Finite Strain Pattern Research Articles

Strain Localization: Analog Modeling and Anisotropy of Magnetic Susceptibility

AbstractThe majority of the strain in Earth crust and upper mantle is localized to the high strain zones developed at ductile‐to‐brittle condition at kilometer‐to‐micrometer scale. Therefore, they represent the key to understanding the deformation evolution of the lithosphere. The finite strain pattern recorded within these zones has been therefore a subject of research in geology. The methods studying rock magnetism such as the anisotropy of magnetic susceptibility (AMS) are frequently used techniques to characterize and quantify deformation and flow record in rocks. Numerous sedimentary, subsolidus and submagmatic deformation zones exhibit typical evolution of the AMS ellipsoid across the strain gradient suggesting indirect not straightforward correlation between AMS and strain ellipsoids. To document spatiotemporal and internal fabric evolution during strain localization, pure shear, simple shear, and shear zone (SZ) analog experiments were performed using shear‐thinning thixotropic material of plaster of Paris. The experimental results closely resemble the record from natural SZs in sedimentary rock systems but also in subsolidus SZs and submagmatic mushy systems. The magnetic fabric evolution across deformation zones is interpreted to be associated with the intersection and transposition of preexisting primary fabric with shear fabrics and evolution of synkinematic subfabrics. Their development is attributed to localization of deformation at microscale due to the self‐organized slip of anisometric particles forming microshear planes reflecting the symmetry of deformation. The experimental results when confronted with the natural examples implies that the localization and partitioning of deformation is one of the most important factors for the interpretation of AMS in deformation zones.

Deciphering the tectonometamorphic history of subducted metapelites using quartz‐in‐garnet and Ti‐in‐quartz (QuiG–TiQ) geothermobarometry—A key for understanding burial in the Scandinavian Caledonides

AbstractThe Seve Nappe Complex is a subduction‐related high‐grade metamorphic unit that was emplaced onto the margin of Baltica during Caledonian orogenesis. In this paper, the tectonometamorphic evolution of the Lower Seve Nappe in the Scandinavian Caledonides was characterized with the help of the continuous Collisional Orogeny in the Scandinavian Caledonides (COSC‐1) drill core, using a combination of various P–T estimation techniques based on garnet–quartz mineral pairs (quartz‐in‐garnet and Ti‐in‐quartz [QuiG–TiQ]), conventional thermobarometry and thermodynamic modelling of phase equilibria. This multi‐method approach yields complementary results and delivers critical data to constrain a comprehensive pressure–temperature–deformation–time (P–T–D–t) evolutionary path for the metasedimentary rocks of the Lower Seve Nappe. In the garnetiferous metasedimentary rocks, quartz inclusions in garnet preserve the P–T conditions of three distinct garnet growth stages corresponding to three metamorphic stages Ms1 to Ms3, including prograde and peak metamorphic conditions. Ms1 and Ms2 stages were constrained via quartz inclusions in garnet core and mantle. They are relatively close in the P–T space and could be considered as one single continuous prograde event occurring at epidote–amphibolite facies conditions of 460–520°C and 0.6–0.85 GPa. The growth of the garnet outermost rim defines the Ms3 stage at amphibolite facies conditions of 590–610°C and 1.13–1.18 GPa and corresponds to the peak metamorphic conditions. The microstructural analysis shows that the finite ductile strain pattern of the Lower Seve Nappe results from the superposition of four deformation phases. The initial phase D1 is defined by the S1 foliation that is still preserved as a curved inclusion trail in the garnet core. The D2 phase initiated contemporaneously with garnet core growth and the development of muscovite–biotite–plagioclase S2 foliation. Garnet outermost rim growth marks the end of the prograde path and peak metamorphic conditions. This stage is overprinted by the D3 phase and Ms4 stage associated with the development of the main regional metamorphic and mylonitic fabric S3 associated with C′‐type shear bands along the retrograde path. Ms4 stage, which was constrained using traditional thermobarometric techniques, corresponds to the chemical re‐equilibration of the metasedimentary minerals and occurred under amphibolite facies conditions at ~570–610°C and 0.78–1.00 GPa. The D3 phase is then generally weakly to strongly overprinted by later lower grade deformation D4 phase at greenschist facies conditions (Ms5). 40Ar/39Ar ages of syn‐kinematic white mica and biotite indicate that the final stage of the thrusting of the Lower Seve Nappe and thus the timing of its emplacement onto the Offerdal Nappe occurred at c. 423 Ma. Collectively, these results are consistent with previous estimates of the timing and conditions of metamorphism derived from the Lower Seve Nappe especially in west‐central Jämtland. However, application of QuiG–TiQ thermobarometry demonstrated that quartz inclusions in garnet can preserve different aspects of garnet growth, which are not accessible by traditional methods especially in complex terranes, and therefore provided new significant insights into the Lower Seve prograde evolution.

