Geometric quantization and foliation reduction

A standard question in the study of geometric quantization is whether symplectic reduction interacts nicely with the quantized theory, and in particular whether “quantization commutes with reduction.” Guillemin and Sternberg first proposed this question, and answered it in the affirmative for the case of a free action of a compact Lie group on a compact Kähler manifold. Subsequent work has focused mainly on extending their proof to non-free actions and non-Kähler manifolds. For realistic physical examples, however, it is desirable to have a proof which also applies to non-compact symplectic manifolds.

In this thesis we give a proof of the quantization-reduction problem for general symplectic manifolds. This is accomplished by working in a particular wavefunction representation, associated with a polarization that is in some sense compatible with reduction. While the polarized sections described by Guillemin and Sternberg are nonzero on a dense subset of the Kähler manifold, the ones considered here are distributional, having support only on regions of the phase space associated with certain quantized, or “admissible”, values of momentum.

We first propose a reduction procedure for the prequantum geometric structures that “covers” symplectic reduction, and demonstrate how both symplectic and prequantum reduction can be viewed as examples of foliation reduction. Consistency of prequantum reduction imposes the above-mentioned admissibility conditions on the quantized momenta, which can be seen as analogues of the Bohr-Wilson-Sommerfeld conditions for completely integrable systems.

We then describe our reduction-compatible polarization, and demonstrate a one-to-one correspondence between polarized sections on the unreduced and reduced spaces.

Finally, we describe a factorization of the reduced prequantum bundle, suggested by the structure of the underlying reduced symplectic manifold. This in turn induces a factorization of the space of polarized sections that agrees with its usual decomposition by irreducible representations, and so proves that quantization and reduction do indeed commute in this context.

A significant omission from the proof is the construction of an inner product on the space of polarized sections, and a discussion of its behavior under reduction. In the concluding chapter of the thesis, we suggest some ideas for future work in this direction.

Desingularization of singular Riemannian foliation

Let F be a singular Riemannian foliation on a compact Riemannian manifold M. By successive blow-ups along the strata of F we construct a regular Riemannian foliation (F) over cap on a compact Riemannian manifold (M) over cap and a desingularization map (rho) over cap : (M) over cap -> M that projects leaves of (F) over cap into leaves of F. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of F are compact, then, for each small epsilon > 0, we can find (M) over cap and (F) over cap so that the desingularization map induces an epsilon-isometry between M/F and (M) over cap/(F) over cap. This implies in particular that the space of leaves M/F is a Gromov-Hausdorff limit of a sequence of Riemannian orbifolds {((M) over cap (n)/(F) over cap (n))}.

