Principal Extension Research Articles

Deformation style in the damage zone of the Mondy fault: GPR evidence (Tunka basin, southern East Siberia)

The Mondy strike-slip fault connects the W-E Tunka and N-S Hovsgol basins on the southern flank of the Baikal rift system. Ground penetrating radar (GPR) surveys in its damage zone provide constraints on thicknesses, dips, and plunges of fault planes, as well as on the amount and sense of vertical slip. Strike-slip faulting in the southern segment of the Mondy fault within the territory of Russia bears a normal slip component of motion along the W-E and NW planes. These motions have produced negative flower structures in shallow crust appearing as grabens upon Pleistocene fluvioglacial terraces. The amount of normal slip estimated from the displacement of reflection events varies over the area and reaches its maximum of 3.4 m near Mondy Village. In the Kharadaban basin link, left-lateral strike slip displaces valleys of ephemeral streams to 22 m, while normal slip detected by GPR reaches 2.2 m; this normal-to-strike slip ratio corresponds to a direction of ~6° to the horizon. The angles of dips of faults are in the range 75°-79°; the thicknesses of fault planes marked by low- or high-frequency anomalies in GPR records vary from 2.5 to 17.0 m along strike and decrease with depth within a few meters below the surface, which is common to near-surface coseismic motions. Many ruptures fail to reach the surface but appear rather as sinkholes localized mainly in fault hanging walls. The deformation style in the damage zone of the Mondy fault bears impact of the NW Yaminshin fault lying between its two segments. According to photoelasticity, the stress field changes locally at the intersection of the two faults, under NE compression at 38°, till the inverse orientations of principal compression and extension stresses. This stress pattern leads to a combination of normal and left-lateral strike slip components.

Cavitonics: Using caves in active tectonic studies (Western Carpathians, case study)

The aim of the contribution is to demonstrate the usefulness of the cave passage pattern analysis for neotectonics in suitable regions. The principal presumption is that the orientation of cave passages is perpendicular to the horizontal minimum stress (Shmin). The comparison of the obtained data with the neotectonic structures and the orientation of the Pliocene – Quaternary principal stress field (Shmin) is presented. The back-arc extension dominated in the Western Carpathians during the Pliocene–Early Pleistocene. The orogen-parallel extension has been determined for central part of the Western Carpathians (Slovakia) for the Late Pleistocene–Holocene. The results revealed a link between the passage patterns of the Western Carpathian caves and orientation of the principal extension obtained from structural data.

Fault damage zones in mechanically layered rocks: The effects of planar anisotropy

AbstractThis study shows how inherited strength anisotropy influences damage localization at both the tip and wall regions of a fault or fracture. We performed analogue and numerical compression experiments on transversely isotropic models with single and multiple cuts of finite length, simulating the propagation of preexisting faults and cracks in layered rock. The stress‐strain curves from the analogue experiments show a change in bulk yield behavior with fault inclination and anisotropy orientation with respect to the stress direction. Earlier isotropic models demonstrated a brittle (wing fracturing) to ductile (shear‐zone formation) transition as the fault angle (α) to the principal compression direction increased. The experiments with anisotropic models show patterns of damage localization change dramatically with the orientation of transversely isotropic planes (θ, measured with respect to principal extension direction). Under layer‐normal (θ = 0°) and layer‐parallel compression (θ = 90°), preexisting faults undergo significant reactivation when 0 < α < 90°, and fault slip eventually leads to mechanical instabilities within the anisotropic layering, causing damage zones in the tip regions. For layer‐normal (θ = 0°) compression, the damage processes involve intense extensional shear localization, whereas for layer‐parallel compression, contractional shear localization and tensile opening result in characteristic internal shear‐band structures. In contrast, for 0 < θ < 90°, the faults undergo little or no reactivation, irrespective of α. In this case, bulk compression leads to an interlayer slip‐mediated global deformation. Obliquely anisotropic models thus produce weak or no fault damage zones. We also show that the fault‐parallel principal damage localized at the tips can be coupled with transversely oriented, antithetic secondary damage in the wall regions. However, secondary damage develops predominantly when θ = 90°. Field examples of fault damage in anisotropic rocks and numerical experiments are in good accord with our experimental damage patterns.