Deciphering large-scale superposed fold systems at shallow crustal levels in collision zones: insights from the Marguareis Massif (southwestern Alps)

ABSTRACT We present and discuss the results of a field-based approach including accurate geological mapping and micro- to map-scale structural analysis to highlight the finite strain pattern recorded in Marguareis Unit, a massif deformed at shallow crustal levels at the boundary between Maritime and Ligurian Alps. We describe superposed tectonic structures developed under low-grade metamorphic conditions during the Alpine collision and nowadays exceptionally well recorded in the area of interest. We demonstrate that the structural frame of the Marguareis Unit results from superposition of fourfold systems, later segmented, but without significant displacements, by brittle faults.

Strain Partitioning Within Bending Orogens, New Insights From the Variscan Belt (Chiroulet‐Lesponne Domes, Pyrenees)

AbstractThis study investigates how strain is partitioned within hot orogenic belts in a context of plate reorganization. We document crustal‐scale strike‐slip shear zones, plate‐scale oroclinal bending, and widespread exhumation of deep crustal domains in the core of nascent Pangea plate during late‐Variscan times (ca. 310–290 Ma). The role of strain partitioning in the finite strain patterns is first highlighted at regional scale by a new detailed structural, kinematic, and petrologic analysis of the Chiroulet and Lesponne gneiss domes in the Pyrenees. Vertical strain partitioning in response to N‐S shortening‐dominated dextral transpression is secondly documented at the scale of the Variscan domains of the Pyrenees, based on a synthesis of recent geochronological, thermobarometrical, and structural data. We show that the mid‐lower crust is affected by eastward lateral flow and the upper crust by penetrative thickening and localized thrusting. Local transverse extension in the mid‐lower crust illustrates gravity‐driven instability favored by the accumulation of anatectic melts in gneiss domes. Finally, we highlight the respective position of extended and shortened area within the Variscan belt during late‐Carboniferous/early‐Permian that suggests large‐scale lateral strain partitioning and reorganization of the weak continental crust in the core of the Pangea. This distribution appears significantly different from other orogens in a similar context of oroclinal bending, resulting in localization of the shortened zones in the core of the belt. This highlights the influence of the initial and boundary conditions, such as the obliquity of the belt to the applied stress field and the location of free‐boundaries, on finite strain patterns.

Structural relationships between Helminthoid Flysch and Briançonnais Units in the Marguareis Massif: A key for deciphering the finite strain pattern in the external southwestern Alps

The structural setting and tectonic evolution of the Marguareis Massif (located at the boundary between the Maritime and Ligurian Alps) has long been matter of debate. After new meso‐ and micro‐structural studies and field investigations, the tectonic unit interplay outlines a finite structural architecture more complex than that proposed in previous interpretations. We depict a stack of Briançonnais Units stemming from the Europe continental margin, and the Helminthoid Flysch Unit, detached from its original basement whose original palaeogeographic domain is still a matter of debate. Our results highlight for the first time that each unit recorded different pre‐stacking folding events progressively developed at different structural levels. The events occurred during the stacking of the units produced shear zones with top‐to‐SW sense of movement. After the syn‐stacking tectonics achieved during the Late Eocene‐Early Oligocene collisional events, the whole stack recorded the same post‐stacking deformation history here represented by a fold system with sub‐horizontal axial planes and faults. Similar tectonic evolution was documented in other sectors of the Western Alps by previous authors.