Foliation boudinage

In this thesis foliation boudinage and related structures have been studied based on field observations and numerical modeling. Foliation boudinage occurs in foliated rocks independent of lithology contrast. The developing structures are called ‘Foliation boudinage structures (FBSs)’ and show evidence for both ductile and brittle deformation. They are recognized in rocks by perturbations in monotonous foliation adjacent to a central discontinuity, mostly filled with vein material. Foliation boudinage structures have been studied in the Çine Massif in SW-Turkey and the Furka Pass-Urseren Zone in central Switzerland. Four common types have been distinguished in the field, named after vein geometries in their boudin necks in sections normal to the boudin axis: lozenge-, crescent-, X- and double crescent- type FBSs. Lozengetype FBSs are symmetric and characterized by lozenge-shaped veins in their boudin neck with two cusps facing opposite sides. A symmetrical pair of flanking folds occurs on the two sides of the vein. Crescent-type FBSs are asymmetric with a single smoothly curved vein in the boudin neck, with vein contacts facing to one side. X- and double crescent- type FBSs are asymmetric. The geometry of the neck veins resembles that of cuspate-lobate structures. The geometry of flanking structures is related to the shape of the veins. The veins are mostly filled with massive quartz in large single crystals, commonly associated with tourmaline, feldspar and biotite and in some cases with chlorite. The dominance of large facetted single quartz crystals and spherulitic chlorite in the veins suggest that the minerals grew into open fluidfilled space. FLAC experiments show that fracture propagation during ductile deformation strongly influences the geometry of developing veins. The cusps of the veins are better developed in the case of propagating fractures. The shape of the boudin neck veins in foliation boudinage depends on the initial orientation and shape of the fracture, the propagation behaviour of the fracture, the geometry of bulk flow, and the stage at which mineral filling takes place. A two dimensional discrete element model was used to study the progressive development of foliation boudinage structures and the behavior of visco-elastic material deformed under pure shear conditions. Discrete elements are defined by particles that are connected by visco-elastic springs. Springs can break. A number of simulations was Abstract vii performed to investigate the effect of material properties (Young’s modulus, viscosity and breaking strength) and anisotropy on the developing structures. The models show the development of boudinage in single layers, multilayers and in anisotropic materials with random mica distribution. During progressive deformation different types of fractures develop from mode I, mode II to the combination of both. Voids develop along extension fractures, at intersections of conjugate shear fractures and in small pull-apart structures along shear fractures. These patterns look similar to the natural examples. Fractures are more localized in the models where the elastic constants are low and the competence contrast is high between the layers. They propagate through layers where the constants are high and the competence contrast is relatively low. Flow localize around these fractures and voids. The patterns similar to symmetric boudinage structures and extensional neck veins (e.g. lozenge type) more commonly develop in the models with lower elastic constants and anisotropy. The patterns similar to asymmetric foliation boudinage structures (e.g. X-type) develop associated with shear fractures in the models where elastic constants and anisotropy of the materials are relatively high. In these models boudin neck veins form commonly at pull-aparts along the shear fractures and at the intersection of fractures.

Networking of shear zones at the brittle-to-viscous transition (Cap de Creus, NE Spain)

A crustal-scale shear zone network at the fossil brittle-to-viscous transition exposed at Cap de Creus, NE Spain evolved by coeval fracturing and viscous, mylonitic overprinting of an existing foliation. Initial fracturing led to mylonitic shearing as rock softened in ductilely deformed zones surrounding the fractures. Mylonitic shear zones widened by lateral branching of fractures from these shear zones and by synthetic rotation of the existing foliation between the fractures and shear zones. Shear zones lengthened by a combination of fracturing and mylonitic shearing in front of the shear zone tips. Shear zones interconnected along and across their shearing planes, separating rhomb-shaped lozenges of less deformed rock. Lozenges were subsequently incorporated into the mylonitic shear zones by widening in the manner described above. In this way, deformation became homogeneous on the scale of initial fracturing (metre- to decametre-scale). In contrast, the shear zone network represents localisation of strain on a decametre-length scale. The strength of the continental crust at the time of coeval fracturing and viscous shearing is inferred to have decreased with time and strain, as fracturing evolved to mylonitic shearing, and as the shear zones coalesced to form a through-going network subparallel to the shearing plane. Crustal strength must therefore be considered as strain- and scale-dependent.

Tectonometamorphic evolution of the Åreskutan Nappe-Caledonian history revealed by SIMS U–Pb zircon geochronology

Secondary ionization mass spectrometry (SIMS) U–Pb dating of zircons from the Åreskutan Nappe in the central part of the Seve Nappe Complex of western central Jämtland provides new constraints on the timing of granulite–amphibolite-facies metamorphism and tectonic stacking of the nappe during the Caledonian orogeny. Peak-temperature metamorphism in garnet migmatites is constrained to c. 442 ± 4 Ma, very similar to the ages of leucogranites at 442 ± 3 and 441 ± 4 Ma. Within a migmatitic amphibolite, felsic segregations crystallized at 436 ± 2 Ma. Pegmatites, cross-cutting the dominant Caledonian foliation in the Nappe, yield 428 ± 4 and 430 ± 3 Ma ages. The detrital zircon cores in the migmatites and leucogranites provide evidence of Late Palaeoproterozoic, Mesoproterozoic to Early Neoproterozoic source terranes for the metasedimentary rocks. The formation of the ductile and hot Seve migmatites, with their inverted metamorphism and thinning towards the hinterland, can be explained by an extrusion model in which the allochthon stayed ductile for a period of at least 10 million years during cooling from peak-temperature metamorphism early in the Silurian. In our model, Baltica–Laurentia collision occurred in the Late Ordovician–earliest Silurian, with emplacement of the nappes far on to the Baltoscandian platform during the Silurian and early Devonian, Scandian Orogeny lasting until c. 390 Ma.

