetivo de este trabajo es describir e integrar una sección transversal geológica regional, desde la llanura del Ganges hasta las montañas del Alto Himalaya del Parque Nacional del Nanda Devi en la frontera con el Tíbet, hoy parte de China. Cerca de la ciudad de Dehradun se realizó la observación del denominado Main Boundary Thrust (MBT) o Cabalgamiento principal limítrofe, un importante contacto entre esquistos neoproterozoicos y conglomerados eocenos de la unidad Siwalik, los depósitos de tipo molasa que registran la flexura de la placa India. Siguiendo el viaje hacia el norte se atraviesa el denominado Bajo Himalaya constituido por imbricados de calizas, cuarcitas y metabasitas neoproterozoicas del Grupo Krol, todos expuestos a lo largo del valle del río Ganges, en este sector se atraviesa el cabalgamiento de Tons. Más al norte, en el área de Helang, al sur de Josimath, se encuentra una gran zona de cizalla cortical conocida como el Main Central Thrust (MCT) o Cabalgamiento Principal Central. En este sector se describirá en este trabajo la estructura asociada a esta amplia zona de cizallamiento compresional de escala kilométrica. De hecho, dos importantes cabalgamientos definen esta zona de deformación, el cabalgamiento de Munsiari y el de Vaikrita, que ponen las rocas de la corteza media en contacto con las unidades de la corteza superior. La zona está definida por estructuras de tipo C-S, milonitas y pliegues isoclinales con esquistosidad de plano axial. Avanzando hacia el norte se encuentran algunas estructuras extensionales que afectan a estas unidades. Más al norte, cerca de la pequeña aldea de Malari, cerca de la frontera con el Tíbet, se encuentra un importante despegue extensional, el llamado South Tibetan Detachment (STD) o despegue meridional del Tíbet, que pone en contacto los denominados Cristalinos del Alto Himalaya de rocas metamórficas de alto grado tipo migmatitas intruidas por leucogranitos ricos en turmalina de unidades neoproterozoicas y paleozoicas de bajo grado o no metamórficas de las secuencias del Tetis Himalaya. Integrando observaciones de campo propias con trabajos anteriores, se concluye que el empuje y emplazamiento a lo largo del MCT es en parte coetáneo con la extensión a través del STD, lo que sugiere un colapso extensional sinorogénico de las rocas corticales de la corteza media más dúctiles durante el Mioceno Inferior, posteriormente actividad contraccional en el MCT continua después del cese de deformación dúctil en el STD (Mioceno Medio) y el colapso extensional se concentra en fallas normales frágiles a partir de entonces.
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M. Ramji and K. Ramesh. "Stress Separation in Digital Photoelasticity Part A - Photoelastic Data Unwrapping and Smoothing." Journal of Aerospace Sciences and Technologies, August 12, 2023, 5–15. http://dx.doi.org/10.61653/joast.v60i1.2008.811.
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The advent of digital photoelasticity saw the development of various techniques to get photoelastic data of isoclinics and isochromatics at every pixel in the domain. Unlike in other interferometric techniques, in photoelasticity one gets phase data of two quantities and their mutual dependence and interaction affect their evaluation. For stress separation studies, one requires both isochromatics and isoclinics accurately free of any kinks in the domain. With this in view, a robust approach is evolved to get these parameters. Initially wrapped isoclinics are obtained using a plane polariscope based phase shifting technique. These are unwrapped by a quality guided approach. However, the result has several kinks due to isochromatic-isoclinic interaction. An outlier smoothing algorithm is proposed for getting a smooth variation of the isoclinics. Six-step phase shifting method using a circular polariscope is used for determining the isochromatic data. The smoothed isoclinic values obtained are used in isochromatic calculation to get isochromatic phasemap free of ambiguities. This phasemap is also unwrapped by a quality guided approach and smoothed by the outlier algorithm. These methodologies are validated for two benchmark problems of a disk under diametral compression and a ring subjected to internal pressure. The models are subjected to moderate loads showing a high level of isochromatic-isoclinic interaction.
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Et-Taoui, Boumediene. "Equi-isoclinic planes in Euclidean even dimensional spaces." Advances in Geometry 7, no. 3 (January 20, 2007). http://dx.doi.org/10.1515/advgeom.2007.023.
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Betka, Paul, Sharon Mosher, and Keith Klepeis. "Progressive Development of a Distributed Ductile Shear Zone beneath the Patagonian Retroarc Fold-Thrust Belt, Chile." Lithosphere 2022, no. 1 (May 5, 2022). http://dx.doi.org/10.2113/2022/3820115.