Control of 3-D tectonic inheritance on fold-and-thrust belts: insights from 3-D numerical models and application to the Helvetic nappe system

Abstract. We apply three-dimensional (3-D) thermo-mechanical numerical simulations of the shortening of the upper crustal region of a passive margin in order to investigate the control of 3-D laterally variable inherited structures on fold-and-thrust belt evolution and associated nappe formation. We consider tectonic inheritance by employing an initial model configuration with basement horst and graben structures having laterally variable geometry and with sedimentary layers having different mechanical strength. We use a visco-plastic rheology with a temperature-dependent flow law and a Drucker–Prager yield criterion. The models show the folding, detachment (shearing off) and horizontal transport of sedimentary units, which resemble structures of fold and thrust nappes. The models further show the stacking of nappes. The detachment of nappe-like structures is controlled by the initial basement and sedimentary layer geometry. Significant horizontal transport is facilitated by weak sedimentary units below these nappes. The initial half-graben geometry has a strong impact on the basement and sediment deformation. Generally, deeper half-grabens generate thicker nappes and stronger deformation of the neighbouring horst, while shallower half-grabens generate thinner nappes and less deformation in the horst. Horizontally continuous strong sediment layers, which are not restricted to initial graben structures, cause detachment (décollement) folding and not overthrusting. The amplitude of the detachment folds is controlled by the underlying graben geometry. A mechanically weaker basement favours the formation of fold nappes, while stronger basement favours thrust sheets. The model configuration is motivated by applying the 3-D model to the Helvetic nappe system of the Central Alps of France and Switzerland. Our model reproduces several first-order features of this nappe system, namely (1) closure of a half-graben and associated formation of the Morcles and Doldenhorn nappes, (2) overthrusting of a nappe resembling the Wildhorn and Glarus nappes, and (3) formation of a nappe pile resembling the Helvetic nappes resting above the Infrahelvetic complex. Furthermore, the finite strain pattern, temperature distribution and timing of the 3-D model is in broad agreement with data from the Helvetic nappe system. Our model, hence, provides a 3-D reconstruction of the first-order tectonic evolution of the Helvetic nappe system. Moreover, we do not apply any strain softening mechanisms. Strain localization, folding and nappe transport are controlled by initial geometrical and mechanical heterogeneities showing the fundamental importance of tectonic inheritance on fold-and-thrust belt evolution.

Precambrian deformation belts in compressive tectonic regimes: A numerical perspective

The thermal state of the lithosphere is often considered as the main factor controlling the distribution of the structural and metamorphic features in tectonic systems (ancient versus modern tectonics). Deformation in ancient (weak and hot) lithospheres is distributed whereas deformation in modern (strong and cold) lithospheres is localised into prominent shear zones. The distributed deformation during the Precambrian suggests lower compressive strain rates are required, implying a long compression duration. However, the effects of variable strain rate on the compression of ancient lithospheres remain under-explored. A series of numerical models mimicking Precambrian lithospheric conditions is proposed and a broad range of thermal profiles and shortening rates is tested to investigate their influence on the resultant deformation modes. Two broad deformation styles were found to be significantly influenced by the magnitude of the shortening rates and stand out from the parametric study: (i) pop-downs and upper crustal thrusting at high strain rates that favour the formation of shear zones, and (ii) sedimentary cusping deformation at slower strain rates that generates well-defined vertical finite strain patterns. These two deformation modes were compared with natural examples, providing further insight into the evolution of their respective deformations. The vertical structures at the Hearne Craton (western Canadian Shield) could be explained via the sedimentary cusping mechanism by constraining our models with available geological data. Meanwhile, the vertical finite strain patterns from the proposed reference model now provide a tectonic template for future fluid-thermal convection simulations, to predict fluid flow and mineralisation potential.