Magnetic fabrics indicating Late Quaternary seismicity in the Himalayan foothills

The anisotropy of magnetic susceptibility (AMS) study was performed on soft sediment samples from a trenched fault zone across the Himalayan frontal thrust (HFT), western Himalaya. AMS orientation of K-min axes in the trench sediments is consistent with lateral shortening revealed by geometry of deformed regional structures and recent earthquakes. Well-defined vertical magnetic foliation parallel to the flexure cleavage in which a vertical magnetic lineation is developed, high anisotropy, and triaxial ellipsoids suggest large overprinting of earth-quake- related fabrics. The AMS data suggest a gradual variation from layer parallel shortening (LPS) at a distance from the fault trace to a simple shear fabric close to the fault trace. An abrupt change in the shortening direction (K-min) from NE-SW to E-W suggests a juxtaposition of pre-existing layer parallel shortening fabric, and bending-related flexure associated with an earthquake. Hence the orientation pattern of magnetic susceptibility axes helps in identifying co-seismic structures in Late Holocene surface sediments.

Embracing Integrability in Stellar and Planetary Dynamics

Hamiltonian systems in stellar and planetary dynamics are typically near integrable. For example, Solar System planets are almost in two-body orbits, and in simulations of the Galaxy, the orbits of stars seem regular. For such systems, sophisticated numerical methods can be developed through integrable approximations. Following this theme, we discuss three distinct problems. We start by considering numerical integration techniques for planetary systems. Perturbation methods (that utilize the integrability of the two-body motion) are preferred over conventional "blind" integration schemes. We introduce perturbation methods formulated with Cartesian variables. In our numerical comparisons, these are superior to their conventional counterparts, but, by definition, lack the energy-preserving properties of symplectic integrators. However, they are exceptionally well suited for relatively short-term integrations in which moderately high positional accuracy is required. The next exercise falls into the category of stability questions in solar systems. Traditionally, the interest has been on the orbital stability of planets, which have been quantified, e.g., by Liapunov exponents. We offer a complementary aspect by considering the protective effect that massive gas giants, like Jupiter, can offer to Earth-like planets inside the habitable zone of a planetary system. Our method produces a single quantity, called the escape rate, which characterizes the system of giant planets. We obtain some interesting results by computing escape rates for the Solar System. Galaxy modelling is our third and final topic. Because of the sheer number of stars (about 10^11 in Milky Way) galaxies are often modelled as smooth potentials hosting distributions of stars. Unfortunately, only a handful of suitable potentials are integrable (harmonic oscillator, isochrone and Stäckel potential). This severely limits the possibilities of finding an integrable approximation for an observed galaxy. A solution to this problem is torus construction; a method for numerically creating a foliation of invariant phase-space tori corresponding to a given target Hamiltonian. Canonically, the invariant tori are constructed by deforming the tori of some existing integrable toy Hamiltonian. Our contribution is to demonstrate how this can be accomplished by using a Stäckel toy Hamiltonian in ellipsoidal coordinates.