Kinematics of the Neogene Terror Rift: Constraints from calcite twinning strains in the ANDRILL McMurdo Ice Shelf (AND-1B) core, Victoria Land Basin, Antarctica

We report new strain analyses of mechanically twinned calcite in veins hosted by Neogene (13.6–4.3 Ma) sedimentary and volcanic rocks recovered from the Terror Rift system in the southern Ross Sea, Antarctica, by the ANDRILL (ANtarctic geological DRILLing) McMurdo Ice Shelf (MIS) Project. Strain analyses of the ANDRILL MIS AND-1B drill core samples yield prolate and oblate ellipsoids with principal shortening and extension strains ranging from −7% to 9%, respectively. The majority of samples show ≤25% negative expected values, indicating homogeneous coaxial strain characterized predominantly by subvertical shortening. We attribute the subvertical shortening strains to mechanical twinning at relatively shallow depths in an Andersonian normal faulting stress regime induced by sedimentary and ice sheet loading of the stratigraphic sequence and characterized by low stress magnitudes. Oriented samples yield a northwest-southeast average extension direction that is subparallel to other indicators of Neogene extension. This northwest-southeast extension is consistent with strain predicted by Neogene orthogonal rifting in a north-northeast–trending rift segment, as well as models of right-lateral transtensional rifting. The overall paucity of a noncoaxial layer-parallel shortening signal in the AND-1B twin populations favors orthogonal extension in the Neogene Terror Rift system, but could also be due to spatial partitioning of strain in a transtensional rift regime.

Extension structural records in the Qinshui basin (North China) since the Late Mesozoic

Qinshui basin has abundant coal-bed methane resources and has been undergoing intensive intracontinental rifting and extensional tectonics since the Late Mesozoic. Some fractures, which were previously considered as conjugate shear fractures, are interpreted as joint sets with extension characteristics, for the first time in the Qinshui basin. The widely distributed joint sets with stable attitudes can be divided into four sets. This paper presents updated results of fault-slip datasets collected in different zones of the Qinshui basin and addresses the changes in the direction of extensional stresses since the Late Mesozoic. Based on the analysis results of the slickenline of normal faults, joint sets in the field, and focal mechanism solutions data from the Shanxi Province, we identified four main directions of extension since the Late Mesozoic in the Qinshui basin: (1) Early Cenozoic ENE–WSW (85 ± 15°) extension; (2) Palaeogene NNE–SSW (30 ± 5°) extension; (3) Miocene NW–SE (135 ± 15°) extension; and (4) Late Pliocene–quaternary NNW–SSE (170 ± 5°) extension. The principal extension directions in the Qinshui basin seem to have undergone a counterclockwise rotation from the Early Cenozoic to the Miocene. We prefer that the extension deformation events in the Qinshui basin since the Late Mesozoic were mainly related to the back-arc spreading induced by westward subduction of the paleo-Pacific plate under the Eurasian continent.

Extensions of L-fuzzy closure spaces

Abstract In this paper, we study the extension theory to L -fuzzy closure spaces, where L is a strictly two-sided, commutative quantale lattice. We give new notions such as L -fuzzy stack, L -fuzzy c-grill and trace of a point. Also, we construct order relation and equivalence relation between two extensions. Also, We introduce the concept of a principal extension of L -fuzzy closure space and study some of its applications.

Zero-Dimensional Principal Extensions

We prove that every topological dynamical system (X,T) has a zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measure ? on Y the conditional entropy h(?|X) is zero. This reduces the discussion of many entropy-related properties to the zero-dimensional case which gives access to the various useful tools of symbolic dynamics.

