A structural and metamorphic study of the southern Menderes Massif (Western Turkey)

P-T conditions, paragenetic studies and the relation between mineral growth, deformation and - when possible- isograd minerals have been used to describe the type of metamorphism involved within lower units of the southern Menderes Massif of the Anatolide Belt in western Turkey. The study areas mainly consist of Proterozoic orthogneiss and surrounding schists of presumed Paleozoic age. Both units are seen as nappes in the southern study area, the Çine and the Selimiye nappe, on the whole corresponding to Proterozoic orthogneiss and surrounding schists, respectively. The Çine and Selimiye nappes are part of a complex geological structure within the core series of the Menderes Massif. Their emplacement under lower greenschist facies conditions, would result from closure of the northern Neo-Thethys branch during the Eocene. These two nappes are separated by a major tectonic structure, the Selimiye shear zone, which records top-to-the-S shearing under greenschist facies conditions. Amphibolite to upper amphibolite facies metamorphism is widely developed within the metasedimentary rocks of the Çine nappe whereas no metamorphism exceeding lower amphibolite facies has been observed in the Selimiye nappe. In the southern margin of the Çine Massif, around Selimiye and Millas villages, detailed sampling has been undertaken in order to map mineral isograds within the Selimiye nappe and to specify P-T conditions in this area. The data collected in this area reveals a global prograde normal erosion field gradient from south to north and toward the orthogneiss. The mineralogical parageneses and P-T estimates are correlated with Barrovian-type metamorphism. A jump of P-T conditions across the Selimiye shear zone has been identified and estimated c. 2 kbar and 100 °C which evidences the presence of amphibolite facies metasedimentary rocks near the orthogneiss. Metasedimentary rocks from the overlying Selimiye nappe have maximum P-T conditions of c. 4-5 kbar and c. 525 °C near the base of the nappe. Metasedimentary rocks from the Çine nappe underneath the Selimiye shear zone record maximum P-T conditions of about 7 kbar and >550 °C. Kinematic indicators in both nappes consistently show a top-S shear sense. Metamorphic grade in the Selimiye nappe decreases structurally upwards as indicated by mineral isograds defining the garnet-chlorite zone at the base, the chloritoid-biotite zone and the biotite-chlorite zone at the top of the nappe. The mineral isograds in the Selimiye nappe run parallel to the regional SR foliation. 40Ar/39Ar mica ages indicate an Eocene age of metamorphism in the Selimiye nappe and underneath the Çine nappe in this area. Metasedimentary rocks of the Çine nappe 20-30 km north of the Selimiye shear zone record maximum P-T conditions of 8-11 kbar and 600-650 °C. Kinematic indicators show mainly top-N shear sense associated with prograde amphibolite facies metamorphism. An age of about 550 Ma could be indicated for amphibolite facies metamorphism and associated top-N shear in the orthogneiss and metasedimentary rocks of the Çine nappe. However, there is no evidence for polymetamorphism in the 6 metasedimentary rocks of the Çine nappe, making tectonic interpretations about late Neoproterozoic to Cambrian and Tertiary metamorphic events speculative. In the western margin of the Çine Massif metamorphic mineral parageneses and pressure– temperature conditions lead to similar conclusion regarding the erosion field gradient, prograde normal toward the orthogneiss. The contact between orthogneiss and surrounding metasedimentary rocks is mylonitic and syn-metamorphism. P-T estimates are those already observed within the Selimiye nappe and correlated with lower amphibolite facies parageneses. Finally additional data in the eastern part and a general paragenetic study within the Menderes Massif lower units, the Çine and the Selimiye nappes, strongly suggest a single Barrovian-type metamorphism predating Eocene emplacement of the high pressure–low temperature Lycean and Cycladic blueschist nappes. Metamorphic mineral parageneses and pressure–temperature conditions do not support the recently proposed model of high pressure–low temperature metamorphic overprinting, which implies burial of the lower units of the Menderes Massif up to depth of 30 km, as a result of closure of the Neo-Tethys. According to the geochronological problem outlined during this thesis, there are two possible schemes: either Barrovian-type metamorphism is Proterozoic in age and part of the sediments from Selimiye nappe (lower amphibolite facies) has to be proterozoic of age too, or Barrovian-type metamorphism in Eocene of age. In the first case the structure observed now in the core series would correspond to simple exhumation of Proterozoic basement. In the latter case a possible correlation with closure of Neo-Tethys (sensu stricto, southern branch) is envisaged.