Evolução estrutural das zonas de cisalhamento dúcteis na porção centro-leste do domínio da Zona Transversal na Província Borborema

A área estudada está inserida no Domínio Transversal da Província Borborema. As unidades litoestratigráficas que compõem o embasamento paleoproterozócio (riaciano) são representadas por rochas ortoderivadas dos Complexos Salgadinho e Cabaceiras. Esses complexos foram individualizados de acordo com as suas diferenças composicionais, texturais e/ou geocronológicas. As rochas metassedimentares de idade paleoproterozóica (Orosiriano) foram interpretadas como constituintes do Complexo Sertânia. O magmatismo no estateriano é caracterizado por ortognaisses sienogranítcos da Suíte Carnoió-Caturité e por metanortositos do Complexo Metanortosítico Boqueirão. As unidades litoestratigráficas do Neoproterozóico são representadas por sucessões metassedimentares Criogenianas do Complexo Surubim e ortognaisses granodioríticos e sienograníticos do início do Ediacarano, denominados de Complexo Sumé e Ortognaisse Riacho de Santo Antônio, respectivamente. O magmatismo granítico do Ediacarano foi caracterizado pelo alojamento dos Plutons Inácio Pereira e Marinho. Os dados geocronológicos (U-Pb em zircão) obtidos indicam, no mínimo, o desenvolvimento de três eventos tectono-magmáticos. As idades de 2042 + 11Ma e 1996 + 13Ma obtidas nos ortoanfibolitos do Complexo Cabaceiras foram interpretadas como a idade de cristalização do protólito e metamorfismo, respectivamente. A idade de 1638 + 13Ma proveniente de hornblenda ortognaisse sienogranítico da Suíte Carnoió-Caturité foi interpretada como a idade de cristalização do protólito, marcando um evento magmático Estateriano de afinidade anorogênica. A idade de 550 + 3.1Ma encontrada em monzogranito porfirítico do Pluton Marinho é um registro do último evento magmático no final do Ediacarano, associado ao estágio tardio de desenvolvimento da Zona de Cisalhamento Coxixola. Os dados estruturais permitiram a individualização de três fases de deformação dúcteis, individualizadas como D1, D2 e D3. A fase D1 foi responsável pela geração de uma foliação S1, observada somente na charneira de dobras F2. O evento D2 é assinalado por uma tectônica contracional com transporte para NNW, observado a partir de bandas de cisalhamento assimétricas e dobras de arrasto em cortes paralelos a lineação de estiramento (L2x). Zonas de cisalhamento dúcteis de geometria e cinemática distintas desenvolveram-se durante a fase D3. As zonas de Cisalhamento Boa Vista, Carnoió e Congo estão orientadas na direção NE-SW e exibem cinemática sinistral em cortes paralelos à lineação de estiramento (L3x). As terminações meridionais dessas zonas de cisalhamento estão conectadas com a Zona de Cisalhamento Coxixola. Essa zona de cisalhamento, de direção WSW-ENE e cinemática destral, atravessa toda a área de estudo, com uma espessura média de rochas miloníticas de 300m. A Zona de Cisalhamento Inácio Pereira ocorre na porção leste da área de estudo, orientada na direção WNW-ESE. A análise geométrica e cinemática dessa zona de cisalhamento sugere uma evolução deformacional através de regime transpressivo oblíquo sinistral. O padrão anastomosado final resultante do desenvolvimento de todas as zonas de cisalhamento da área é relacionado à evolução estrutural de um sistema de zonas de cisalhamento dúcteis conjugadas.

Análise da tectônica de colocação de diques cretácicos na região de São Sebastião, SP