Polyphase or time-dependent kinematics and quaternary reactivation of thrust bounding Baijnath Klippe: western Kumaun Himalaya, India

The morphotectonic elements of the Baijnath Klippe (BK) have been examined to understand the kinematics of the Inner Kumaun Lesser Himalaya from Tertiary to Late Quaternary. The BK is bounded by two thrusts: the Askot Thrust (AT), to the north and the Baijnath Thrust (BjT), to the south. The older (20 Ma) hanging wall rocks (mylonites and phyllites) are underlain and surrounded by quartzites (equivalent to Nagthat Formation of Outer Lesser Himalaya). The kinematics study and strain analysis along Dewal–Narayanbagarh transect provides the varied intensity of deformation (D1, D2, and D3) within the zone of BK. The D1 event is characterized by isoclinal tight folds in phyllite and mylonite; the D2 phase is characterized by open folding in mylonite. However, the youngest event D3 phase is observed as a regional synclinal folding of BK and associated rocks. The presence of 1–3-km-thick mylonite zone parallel to the thrust planes is related to the compressional event of Miocene age. The geomorphic pattern and chronologically constraints (OSL ages) with spatial variability in the incision/uplift rate suggests that the terrain is undergoing differential crustal deformation during Late Quaternary. Kinematic indicators such as streaky foliations, S–C foliation, mantled porphyroclasts, micro-shears with bookshelf gliding, and mica fish found in mylonites (macroscopic as well as microscopic) indicate ductile deformation in the area. We used Flinn plot (Rf/ϕ) and Fry (Tectonophysics 60:89–105, 1979) analysis to delineate the finite strain pattern in 21 oriented samples collected across the BK bound thrusts (BjT and AT). The strain analysis revealed an increasing trend of strained quartz grains, which presents triaxialoblate strain geometry (flattening i.e., 0 < k < 1) towards the structural discontinuity. The textural (chessboard, myrmekite, undulose extinction and fracturing in quartz and feldspar) and mineralogical properties (non-flaky) of quartz and feldspar indicate the temperature of deformation and mylonitization ranging 300–500 °C.

NanoSIMS study of seismically deformed zircon: Evidence of Y, Yb, Ce, and P redistribution and resetting of radiogenic Pb

Lattice defects in zircon can cause trace elements redistribution and disturbance of isotopic systems. This study investigates in detail how seismically induced deformation microstructures in zircon correlate with trace element and isotope re-equilibration. Felsic mylonites with pseudotachylyte veins from the Ivrea-Verbano Zone in Northern Italy were studied with special focus on deformed zircon. We have revealed the following post-growth deformation microstructures: planar deformation bands (PDBs), planar fractures (PFs), non-planar fractures (both healed and open), and finite strain patterns. PDBs are planar portions of crystal lattice that are strictly parallel to {100} crystallographic planes, and are rotated to up to 3° with respect to the host grain. They are from 0.5 to 1 μm wide and have average spacing of 5 μm. PDBs originate in seismically active environment at elevated differential stress, strain rate and temperature. Several grains, in which PDBs are observed, were analyzed with ion microprobe. Ion maps indicate redistribution of radiogenic Pb isotopes associated with PDB formation. Isotopic redistribution preferably occurs in PDBs with larger crystallographic misorientation. Profiling demonstrated clear spatial correlation of PDBs with variations of REE abundances (both gain and loss), and possible correlations with increased and decreased Hf, Ti, and P abundances. Trace elements can be depleted or enriched (compared to the abundance in surrounding matrix) in deformed domains, depending on the spacing of PDBs and the proximity of the analyzed volume to grain boundary or to detrital core. 207 Pb/ 206 Pb ratio demonstrates systematic Pb-loss in the PDB-bearing lattice domains with respect to PDB-free domains; in some cases Pb-gain is observed, where the PDBs source radiogenic Pb from older detrital cores. Our study has important implications for geochronology and microchemistry of zircon from seismically deformed sections of Ivrea-Verbano Zone and from other paleo-seismic zones of the world. Zircon found in seismically deformed rocks near pseudotachylyte veins may demonstrate distorted and even reset isotopic ages, and altered trace element abundances. Enhanced trace element exchange between deformed zircon and host mylonite can influence mass-balance calculations for the bulk rock.