Structural and strain analysis in the Late Paleozoic coastal accretionary wedge of central Chile

Abstract In this study structural and finite strain data are used to explore the tectonic evolution and the exhumation history of the Chilean accretionary wedge. The Chilean accretionary wedge is part of a Late Paleozoic subduction complex that developed during subduction of the Pacific plate underneath South America. The wedge is commonly subdivided into a structurally lower Western Series and an upper Eastern Series. This study shows the progressive development of structures and finite strain from the least deformed rocks in the eastern part of the Eastern Series of the accretionary wedge to higher grade schist of the Western Series at the Pacific coast. Furthermore, this study reports finite-strain data to quantify the contribution of vertical ductile shortening to exhumation. Vertical ductile shortening is, together with erosion and normal faulting, a process that can aid the exhumation of high-pressure rocks. In the east, structures are characterized by upright chevron folds of sedimentary layering which are associated with a penetrative axial-plane foliation, S1. As the F1 folds became slightly overturned to the west, S1 was folded about recumbent open F2 folds and an S2 axial-plane foliation developed. Near the contact between the Western and Eastern Series S2 represents a prominent subhorizontal transposition foliation. Towards the structural deepest units in the west the transposition foliation became progressively flat lying. Finite-strain data as obtained by Rf/Phi and PDS analysis in metagreywacke and X-ray texture goniometry in phyllosilicate-rich rocks show a smooth and gradual increase in strain magnitude from east to west. There are no evidences for normal faulting or significant structural breaks across the contact of Eastern and Western Series. The progressive structural and strain evolution between both series can be interpreted to reflect a continuous change in the mode of accretion in the subduction wedge. Before ~320-290 Ma the rocks of the Eastern Series were frontally accreted to the Andean margin. Frontal accretion caused horizontal shortening and upright folds and axial-plane foliations developed. At ~320-290 Ma the mode of accretion changed and the rocks of the Western Series were underplated below the Andean margin. This basal accretion caused a major change in the flow field within the wedge and gave rise to vertical shortening and the development of the penetrative subhorizontal transposition foliation. To estimate the amount that vertical ductile shortening contributed to the exhumation of both units finite strain is measured. The tensor average of absolute finite strain yield Sx=1.24, Sy=0.82 and Sz=0.57 implying an average vertical shortening of ca. 43%, which was compensated by volume loss. The finite strain data of the PDS measurements allow to calculate an average volume loss of 41%. A mass balance approximates that most of the solved material stays in the wedge and is precipitated in quartz veins. The average of relative finite strain is Sx=1.65, Sy=0.89 and Sz=0.59 indicating greater vertical shortening in the structurally deeper units. A simple model which integrates velocity gradients along a vertical flow path with a steady-state wedge is used to estimate the contribution of deformation to ductile thinning of the overburden during exhumation. The results show that vertical ductile shortening contributed 15-20% to exhumation. As no large-scale normal faults have been mapped the remaining 80-85% of exhumation must be due to erosion.

Mean curvature flow in SE (2) and applications to visual perception

Our goal in this thesis is to provide a result of existence of the degenerate non-linear, non-divergence PDE which describes the mean curvature flow in the Lie group SE(2) equipped with a sub-Riemannian metric. The research is motivated by problems of visual completion and models of the visual cortex.