O trabalho foi desenvolvido no litoral norte do estado de São Paulo, onde ocorrem boas exposições de rochas intrusivas da porção meridional do Enxame de Diques da Serra do Mar, de idade eocretácica. O objetivo principal da dissertação é caracterizar os regimes tectônicos associados à colocação e à deformação de diques máficos na área de São Sebastião (SP) e sua distribuição espacial, a partir de interpretações de imagens de sensores remotos, análise de dados estruturais de campo e descrição petrográfica das rochas ígneas. A área apresenta grande complexidade no tocante ao magmatismo, uma vez que ocorrem diques de diabásios toleítico e alcalino, lamprófiro e rochas alcalinas félsicas como fonolitos, traquitos e sienitos, estes sob a forma diques, sills e plugs. Os diabásios toleíticos tem idades em torno 134 Ma, correlatas com o início do rifteamento sul-atlântico, enquanto que as rochas alcalinas datam de 86 Ma e estão relacionadas com um magmatismo intraplaca posterior. Os lineamentos estruturais orientam-se majoritariamente na direção ENE-WSW, paralela às foliações metamórficas e zonas de cisalhamento observadas no campo e descritas na literatura, referentes ao Domínio Costeiro da Faixa Ribeira. Os diques se orientam na direção NE-SW, com azimute semelhante porém ângulos de mergulho discordantes da foliação em grande parte da área, onde as foliações são de baixo ângulo. Um segundo conjunto de lineamentos orientado NW-SE ocorre como um importante conjunto de fraturas que cortam tanto as rochas do embasamento proterozóico quanto as rochas alcalinas neocretácicas. Diques com esta orientação são escassos. Um terceiro conjunto NNE-SSW ocorre na porção oeste da área, associado à presença de diques de diabásio que por vezes mostram indicadores de movimentação sinistral. A análise cinemática dos diques mostra um predomínio de distensão pura durante sua colocação, com um tensor de compressão mínima de orientação NW-SE, ortogonal ao principal trend dos diques. Componentes direcionais, por vezes ambíguas, são comumente observadas, com um discreto predomínio de componente sinistral. O mesmo padrão cinemático é observado para os diques toleíticos e para os alcalinos, sugerindo que o campo de tensões local pouco variou durante o Cretáceo. Embora o embasamento não tenha sido diretamente reativado durante a colocação dos diques, sua anisotropia pode ter controlado de certa forma a orientação do campo de tensões local durante o Cretáceo. Os mapas geofísicos da bacia de Santos existentes na literatura sugerem certo paralelismo entre as estruturas observadas na área de estudo e aquelas interpretadas na bacia. As estruturas NNE-SSW são paralelas ao trend das sub-bacias e ao gráben de Merluza, enquanto que as estruturas NW-SE são paralelas a zonas de transferência descritas na literatura.

Métodos espectrais aplicados à relatividade numérica: determinação dos dados iniciais

Neste trabalho aplicamos métodos espectrais para a determinação da configuração inicial de três espaços-tempos contendo buracos negros. Para isto apresentamos primeiro a foliação do espaço-tempo em hipersuperfícies tridimensionais espaciais parametrizadas pela função temporal t. Este processo é chamado de decomposição 3+1 [2] [5]. O resultado deste processo são dois conjuntos de equações classificadas em equações de vínculo e evolução [4]. As equações de vínculo podem ser divididas em vínculos Hamiltoniano e dos momentos. Para a obtenção dos dados iniciais dos problemas estudados aqui, apenas a equação de vínculo Hamiltoniano será resolvida numericamente, pois as equações de vínculo dos momentos possuem solução analítica nestes casos. Uma pequena descrição dos métodos espectrais é apresentada, destacando-se os método de Galerkin, método pseudoespectral ou de colocação e método de Tau, que são empregados na resolução das equações de vínculo Hamiltoniano dos problemas estudados. Verificamos que os resultados obtidos neste trabalho superam aqueles produzidos por Kidder e Finn [15], devido a uma escolha diferente das funções de base, que aqui satisfazem uma das condições de contorno.

Tectônica de emplacement dos diques toleíticos do Arco de Ponta Grossa, entre Curitiba e Paranaguá (PR)