Entropy-expansiveness for partially hyperbolic diffeomorphisms

We show that diffeomorphisms with a dominated splitting ofthe form $E^s\oplus E^c\oplus E^u$, where $E^c$ is a nonhyperboliccentral bundle that splits in a dominated way into1-dimensional subbundles, are entropy-expansive.In particular, they have a principal symbolic extension and equilibrium states.

A material model for multiaxial stretching and stress relaxation of polypropylene under process conditions

Polypropylene sheets have been stretched at 160°C to a state of large biaxial strain of extension ratio 3, and the stresses then allowed to relax at constant strain. The state of strain is reached via a path consisting of two sequential planar extensions, the second perpendicular to the first, under plane stress conditions with zero stress acting normal to the sheet. This strain path is highly relevant to solid phase deformation processes such as stretch blow moulding and thermoforming, and also reveals fundamental aspects of the flow rule required in the constitutive behaviour of the material. The rate of decay of stress is rapid, and such as to be highly significant in the modelling of processes that include stages of constant strain. A constitutive equation is developed that includes Eyring processes to model both the stress relaxation and strain rate dependence of the stress. The axial and transverse stresses observed during loading show that the use of a conventional Levy–Mises flow rule is ineffective, and instead a flow rule is used that takes account of the anisotropic state of the material via a power law function of the principal extension ratios. Finally the constitutive model is demonstrated to give quantitatively useful representation of the stresses both in loading and in stress relaxation.

Faithful zero-dimensional principal extensions

We prove that every topological dynamical system (X,T) has a faithful zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measureon Y the conditional entropy h(�|X) is zero, and, in addition, every invariant measure on X has exactly one preimage on Y. This is a strengthening of the result in (D-H) (in which the extension was principal, but not necessarily faithful).

Magnetic fabric and tectonic setting of the Early to Middle Jurassic felsic dykes at Pitt Point and Mount Reece, eastern Graham Land, Antarctica

AbstractAt Pitt Point, the east coast of Graham Land (Antarctic Peninsula), the Early to Middle Jurassic (Toarcian–Aalenian) rhyolite dykes form two coevally emplaced NNE–SSW and E–W trending sets. The nearly perpendicular dyke sets define a large-scale chocolate-tablet structure, implying biaxial principal extension in the WNW–ESE and N–S directions. Along the nearby north-eastern slope of Mount Reece, the WNW–ESE set locally dominates suggesting variations in the direction and amount of extension. Magnetic fabric in the dykes, revealed using the anisotropy of magnetic susceptibility (AMS) method, indicates dip-parallel to dip-oblique (?upward) magma flow. The dykes are interpreted as representing sub-volcanic feeder zones above a felsic magma source. The dyke emplacement was synchronous with the initial stages of the Weddell Sea opening during Gondwana break-up, but it remains unclear whether it was driven by regional stress field, local stress field above a larger plutonic body, or by an interaction of both.

Destruction of the eastern North China Craton in a backarc setting: Evidence from crustal deformation kinematics

The eastern North China Craton (NCC) west of the Pacific Ocean has a long history of rifting from Early Cretaceous to the end of Paleogene when the craton experienced destruction and significant thinning of the lithosphere. The cause and geotectonic environment for this destruction remain controversial. We use a set of field observation including basin patterns, fault geometry and kinematics, fault plane slip data, dike distribution, and fabric data from metamorphic core complexes to determine the kinematic evolution of the deformation in the eastern NCC during this period. We show that the principal extension direction in the eastern NCC evolved from WNW–ESE in the earliest-middle Early Cretaceous, via NW–SE in the latest Early Cretaceous, to nearly N–S in the Late Cretaceous–Paleogene. The movement history, from Late Mesozoic to Early Cenozoic, of the oceanic plates in the Pacific Ocean with respect to the eastern NCC is available from previous studies. The Izanagi Plate first subducted nearly orthogonally (WNW-wards) during earliest-middle Early Cretaceous time, and then moved obliquely (NNW-wards) in the latest Early Cretaceous while the relaying Pacific Plate moved generally northwards from the Late Cretaceous to Paleogene. Both the movement direction of oceanic plates and the principal extension direction of the continental deformation rotated clockwise. We suggest that such a correlation can be explained by the eastern NCC being in a backarc setting in the Cretaceous–Paleogene period. The results support the backarc extensional model for the destruction and significant lithospheric thinning of the eastern NCC.