A 300 million year-long history. The metamorphic evolution of the Northern Apennine Variscan basement

The Variscan basement of Northern Apennines (Northern Italy) is a polymetamorphic portion of continental crust. This thesis investigated the metamorphic history of this basement occurring in the Cerreto Pass, in the Pontremoli well, and in the Pisani Mountains. The study comprised fieldwork, petrography and microstructural analysis, determination of the bulk rock and mineral composition, thermodynamic modelling, conventional geothermobarometry, monazite chemical dating and Ar/Ar dating of muscovite. The reconstructed metamorphic evolution of the selected samples allowed to define a long-lasting metamorphic history straddling the Variscan and Alpine orogenesis. Some general petrological issues generally found in low- to medium-grade metapelites were also tackled: (i) With middle-grade micaschist it is possible to reconstruct a complete P-T-D path by combining microstructural analysis and thermodynamic modelling. Prekinematic white mica may preserve Mg-rich cores related to the pre-peak stage. Mn-poor garnet rim records the peak metamorphism. Na-rich mylonitic white mica, the XFe of chlorite and the late paragenesis may constrain the retrograde stage. (ii) Metapelites may contain coronitic microstructures of apatite + Th-silicate, allanite and epidote around unstable monazite grains. Chemistry and microstructure of Th-rich monazite relics surrounded by this coronitic microstructure may suggest that monazite mineral was inherited and underwent partial dissolution and fluid-aided replacement by REE-accessory minerals at 500-600°C and 5-7 kbar. (iii) Fish-shaped white mica is not always a (prekinematic) mica-fish. Observed at high-magnification BSE images it may consist of several white mica formed during a mylonitic stage. Hence, the asymmetric foliation boudin is a suitable microstructure to obtain geochronological information about the shearing stage. (iv) Thermodynamic modelling of a hematite-rich metasedimentary rock fails to reproduce the observed mineral compositions when the bulk Fe2O3 is neglected or determined through titration. The mismatch between observed and computed mineral compositions and assemblage is resolved by tuning the effective ferric iron content by P-XFe2O3 diagrams.

Decompression during Late Proterozoic Al2SiO5 Triple-Point Metamorphism at Cerro Colorado, New Mexico

An outstanding problem in understanding the late Proterozoic tectonic assembly of the southwest is identifying the tectonic setting associated with regional metamorphism at 1.4 Ga. Both isobaric heating and cooling, and counter-clockwise looping PT paths are proposed for this time. We present a study of the Proterozoic metamorphic and deformation history of the Cerro Colorado area, southern Tusas Mountains, New Mexico, which shows that the metamorphism in this area records near-isothermal decompression from 6 to 4 kbar at ca. 1.4 Ga. We do not see evidence for isobaric heating at this time. Decompression from peak pressures is recorded by the reaction Ms + Grt = St + Bt, with a negative slope in PT space; the reaction Ms + Grt = Sil + Bt, which is nearly horizontal in PT space; and partial to total pseudomorphing of kyanite by sillimanite during the main phase of deformation. The clearest reaction texture indicating decompression near peak metamorphic temperature is the replacement of garnet by clots of sillimanite, which are surrounded by halos of biotite. The sillimanite clots, most without relict garnet in the cores and with highly variable aspect ratios, are aligned. They define a lineation that formed with the dominant foliation. An inverted metamorphic gradient is locally defined by sillimanite-garnet schists (625 degrees C) structurally above staurolite-garnet schists (550 degrees C) and implies ductile thrusting during the main phase of deformation. The exhumation that led to the recorded decompression was likely in response to crustal thickening due to ductile thrusting and subsequent denudation.

Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.

The effect of projections on dimension in the Heisenberg group

We prove analogs of classical almost sure dimension theorems for Euclidean projection mappings in the first Heisenberg group, equipped with a sub-Riemannian metric.

Seismic anisotropy in the Morcles nappe shear zone: Implications for seismic imaging of crustal scale shear zones