Apesar da grande quantidade de estudos geoquímicos e geocronológicos que têm sido executados no enxame de diques de Ponta Grossa (EDPG), pouco se sabe a respeito da tectônica associada ao seu sin e pós emplacement. O objetivo desse estudo é identificar nos diques possíveis indicadores cinemáticos a fim de compreender essa dinâmica, além de caracterizar a tectônica rúptil Meso-cenozóica associada à área, afetando todas as rochas. A área de estudo está situada no entorno da Baía de Paranaguá, estado do Paraná, onde os diques do EDPG afloram intrudindo domínios pré-cambrianos, compostos por gnaisses, sequências metassedimentares e suítes graníticas pertencentes ao Terreno Paranaguá e uma pequena parte às Microplacas Curitiba e Luís Alves, ambos em contato através de Zonas de cisalhamento (SIGA JR, 1995). Essas rochas possuem direção de foliação marcante NE-SW. Os diques estudados foram divididos em dois grupos com base em estudos petrográficos, com forte predomínio dos básicos toleíticos e subordinadamente, os básicos alcalinos. Alguns diques compostos também foram encontrados, o que demonstra ao menos dois pulsos magmáticos possivelmente associados ao mesmo evento. São diques verticais a subverticais e possuem direção principal NW-SE. Com frequência apresentam fraturamento interno de direção NE-SW, provavelmente associados ao seu processo de resfriamento. Possuem formato tabular, porém não é raro que ocorram irregulares. As principais feições indicativas de movimentação oblíqua na intrusão desses diques são as estruturas de borda em degraus, tocos e zigue-zague, que demonstram em geral uma componente distensional destral de deslocamento. Agregando dados dos demais enxames de diques toleíticos principais, chegou-se a um valor médio de N80E para o tensor σ3 da abertura do Atlântico Sul, coerente com o esperado também para EDPG, visto que foram intrudidos em um ambiente transtensivo (CORREA GOMES, 1996). Falhas e fraturas são observadas cortando tanto as rochas encaixantes quanto os diques, caracterizando uma tectônica posterior à intrusão. As principais famílias de fraturas são N20-30E, N30-40W, N80W e N60-70E, formando zonas preferenciais de erosão no cruzamento entre elas. As falhas podem apresentar plano de falha bem definido com estrias e ressaltos, ocorrendo preenchidas ou não, tendo sido observados preenchimento de sílica e material carbonático. Predomina nas falhas observadas, cinemática sinistral demonstrando mudança no campo de esforços com relação ao emplacement dos diques. O estudo da tectônica rúptil assim como do emplacement dos diques da área vem a contribuir para o melhor entendimento dos processos de abertura do Oceano Atlântico Sul, além de abranger a região emersa do que constitui o embasamento da bacia de Santos, foco de extensivos estudos atualmente, podendo-se inferir que os mesmos processos tenham afetado a região offshore.

山东莒南地区韧性剪切带的变形特征与形成演化

Ju Nan of Shandong province is located at southwest of Sulu UHP (ultrahigh-pressure) metamorphic terrane. It is composed of gneiss, paragneiss, eclogites, ultramafic rocks, marble and quartzite. A large ductile shear zone extends east-west has been found at the Zhubian, The south of Junan county. The Zhubian ductile shear zone is composed of high srain rock and mylonites. The mylonites fall into 3 types: Initial gneiss mylonite, mylonite and altramylonit.obvious lineation of penetration,foliation,S-Cfabrics,porphyroclasts,folds,irregularundulatory,extinction,subgrain boundary, dynamic recrystallization microstructure, core-mantle structure and are common in the ductile shear zone. Based on field work and microstructural analyse, a conclution is arrived: The ductile shear zone is an approximately SE trending faults. The Zhubian ductile shear zone formed at Ep ―Hb facies conditions which could be proved by deformaed and metamorphosed mineral aggregates, Deformation behavior, Ternary-feldspar geothermometry and so on. Zircon MC―ICP―MS U-Pb analysis is performed on the mylonite and have an average age ―835.9±13.9Ma, it’s the primary rocks formed age. The Zhubian ductile shear zone maybe formed at 224-242Ma.