Generalized Principal Extensions in Topological Algebras

The “generalized principal extension” of a subset of a topological algebra is, by definition, a subset of another topological algebra. Hence, the generalized spectrum of an element, “local spectrum”, of a topological algebra is thus a subset of a topological algebra, not necessarily of \({{\mathbb C}}\) . We also give a criterion for the continuity of the (generalized) Newburg map (Theorem 3.1).

Coexisting tectonic settings: the example of the southern Tyrrhenian Sea

We performed geodetic strain rate analyses in southern Italy, using new GPS velocities. Two-dimensional strain and rotation rate fields were estimated and results show that most of the shortening is distributed in the northern Sicily offshore. Extension becomes more evident and comparable with shortening on the eastern side of the same margin, and greater in the eastern Sicily offshore. Principal shortening and extension rate axes are consistent with long-term geological features: seismic reflection profiles show both active compressive and extensional faults affecting Pleistocene strata. We show evidence for contemporaneous extension and transtension in the Cefalu Basin. Combining geodetic data and geological features point to the coexistence of independent geodynamic processes, i.e., the active E–W backarc spreading in the hangingwall of the Apennines subduction zone and shortening along the southern margin of the Tyrrhenian backarc basin operated by the NNW-motion of Africa relative to Eurasia.

The role of bedding in the formation of fault–fold structures, Portalegre‐Esperança transpressional shear zone, SW Iberia

AbstractFold‐fault structures within a major transpressional shear zone of the SW Iberian Massif were investigated by combining geological mapping, cross‐section analysis and microtectonic studies. A significant example of contractional deformation is displayed in the Portalegre‐Esperança Shear Zone (PESZ) where a heterogeneous Ordovician stratigraphic sequence, showing a strong competence contrast between quartzites, slates and quartzo‐feldspathic rocks favoured strain localization and fault nucleation that controlled fold formation. The presence of pelitic layers within the thick‐bedded quartzites had probably provided weakness zones that were more favourable for the strain localization than the previous foliation present in the quartzites. The quartzites and the quartzo‐feldspathic rocks (granites and volcaniclastic rocks) accommodated heterogeneous high strain developing different degrees of mylonitization. The quartzites with protomylonitic textures are dominant and represent coarse‐grained siliciclastic sediments that suffered metamorphism and partial dynamic recrystallization. Ultramylonites occur within discrete high‐strain shear zones. It is probable that the strain localization in the PESZ involved both the effect of having layers of different competence and layers or stratigraphic contacts with rocks that experienced grain size reduction dominated by cataclasis and dislocation creep.Folds within quartzites with sub‐horizontal to gently plunging hinges vary from closed to open in thick‐bedded quartzites and from tight to closed in thin‐bedded quartzites. Observed changes in structural style of deformed quartzites, slates and quartzo‐feldspathic rocks are interpreted to result from the constraints imposed by the mechanical properties of the different lithologies.As the folds tightened during shortening, the alternating zones of contrasting competence favoured the disruption of the bedding. The deformation history in the PESZ was dominated by thrusting and strike‐slip faulting along incompetent layers that locally developed staircase geometry and transected the lower Ordovician stratigraphic sequence. The kinematic model proposed for the PESZ is consistent with the models of transpressional shear zones stretched along strike with the development of coeval strike‐slip and low angle oblique‐slip faults associated to active buckle folds with axes parallel to the principal extension direction. Copyright © 2010 John Wiley & Sons, Ltd.