Microstructures and textures of calcite mylonites from the Morcles nappe large-scale shear zone in southwestern Switzerland develop principally as a function of 1) extrinsic physical parameters including temperature, stress, strain, strain rate and 2) intrinsic parameters, such as mineral composition. We collected rock samples at a single location from this shear zone, on which laboratory ultrasonic velocities, texture and microstructures were investigated and quantified. The samples had different concentration of secondary mineral phases (< 5 up to 40 vol.%). Measured seismic P wave anisotropy ranges from 6.5% for polyphase mylonites (~ 40 vol.%) to 18.4% in mylonites with < 5 vol.% secondary phases. Texture strength of calcite is the main factor governing the seismic P wave anisotropy. Measured S wave splitting is generally highest in the foliation plane, but its origin is more difficult to explain solely by calcite texture. Additional texture measurements were made on calcite mylonites with low concentration of secondary phases (≤ 10 vol.%) along the metamorphic gradient of the shear zone (15 km distance). A systematic increase in texture strength is observed moving from the frontal part of the shear zone (anchimetamorphism; 280 °C) to the higher temperature, basal part (greenschist facies; 350–400 °C). Calculated P wave velocities become increasingly anisotropic towards the high-strain part of the nappe, from an average of 5.8% in the frontal part to 13.2% in the root of the basal part. Secondary phases raise an additional complexity, and may act either to increase or decrease seismic anisotropy of shear zone mylonites. In light of our findings we reinterpret the origin of some seismically reflective layers in the Grône–Zweisimmen line in southwestern Switzerland (PNR20 Swiss National Research Program). We hypothesize that reflections originate in part from the lateral variation in textural and microstructural arrangement of calcite mylonites in shear zones.

Dating polygenetic metamorphic assemblages along a transect across the Western Alps

Multichronometric analyses were performed on samples from a transect in the French-Italian Western Alps crossing nappes derived from the Briançonnais terrane and the Piemonte-Liguria Ocean, in an endeavour to constrain the high-pressure (HP) metamorphism and the retrogression history. 12 samples of white mica were analysed by 39Ar-40Ar stepwise heating, complemented by 2 samples from the Monte Rosa 100 km to the NE and also attributed to the Briançonnais terrane. One Sm-Nd and three Lu-Hf garnet ages from eclogites were also obtained. White mica ages decrease from ca. 300 Ma in the westernmost samples (Zone Houillère), reaching ca. 300 °C during Alpine metamorphism, to < 48 Ma in the internal units to the East, which reached ca. 500 °C during Alpine orogeny. The conventional “thermochronological” interpretation postulates Cretaceous Eo-Alpine HP metamorphism and younger “cooling ages” in the higher-temperature samples. However, Eocene Lu-Hf and Sm-Nd ages from the same samples cannot be interpreted as post-metamorphic cooling ages, which makes a Cretaceous eclogitization untenable. The age date from this transect require instead to replace conventional “thermochronology” by an approach combining age dating with detailed geochemical, petrological and microstructural investigations. Petrology reveals important mineralogical differences along the transect. Samples from the Zone Houillère mostly contain detrital mica. White mica with Si > 6.45 atoms per formula unit becomes more abundant eastward. Across the whole traverse, HP phengitic mica forms the D1 foliation. Syn-D2 mica is Si-poorer and associated with nappe stacking, exhumation, and hydrous retrogression under greenschist facies conditions. D1 phengite is very often corroded, overgrown or intergrown by syn-D2 muscovite. Most importantly, syn-D2 recrystallization is not limited to S2 schistosity domains; microchemical fingerprinting shows that it also can form pseudomorphs after crystals that could be mistaken to have formed during D1 based on microstructural arguments alone. Thereby the Cl concentration in white mica is a useful discriminator, since D2 retrogression was associated with a less saline fluid than eclogitization. Once the petrological stage is set, geochronology is straightforward. All samples contain mixtures of detrital, syn-D1 and syn-D2 mica, and retrogression phases (D3) in greatly varying proportions according to local pressure-temperature-fluid activity-deformation conditions. The correlation of age vs. Cl/K clearly identifies 47 ± 1 Ma as the age of formation of syn-D1 mica along the entire transect, including the Monte Rosa nappe samples. The inferred age of the greenschist-facies low-Si syn-D2 mica generation ranges within 39-43 Ma, with local variations. Coexistence of D1 and D2 ages, and the constancy of non-reset D1 ages along the entire transect, are strong evidence that the D1 white mica ages are very close to formation ages. Volume diffusion of Ar in white mica (activation energy E = 250 kJ/mol; pressure-adjusted diffusion coefficient D’0 < 0.03 cm2 s-1) has a subordinate effect on mineral ages compared to both prograde and retrograde recrystallization in most samples. Eocene Lu-Hf and Sm-Nd garnet ages are prograde and predate the HP peak.