Tectono-metamorphic evolution of the pre-Athabasca basement within the Wollaston–Mudjatik Transition Zone, Saskatchewan

The Paleoproterozoic tectono-metamorphic evolution of the pre-Athabasca basement (∼1.7 Ga) within the Wollaston–Mudjatik Transition Zone (WMTZ) (Saskatchewan, Canada) has been characterized using both exposed basement and drill cores from the Wolly–McClean exploration drilling project. The finite ductile strain pattern of the WMTZ results from the superposition of two tectono-metamorphic events M1–D1 and M2–D2. M1–D1 is associated with the development of a gently dipping foliation striking N90°–N100° and a southward decrease in peak pressures from up to 10 kbar (1 kbar = 100 MPa) in the Cochrane River area down to 6 kbar in the Wolly–McClean exploration drilling project. The M2–D2 event is responsible for the main northeasterly trend of the WMTZ that developed in a sinistral transpressional tectonic regime during the final oblique collision of the Trans-Hudson Orogeny. Thermobarometric estimations on M2–D2 assemblages show that the studied area was reequilibrated at about 4–5 kbar and 750–825 °C. The basement has thus been affected by a differential isothermal decompression event between D1 and D2 that allowed the juxtaposition of the deepest northeastern domains and the Wolly–McClean exploration drilling project, at the same structural level. These results suggest that the basement exposed to the northeast of the Athabasca Basin is not an analog of the basement located beneath the eastern Athabasca Basin where uranium-enriched granitic pegmatites and granites are known. We also suggest that uranium-enriched melts produced during the early M1–D1 stage of partial melting in the deep crust were transferred to the midcrust, owing to D2 shear zones, where they have differentiated to produce uranium-bearing pegmatites.

Static, Dynamic, and Fatigue Finite Element Analysis of Dental Implants with Different Thread Designs.

In this study, we aimed to design an ideal dental implant with respect to stress and strain patterns on the surrounding cortical and cancellous bones. The effects of static loading on dental implants have been previously assessed, but the impact of dynamic loading and fatigue analysis has not been well studied. We evaluated static, dynamic, and fatigue behaviors of dental implants to fully understand the mechanism and acquire a more realistic perspective of the process. In this study, we analyzed three models of a tapered dental implant: model 1 had V-shaped threads; model 2 had microthreads in the upper area and V-shaped threads in the rest of the body; model 3 had reverse buttress threads in all areas. Two types of loading conditions were simulated in a finite element model, and stress and strain patterns in the surrounding bone were evaluated. Minimum von Mises stresses of cortical bone were recorded in model 2. The values for a 100-N load with a 25° angle were 44.5 and 47.4 MPa for static and dynamic analyses, respectively. Considering the obtained stress and strain patterns, we conclude that a tapered implant with microthreads in the upper area and V-shaped threads in the rest of the body is preferred for best uniform stress distribution in both static and dynamic analyses.

Tectonic evolution of Les Saintes archipelago (Guadeloupe, French West Indies): relation with the Lesser Antilles arc system

Abstract In this paper, we provide the first structural map of Les Saintes archipelago (Guadeloupe, Lesser Antilles). The finite strain pattern displays four families of fault systems characterized by their statistical structural orientations: N000-N020, N050-N070, N090-N110 and N130-N140 trending fault systems. Our onshore results thus underline a fault network much more complex than the one depicted by the previous offshore geophysical investigations around Les Saintes archipelago, which show only N120-N150 trending system. According to the available K-Ar dating of the volcanic rocks and the relative chronology of the faults defined in the field, we determine the deformation history in Les Saintes islands since the last 3 Ma. The four highlighted trending fault systems are already active since the Pliocene and are consistent with the present-day extensional tectonics in the Guadeloupe archipelago compatible with the reactivation of inherited structures at the active arc scale. We interpret the tectonic evolution of Les Saintes islands as the result of interplay between subduction of aseismic ridges (Tiburon and Barracuda ridges) and oblique convergence. Furthermore, we recognized an exhumed geothermal paleo-system in Terre-de-Haut island which is a good analogue of the present-day active Bouillante geothermal system. Its duration is estimated at 400 k.y. during the Pliocene.