Knowledge creation and flow in agriculture

PurposeThe motivation for this paper emanates from the continuous success and sustainability of the Japanese agriculture, most remarkably in its technical sense. The agricultural extension services have traditionally been regarded as a bridge between research laboratories and farmers, hence, the purpose of this paper is to explore the preferences and roles played by extension advisors in relation to knowledge creation and sharing among the advisors, farmers, and other stakeholders.Design/methodology/approachData are collected through interviews with 11 principal and senior extension advisors and a consultant from different prefectures and organizations as well as questionnaires from 135 extension advisors in the Ibaraki Prefecture, Japan.FindingsResults show that the Japanese agricultural agencies are actively involved in facilitating an integrated knowledge creation and sharing initiatives within their organizations. On the other hand, the extension advisors, as intermediaries and catalysts, are the key links between farmers and the relevant agencies in terms of providing personalized and need‐based information for decision making by all parties concerned.Research limitations/implicationsFuture research may be conducted by other agro‐based economies and organizations with regards to creating, sharing, and streamlining knowledge towards achieving organizational objectives.Originality/valueThe findings of this paper have provided some insights on how knowledge is created and shared within a strategic sector of the economy and this could serve as an initial framework for leaders to create opportunities and space for such activities to be effectively carried out in their organizations.

Research on Characteristics of Present‐Day Crustal Motion and Deformation in Kamchatka Area

AbstractWe have collected GPS data in the period of 1995~2005 in Kamchatka, Russia to study the presentday crustal horizontal motion in this area. Strain rate components are computed in a spherical coordinate system. Analyses to the spatial distribution of strain rate fields derived from GPS measurements are carried out in comparison with seismological and geological researches. Results show that microplate boundaries are not clear in the northern Kamchatka peninsula. GPS site velocities in the southern Kamchatka peninsula are generally greater than those in the middle and north of this area. The closer to the eastern subduction zone GPS sites are, the greater their velocities are. The horizontal velocity field obviously exhibits a decrease westward across the peninsula. Generally horizontal motions have the same direction as the Pacific plate subduction zone in this region. All strain rate components are characterized by decreasing westward. The Kamchatka peninsula is undergoing compression in terms of EW and NS strain rate components, with extension in certain local portions. Dilation rates show that the Kamchatka peninsula is under compression. Rigidity rotation rates show that this region is experiencing clockwise motion, especially in the northern zone and southern end. Effective strain rates in the eastern zone are greater than those in the west, and it exhibits a remarkable westward decrease. Principal compression strain rates are apparently greater than principal extension strain rates, especially in the eastern zone. In general, directions of principal compressive strain rates are congruent with horizontal projections of principal compressive axes derived from medium and large earthquakes. The spatial non‐uniform crustal deformation field is associated with the subduction depth, orientation, dipping angle and coupling strength of the boundary interface between the Pacific and North American plates beneath the southeastern Kamchatka peninsula.

Which axial and bending stiffnesses of posterior implants are required to design a flexible lumbar stabilization system?

Dynamic stabilization devices have been introduced to clinics as an alternative to rigid fixation. The stiffness of these devices varies widely, whereas the optimal stiffness, achieving a predefined stabilization of the spine, is unknown. This study was focused on the determination of stiffness values for posterior stabilization devices achieving a flexible, semi-flexible or rigid connection between two vertebrae. An extensively validated finite element model of a lumbar spinal segment L4-5 with an implanted posterior fixation device was used in this study. The model was exposed to pure moments of 7.5 and 20 Nm around the three principal anatomical directions, simulating flexion, extension, lateral bending and axial rotation. In parametrical studies, the influence of the axial and bending fixator stiffness on the spinal range of motion was investigated. In order to examine the validity of the computed results, an in-vitro study was carried out. In this, the influence of two posterior stabilization devices (DSS™ and rigidly internal fixator) on the segmental stabilization was investigated. The finite element (FE)-model predicted that each load direction caused a pairing of stiffness relations between axial and bending stiffness. In flexion and extension, however, the bending stiffness had a neglectable effect on the segmental stabilization, compared to the axial stiffness. In contrast, lateral bending and axial rotation were influenced by both stiffness parameters. Except in axial rotation, the model predictions were in a good agreement with the determined in-vitro data. In axial rotation, the FE-model predicted a stiffer segmental behavior than it was determined in the in-vitro study. It is usually expected that high stiffness values are required for a posterior stabilization device to stiffen a spinal segment. We found that already small stiffness values were sufficient to cause a stiffening. Using these data, it may possible to develop implants for certain clinical indications.