Remarks on Lipschitz domains in Carnot groups

In this Note we present the basic features of the theory of Lipschitz maps within Carnot groups as it is developed in [8], and we prove that intrinsic Lipschitz domains in Carnot groups are uniform domains.

Age of cleft monazites in the eastern Tauern Window: constraints on crystallization conditions of hydrothermal monazite

Monazite-bearing Alpine clefts located in the Sonnblick region of the eastern Tauern Window, Austria, are oriented perpendicular to the foliation and lineation. Ion probe (SIMS) Th–Pb and U–Pb dating of four cleft monazites yields crystallization ages of different growth domains and aggregate regions ranging from 18.99 ± 0.51 to 15.00 ± 0.51 Ma. The crystallization ages obtained are overlapping or slightly younger than zircon fission track ages but older than zircon (U–Th)/He cooling ages from the same area. This constrains cleft monazite crystallization in this area to *300–200 �C. LA-ICP-MS data of dated hydrothermal monazites indicate that in graphite-bearing, reduced host lithologies, cleft monazite is poor in As and has higher La/Yb values and U concentrations, whereas in oxidised host rocks opposite trends are observed. Monazites show negative Eu anomalies and variable La/Yb values ranging from 520 to 6050. The positive correlation between Ca and Sr concentration indicates dissolution of plagioclase or carbonates as the source of these elements. The data show that early exhumation and cleft formation in the Tauern is related to metamorphic dome formation caused by the collision of the Adriatic with the European plate and that monazite crystallization in the clefts occurred later. Our data also demonstrate that hydrothermal monazite ages offer great potential in helping to constrain the chronology of exhumation in collisional orogens.

Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Steiner’s formula in the Heisenberg group

Steiner’s tube formula states that the volume of an ϵ-neighborhood of a smooth regular domain in Rn is a polynomial of degree n in the variable ϵ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ϵ-neighborhood with respect to the Heisenberg metric is an analytic function of ϵ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms.

Mineralogy and structural specification of ODP Leg 125 peridotite samples

Abundant serpentinite seamounts are found along the outer high of the Mariana forearc at the top of the inner slope of the trench. One of them, Conical Seamount, was drilled at Sites 778, 779, and 780 during Leg 125. The rocks recovered at Holes 779A and 780C, respectively, on the flanks and at the summit of the seamount, include moderately serpentinized depleted harzburgites and some dunites. These rocks exhibit evidence of resorption of the orthopyroxene, when present, and the local presence of very calcic-rich diopside in veins oblique to the main high-temperature foliation of the rock. The peridotites, initially well-foliated with locally poikiloblastic textures, show overprints of a two-stage deformation history: (1) a high-temperature (>1000°C), low-stress (0.02 GPa), homogeneous deformation that has led to the present Porphyroclastic textures displayed by the rocks and (2) heterogeneous ductile shearing at a much higher stress (0.05 GPa). This heterogeneous shearing probably describes a single tectonic event because it began at high temperatures, producing dynamic recrystallization of olivine in the shear zone, and ended at low temperatures in the stability field of chlorite and serpentine. In a few samples, olivine shows evidence of quasi-hydrostatic recrystallization at a very high temperature. Here, we propose that this recrystallization was related to fluid/magma percolation, a process that can also account for the resorption of the orthopyroxene and for the late crystallization of diopside veins in the rock. The impregnation by fluid or magma, development of the main high-temperature, low-stress deformation, and subsequent migration recrystallization of olivine probably occurred in a mantle fragment involved in the arc formation. In addition, this mantle has preserved structures that may have formed earlier in the oceanic lithosphere upon which the arc formed. Heterogeneous ductile shear zones in the peridotites may have developed during uplift. The "cold" deformation may have taken place during diapiric rise of hot mantle that underwent subsequent serpentinization or gliding along normal faults associated with the extension of the eastern margin of the forearc.