Stress and strain distribution in demineralized enamel: A micro-CT based finite element study.

Physiological oral mechanical forces may play a role on the progression of enamel carious lesions to cavitation. Thus, the aim of this study was to describe, by 3D finite element analysis, stress, and strain patterns in sound and carious enamel after a simulated occlusal load. Micro-CT based models were created and meshed with tetrahedral elements (based on an extracted third molar), namely: a sound (ST) and a carious tooth (CT). For the CT, enamel material properties were assigned according to the micro-CT gray values. Below the threshold corresponding to the enamel lesion (2.5 g/cm(3) ) lower and isotropic elastic modulus was assigned (E = 18 GPa against E1 = 80 GPa, E2 = E3 = 20 GPa for sound enamel). Both models were imported into a FE solver where boundary conditions were assigned and a pressure load (500 MPa) was applied at the occlusal surface. A linear static analysis was performed, considering anisotropy in sound enamel. ST showed a more efficient transfer of maximum principal stress from enamel to the dentin layer, while for the CT, enamel layer was subjected to higher and concentrated loads. Maximum principal strain distributions were seen at the carious enamel surface, especially at the central fossa, correlating to the enamel cavity seen at the original micro-CT model. It is possible to conclude that demineralized enamel compromises appropriate stress transfer from enamel to dentin, contributing to the odds of fracture and cavitation. Enamel fracture over a dentin lesion may happen as one of the normal pathways to caries progression and may act as a confounding factor during clinical diagnostic decisions.

Strain partitioning along the anatectic front in the Variscan Montagne Noire massif (southern French Massif Central)

We decipher late-orogenic crustal flow characterized by feedback relations between partial melting and deformation in the Variscan Montagne Noire gneiss dome. The dome shape and finite strain pattern of the Montagne Noire Axial Zone (MNAZ) result from the superimposition of three deformations (D1, D2 and D3). The early flat-lying S1 foliation is folded by D2 upright ENE-WSW folds and transposed in the central and southern part of the MNAZ into steep D2 high-strain zones consistent with D2 NW-SE horizontal shortening, in bulk contractional coaxial deformation regime that progressively evolved to noncoaxial dextral transpression. The D2 event occurred under metamorphic conditions that culminated at 0.65 ± 0.05 GPa and 720 ± 20°C. Along the anatectic front S1 and S2 foliations are transposed into a flat-lying S3 foliation with top-to-NE and top-to-SW shearing in the NE and SW dome terminations, respectively. These structures define a D3 transition zone related to vertical shortening during coaxial thinning with a preferential NE-SW to E-W directed stretching. Depending on structural level, the metamorphic conditions associated with D3 deformation range from partial melting conditions in the dome core to subsolidus conditions above the D3 transition zone. We suggest that D2 and D3 deformation events were active at the same time and resulted from strain partitioning on both sides of the anatectic front that may correspond to a major rheological boundary within the crust.

Sequential Monte-Carlo sampling based on a committee of artificial neural networks for posterior state estimation and residual lifetime prediction