陇西盆地晚第三纪风尘沉积的地层学研究

In Asia, the significant environment changes in Cenozoic include: uplift of Himalayas and Tibetan Plateau, formation Asian monsoon system, Aridification in Central Asia. One of major advances in recent studies of eolian deposit on the Loess Plateau is the verification of the eolian origin for the Late Tertiary Hipparion Red-Earth (also called red-Clay) underlying the Quaternary loess. Thus, the Late Tertiary eolian deposit, which has been proven a nearly continuous terrestrial record and sensitive to climate change, provides us an important archive to understand these above Cenozoic environment events. The deposit in eastern Loess Plateau has been extensively studied, while the property and age of deposit underlying the Quaternary loess in western plateau remains unclear. In this paper, detail investigations were made on the Sedimentology, geochemistry of Longxi section, a typical section in western Loess Plateau, to address its origin, and on micromammalian fossils and magnetostratigraphy to address its age. The main conclusions are presented as following: 1. The sedimentological and geochemical properties in Longxi section are highly similar to typical Quaternary eolian deposit in Loess Plateau. Nearly 100 paleosols are recognized in the field, and the grain size are very fine with the median grain size centered at 4～7μm. There is a good agreement of both major and trace element compositions between Longxi deposit and the Quaternary Loess. The REE distribution patterns of Longxi deposit and the Quaternary loess are remarkably similar in shape, with enrichment LREE and fairly flat HREE profiles and clear negative Eu anomaly. The mangnetic minerals in Longxi deposit are mainly magnetite, hematite and maghematite, which are similar to those of the Hipparion Red-Earth and Quaternary Loess. The major difference among them is that the samples from Longxi section contain more hematite. The characteristics of anisotropy of magnetic susceptibility (AMS) in Longxi deposit is highly consistent with that of Quaternary loess, while values of the major AMS parameters, e.g. anisotropy degree, magnetic foliation and lineation, are significantly lower than those of fluvial and lake deposits. These evidences indicate an eolian origin for the sediment. 2. An investigation of micromammalian fossils was firstly carried out for determining the approximate age of the sequence because of lack of materials for accurate isotope dating. Three fossil assemblages were obtained which indicate a chronological range from the Middle Miocene to Late Miocene. The magnetostratigraphical study suggests that it is a near continuous terrestrial record for the period from 13.23 to 6.23 MaB.P. The obtained chronology is highly consistent with fossils assemblages. This section is the oldest eolian deposit presently known in Loess Plateau. 3. The magnetic susceptibly value is high in paleosols than in surrounded weak-weathered layers, which suggests that it may be a climate index on orbital time scale. While it cannot be used as a proxy to address the long-term, change of climate on tectonic time scale, as content of the magnetic minerals is highly variable in different parts of the section. 4. The appearance of Middle Miocene eolian deposit in the Loess Plateau marks the strengthening of aridification of Central Asia. The high degree of similarity between the geochemical properties of Longxi eolian deposit, Hipparion Red-Earth and Quaternary loess a suggests that a rather similar source provenance. The dust accumulation rate (DAR) of Longxi section, which is widely used as a proxy to document the aridity in source areas in marine and terrestrial record studies, recorded the aridity condition in northwestern China over a period from Middle Miocene to Late Miocene. The DAR of the section shows that the continent aridity remains moderate and relative stable over that period.

中国黄土的磁组构特征及其古风向指示意义

The transportation and deposition of eolian materials of Chinese loess is correlated and effected by the monsoon from the mid-high latitude. Therefore study of the winter monsoon evolution can help us to understand the dynamic mechanism to climate changes in the east-Asian areas. The anisotropy of magnetic susceptibility (AMS) measurements have been carried out on the samples from the last 250ka wind -blown loess-paleosol sequences at Baicaoyuan and Luochuan. And the main conclusions are following:The magnetic foliation is almost horizontal of the two sections. AMS canthus be represented by an oblate ellipsoid with average K3 perpendicular to thebedding plane and Ki within the bedding plane. It has also shown that the ^-factor isless than 0.5 of the majority of samples. So the two sections are normal magneticfabric for sediments.The degree of anisotropy always shows a strong correlation with the foliationrather than with lineation, therefore the anisotropy is controlled by the foliation.Furthermore the foliation is nearly less than 1.02 and shows the typical wind-blownsediments anisotropy.The intensity of winter monsoon, grain size of the eolian inputs, the foliationand the degree of anisotropy are somewhat inter-related. Generally, the higherintensity of the winter monsoon will carry coarser-grained eolian material, therebyresulting in a larger foliation during deposition. Also the post-depositional compactioncontributes to the anisotropy.The AMS features between loess and paleosol are somewhat different. Wefound that the F, P values of paleosol are lower than that of its parent loess respectively. Moreover, the difference does also exists between the two sections. The anisotropy of Baicaoyuan is more significant than Luochuan section, which maybe related with the location and the intensity of the post-deposition reworks.5. We note that the declination of the long axis is NWW in Baicaoyuan section and the observed NWW direction of the winter monsoon winds based on AMS is consistent with the view that the winter monsoons prevail along the NW-SE direction. But at the Luochuan section, because of the strong affection of the post-deposition reworks, the direction of the long axis is nearly random in the foliation and hardly recognizes the paleowind direction since the last two interglacials.Correlation between the two loess-paleosol sequences implies that it is available in arid or semi-arid areas to take AMS to recognize the paleowind directions on the Loess Plateau.