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Abstract The southern Patagonian Andes record Late Cretaceous–Paleogene compressional inversion of the Rocas Verdes backarc basin (RVB) and development of the Patagonian fold-thrust belt (FTB). A ductile décollement formed in the middle crust and accommodated underthrusting, thickening, and tectonic burial of the continental margin (Cordillera Darwin Metamorphic Complex (CDMC)) beneath the RVB. We present new geologic mapping, quartz microstructure, and crystallographic preferred orientation (CPO) fabric analyses to document the kinematic evolution and deformation conditions of the décollement. Within the CDMC, the décollement is defined by a quartz/chlorite composite schistose foliation (S1-2) that is progressively refolded by two generations of noncylindrical, tight, and isoclinal folds (F3–F4). Strain intensifies near the top of the CDMC, forming a >5 km thick shear zone that is defined by a penetrative L-S tectonite (S2/L2) and progressive noncylindrical folding (F3). Younger kink folds and steeply inclined tight folds (F4) with both north- and south-dipping axial planes (S4) overprint D2 and D3 structures. Quartz textures from D2 fabrics show subgrain rotation and grain boundary migration recrystallization equivalent to regime 3, and quartz CPO patterns indicate mixed prism <a> and [c] slip systems with c-axis opening angles indicative of deformation temperatures between ~500° and >650°C. Approximately 40 km toward the foreland, the shear zone thins (~1 km thick) and is defined by the L-S tectonite (S2/L2) and tightening of recumbent isoclinal folds (F3). Quartz textures and CPO patterns indicate subgrain rotation recrystallization typical of regime 2 and dominantly basal <a> slip, and c-axis opening angles are consistent with deformation temperatures between ~375° and 575°C. Deformation occurred under greenschist and amphibolite facies conditions in the foreland and hinterland, respectively, indicating that the shear zone dipped shallowly toward the hinterland. The Magallanes décollement is an example of a regional ductile shear zone that accommodated distributed middle to lower crustal thickening below a retroarc FTB.
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SALVI, Maurício, and Ruy Paulo PHILIPP. "Geologia e significado tectônico das rochas metavulcanossedimentares do Complexo Coxilha do Batovi, Cinturão Dom Feliciano (São Gabriel, RS)." Pesquisas em Geociências 46, no. 2 (August 20, 2019). http://dx.doi.org/10.22456/1807-9806.95465.
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O Complexo Coxilha do Batovi (CCB) é uma sequência metavulcanossedimentar de idade pré-cambriana exposto em uma janela estrutural ao sul da cidade de São Gabriel. Para entender a evolução estrutural do complexo foi realizado um estudo integrado de estratigrafia, sedimentologia, análise petrográfica, geologia estrutural e petrologia metamórfica. O CCB está situado no extremo sudoeste do limite do Terreno Taquarembó, sobre a Zona de Cisalhamento Ibaré de direção NW-SE. É composto por meta-arenitos quartzíticos e arcoseanos finos a médios e metapelitos, com mármores, rochas metavulcânicas, formações ferríferas bandadas e metagranitos subordinados. As rochas do CCB registram uma complexa trama estrutural, resultante de uma história de deformação progressiva associada a um metamorfismo orogênico de baixo grau, na fácies Xistos Verdes. A espessura original do pacote sedimentar está multiplicada pela ação de dobras isoclinais e pela transposição da xistosidade principal. Em porções menos deformadas observa-se estratificação plano-paralela, cruzada acanalada e cruzada planar de baixo ângulo. Os perfis colunares levantados sugerem uma sequência de sedimentos progradantes caracterizados por sedimentos siliciclásticos quartzosos e carbonáticos depositados provavelmente em um ambiente deltaico em uma bacia intracratônica ou de margem passiva. A deformação do complexo resulta de um encurtamento regional de direção NE-SW, cuja máxima atuação da deformação gerou a Zona de Cisalhamento Ibaré.
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Petersohn, Eliane, Maria José Maluf de Mesquita, and Eleonora Maria Gouvêa Vasconcellos. "GEOLOGIA DO GRANITO ÁGUA COMPRIDA, ANTIFORME SETUVA, ESTADO DO PARANÁ, BRASIL." Boletim Paranaense de Geociências 58 (December 31, 2006). http://dx.doi.org/10.5380/geo.v58i0.10710.
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Os granitóides deformados da Antiforme Setuva estão localizados no Escudo Paranaense, entre osterrenos Apiaí e Curitiba, Estado do Paraná. A antiforme é uma estrutura elíptica de direção EW e NE-SW,dividida em porção central, Suíte Granítica Água Comprida (SGAC), composta por sienogranitos emonzogranitos deformados, e faixa periférica, Seqüência Santana (SS), composta por mica xistos e quartzitos.O Granito Água Comprida (GAC), porfirítico, é o mais recorrente da SGAC, caracterizado por porfiroclastos defeldspatos. A paragênese magmática é composta por microclínio, quartzo, oligoclásio, biotita, e pelos acessóriosalanita, titanita, ilmenita, apatita e zircão. As paragêneses secundárias são: (a) biotita II, mica branca,titanita II, albita e epidoto; e (b) clorita, mica branca, pirita e raro carbonato. O arranjo espacial dessas rochasreúne feições magmáticas, como schlieren e embricamento de feldspatos, e feições deformacionais, comoquartzo em ribbons, sombras de pressão, mantos de recristalização e pertitas tectônicas. Zonas de intensadeformação e ação de fluidos são responsáveis pela geração de faixas de milonitos e filonitos e veios dequartzo. Os filonitos formam um bandamento hidrotermal composto pela alternância de quartzo, mica branca-biotita e relictos de feldspato. O granito e milonitos apresentam uma foliação milonítica marcante (Sn),preferencialmente EW, definida por níveis de filossilicatos e quartzo em ribbons. A Sn é afetada por dobrasassimétricas e isoclinais, com foliação plano-axial (Sn+1). Os granitos da SGAC são cálcio-alcalinos alto K,metaluminosos a fracamente peraluminosos, com evidências de fracionamento magmático.