The application of Bayesian methods to the problem of fatigue crack growth prediction has been growing in recent years. In particular, sequential Monte-Carlo sampling is often presented as an efficient model-based technique to filter the sequential measures of the damage evolution provided as an input to the algorithm. However, a lot of measures are required to reliably identify the system state condition and the underlying model parameters. Many studies rely on the availability of a relatively dense sequence of crack length measures during damage evolution, made in most cases impractical by the consequent maintenance costs. Thus, real-time damage diagnosis is a requirement to enable prognostic health management.This work focuses on the application of sequential Monte-Carlo sampling to estimate the probabilistic residual life of a structural component subjected to fatigue crack propagation, while real-time estimation of crack length is provided through a committee of artificial neural networks, trained with finite element simulated strain patterns. Multiple crack length observations are available at each discrete time and are provided as the input to the prognostic system, based on a sequential importance resampling algorithm. Each time a new set of measures is available, the algorithm evaluates the posterior distribution of the augmented state vector, including the crack length and a material parameter governing damage evolution. This filtered information is used to numerically update the probability density functions of the residual life of the component. The methodology is applied first to a simulated crack and then to a metallic stiffened panel specimen subject to fatigue crack growth.

Ductile deformation and rheology of sub-continental mantle in a hot collisional orogeny: Example from the Bohemian Massif

Fabric patterns of strongly serpentinized peridotite were determined using eigenvector analysis and eigenvalue classification of lattice preferred orientation of olivine and orthopyroxene. This approach has been applied to a rootless fold-shaped body of mylonitized spinel to garnet peridotite surrounded by fine-grained and partially retrogressed ky–kfs granulite. The EBSD data show either axial [010] or [100](0kl) pattern, both characteristic for ‘dry’ slip systems. The former pattern occurs predominantly along the inner margin and southern limb while the latter is mainly developed in the hinge of the fold shaped body. Foliations and lineations deciphered from the LPO data suggest that the [100](0kl) pattern reflects constrictional deformation (prolate strain ellipsoid) in the hinge of the peridotite fold while the axial [010] pattern reflects pure flattening (oblate strain ellipsoid) inherited from the period of emplacement of the peridotite sheet in the crust. Similarity in finite strain pattern of peridotite and surrounding granulites indicates their common thermal and mechanical evolution during folding. The petrology and structural data result in a model of burial of peridotite below thickened crustal root, its exhumation and folding. The burial stage is associated with prograde metamorphism resulting in a coarse-grained microstructure and development of spinel and garnet zones. The emplacement of peridotite into lower crustal granulites occurred along a shear zone associated with grain size reduction in both peridotite and granulite and rapid cooling of mylonitized peridotite to the ambient temperatures of lower crust. Further ascent to mid-crustal levels occurred within the vertical granulite channel. Final fold shape of the peridotite developed during subsequent indentation of the weak vertically anisotropic crust by the adjacent continental promontory. The degree of mechanical coupling between folded peridotite and granulite in mid-crustal levels is estimated using comparison of studied microstructures with experimental data.

Construction of Shape Features for the Representation of Full-Field Displacement/Strain Data

The achievement of high levels of confidence in finite element models involves their validation using measured responses such as static strains or vibration mode shapes. A huge amount of data with a high level of information redundancy is usually obtained in both the detailed finite element prediction and the full-field measurements so that achieving a meaningful validation becomes a challenging problem. In order to extract useful shape features from such data, image processing and pattern recognition techniques may be used. One of the most commonly adopted shape feature extraction procedures is the Fourier transform in which the original data may be expressed as a set of coefficients (coordinates) of the decomposition kernels (bases) in the feature space. Localised effects can be detected by the wavelet transform. The acquired shape features are succinct and therefore simplify the model validation, based on the full-field data, allowing it to be achieved in a more effective and efficient way. In this paper, full-field finite element strain patterns of a plate with a centred circular hole are considered. A special set of orthonormal shape decomposition kernels based on the circular Zernike polynomials are constructed by the Gram-Schmidt orthonormalization process. It is found that the strain patterns can suitably be represented by only a very small number of shape features from the derived kernels.