Evaluation of the MPA Procedure for Estimating Seismic Demands: RC-SMRF Buildings

The modal pushover analysis (MPA) procedure is extended for analysis of reinforced concrete special moment resisting frame (RC-SMRF) buildings, after demonstrating that the theory, assumptions, and approximations underlying this procedure are valid for such systems. The principal extension of the procedure is in the hysteretic model for modal SDF systems, chosen as the peak-oriented model to represent the global monotonic and cyclic behavior of such buildings, characterized by deterioration of stiffness and strength under cyclic deformation. The median seismic demands for 4-, 8-, 12-, and 20-story RC-SMRF buildings—designed to comply with current codes—due to an ensemble of 78 ground motions scaled to four intensity levels were computed by MPA and nonlinear RHA, and compared. It is demonstrated that, even for the most intense ground motions that deform the buildings far into the inelastic range, the MPA procedure demonstrates an adequate degree of accuracy that should make it useful for practical application in estimating seismic demands for RC-SMRF buildings. In contrast the FEMA-356 force distributions are inadequate in estimating seismic demands for the 8-, 12-, and 20-story buildings at all excitation intensities, from the weakest that causes response essentially within the linearly elastic range, to the strongest that drives the buildings far into the inelastic range.

Fault kinematics and tectonic stress in the seismically active Manyara–Dodoma Rift segment in Central Tanzania – Implications for the East African Rift

The Eastern Branch of the East African Rift System is well known in Ethiopia (Main Ethiopian Rift) and Kenya (Kenya or Gregory Rift) and is usually considered to fade away southwards in the North Tanzanian Divergence, where it splits into the Eyasi, Manyara and Pangani segments. Further towards the south, rift structures are more weakly expressed and this area has not attracted much attention since the mapping and exploratory works of the 1950s. In November 4, 2002, an earthquake of magnitude Mb = 5.5 struck Dodoma, the capital city of Tanzania. Analysis of modern digital relief, seismological and geological data reveals that ongoing tectonic deformation is presently affecting a broad N–S trending belt, extending southward from the North Tanzanian Divergence to the region of Dodoma, forming the proposed “Manyara–Dodoma Rift segment”. North of Arusha–Ngorongoro line, the rift is confined to a narrow belt (Natron graben in Tanzania) and south of it, it broadens into a wide deformation zone which includes both the Eyasi and Manyara grabens. The two-stage rifting model proposed for Kenya and North Tanzania also applies to the Manyara–Dodoma Rift segment. In a first stage, large, well-expressed topographic and volcanogenic structures were initiated in the Natron, Eyasi and Manyara grabens during the Late Miocene to Pliocene. From the Middle Pleistocene onwards, deformations related to the second rifting stage propagated southwards to the Dodoma region. These young structures have still limited morphological expressions compared to the structures formed during the first stage. However, they appear to be tectonically active as shown by the high concentration of moderate earthquakes into earthquake swarms, the distribution of He-bearing thermal springs, the morphological freshness of the fault scarps, and the presence of open surface fractures. Fault kinematic and paleostress analysis of geological fault data in basement rocks along the active fault lines show that recent faults often reactivate older fault systems that were formed under E–W to NW–SE horizontal compression, compatible with late Pan-African tectonics. The present-day stress inverted from earthquake focal mechanisms shows that the Manyara–Dodoma Rift segment is presently subjected to an extensional stress field with a N080°E direction of horizontal principal extension. Under this stress field, the rift develops by: (1) reactivation of the pre-existing tectonic planes of weakness, and (2) progressive development of a new fault system in a more N–S trend by the linkage of existing rift faults. This process started about 1.2 Ma ago and is still ongoing.