The influence of rock heterogeneity on the scaling properties of simulated and natural stylolites

Stylolites are among the most prominent deformation patterns in sedimentary rocks that document localized pressure solution. Recent studies revealed that stylolite roughness is characterized by two distinct scaling regimes. The main goal of the present study is to decipher whether this complex scaling behavior of stylolites is caused by the composition of the host-rock, i.e. heterogeneities in the material, or is governed by inherent processes on respective scales, namely the transition from a surface energy to an elastic energy dominated regime, as theoretically predicted. For this purpose we have developed a discrete numerical technique, based on a lattice spring model, to simulate the competition between stress, strain, and dissolution during stylolite roughening. We varied systematically the quenched noise, initially present in the material, which controls the roughening. We also changed the size, amount, and dissolution rate of the heterogeneities introduced in our model and evaluated the influence on the scaling exponents. Our findings demonstrate that the roughness and growth exponents are independent of the exact nature of the heterogeneities. We discovered two coinciding crossover phenomena in space and time that separate length and time scales for which the roughening process is either balanced by surface or elastic energies. Our observations are consistent with analytical predictions and with investigations quantifying the scaling laws in the morphology of natural stylolites. The findings presented here can further be used to refine volume loss (compaction) estimates from the finite strain pattern of stylolites.

Cretaceous collision and indentation in the West Carpathians: View based on structural analysis and numerical modeling

A model of indentation of a rigid promontory into weak metasedimentary rocks during Cretaceous convergence is suggested for tectonic evolution of southern part of West Carpathians. An early arcuate cleavage fan has developed in front of northward moving southern rigid basement block. The interaction of the moving indenter with western stationary basement promontory is responsible for development of the boundary‐parallel shear zone along which the main southern indenter is shifted to the east. This results in development of a new steep transpressional cleavage overprinting the early fabric. Eastward displacement of the southern indenter causes the development of a thrust zone parallel to the margin of the eastern stationary promontory. A proposed numerical model of the deformation of a thin viscous sheet in front of oval rigid indenter reliably simulates the development of the observed deformation pattern. Modeled discrete partitioning between the western promontory and the indenting block fully agrees with the observed secondary cleavage associated with the transpressional shear zone. Our numerical model interconnects this complex kinematic frame with finite strain pattern, which was to date possible only for simple boundary conditions. In addition, the model explains the polyphase cleavage patterns in terms of complex shapes of promontories and changes in movements of indenting blocks.

Finite strain pattern in Andriamena unit (north-central Madagascar): evidence for late Neoproterozoic–Cambrian thrusting during continental convergence

This paper deals with the late Neoproterozoic–Cambrian tectonic evolution of a part of north-central Madagascar, which is characterized by the occurrence of a mafic-ultramafic sequence (the Andriamena unit) overlying a gneissic-granitic basement. The finite strain pattern has been determined by carrying out a SPOT satellite image analysis, structural mapping of specific areas and kinematic analyses of shear zones. Structural investigations reveal the presence of two superposed finite strain patterns, D1 and D2. The D1 event is related to the emplacement of the Andriamena unit on the top of the gneissic-granitic basement. The western contact between these units is a major mylonitic zone characterized by a non-coaxial strain regime consistent with a top-to-east displacement. We suggest that the Andriamena unit originated as a lower crustal fragment of a middle Neoproterozoic continental magmatic arc related to the closure of the Mozambique Ocean. This fragment was thrusted onto the gneissic-granitic basement after 630 Ma, i.e. the age of emplacement of characteristic stratoid granites found only in the lower unit. The D2 event is related to east-west horizontal shortening mainly accommodated by F2 upright folds. In-situ electron microprobe dating of monazites from the Andriamena unit constrains the age of the D1 and D2 events between 530 and 500 Ma under amphibolite to granulite-facies conditions (5–7 kbar, 650–700 °C). The eastward thrust emplacement of the Andriamena unit (D1) followed by the horizontal shortening (D2) are ascribed to the same Cambrian tectonic regime (i.e. east-west convergence). Such D1–D2 bulk strain pattern has been recognized throughout Madagascar and at various structural levels of the crust: in the lower crust in Southern Madagascar and in the uppermost crustal level in the SQC unit (central Madagascar). The D1–D2 event is interpreted to result from the continental convergence of the Australia–Antarctica block and the Madagascar, India, Sri Lanka block during the final amalgamation of Gondwana.