Caratterizzazione geo-petrografica, petrologica e geochimica di rocce anatettiche del nord Sardegna

The High Grade Metamorphic Complex (HGMC) of Variscan basement of north Sardinia is characterized by the widespread of migmatites. This study is focused on two localities of NE Sardinia (Porto Ottiolu and Punta Sirenella) where ortho- and para-derivates migmatites outcrop. A geological and structural survey was carried out, leading to the realization of a geological schematic map of Punta Sirenella area. Several samples of different rocks were collected for petrographic, micro-structural minero-chemical and geochemical analyses. In the Porto Ottiolu area three main deformation phases have been identified; D1, characterized by tight folds with sub-horizontal axes, rarely preserved in paragneisses; D2, that produce a pervasive foliation oriented N100° 45°SW marked by biotite and sillimanite blastesis and locally transposed by shear zone oriented N170°; D3, late deformation phase caused symmetric folds with sub-horizontal axes with no axial plane schistosity. Leucosomes form pods and layers along S2 schistosity but also leucosomes along shear zones have been observed. In the Punta Sirenella area, three main deformation phases have been identified; D1, is manifested by the transposition of centimeter-sized leucosomes and is rarely observed in paragneisses were produce open folds with sub-vertical axes; D2, NW-SE oriented on whose XY plane three mineralogical lineation (quartz+plagioclase, fibrolite+quarz and muscovite) lie; D3, a ductile-brittle deformation phase that produce a mylonitc S3 foliation that locally become the most evident schistosity in the field oriented N140° steeply dipping toward NE. In both areas, leucosomes of sedimentary-derived migmatites are generally trondhjemitic pointing out for a H2O fluxed melting reaction, but also granitic leucosomes have been found, produced by muscovite dehydration melting. Leucosomes of migmatitic orthogneiss instead, have granitic compositions. Migmatization started early, during the compressional and crustal thickening (sin-D1, pre-D2) and was still active during exhumation stage. For each studied outcrop of migmatite pseudosections for the average mesosome composition have been calculated; these pseudosections have been used to model the P-T conditions of anatexis on the basis of the melt volume (%) of melt, Si/Al and Na/K molar ratios, modal content of garnet and Si content in metamorphic white mica. Further pseudosections have been calculated for the average composition of leucosomes in order to define the P-T conditions of the end of the crystallization through intersection of solidus curve and isopleths of Si content in white mica and/or XMg ratio in biotite. Thermodynamic modeling on ortho- and sedimentary-derived migmatites of Punta Sirenella yield P-T conditions of 1.1-1.3 GPa - 670-740°C for migmatitic event and 0.75-0.90 GPa - 660-730°C for the end of crystallization. These conditions are fit well with previous studies on adjacent rocks. Modeling of Porto Ottiolu ortho- and sedimentary-derived migmatites yield P-T conditions of 0.85-1.05 GPa - 690-730°C for migmatitic event and 0.35-0.55 GPa - 630-690°C strongly affected by re-equilibration during exhumation, expecially for crystallization conditions. Geochemical analyses of samples belonging to Porto Ottiolu and Punta Sirenella orthogneisses show a strong link with those of other orthogneisses outcropping in NE Sardinia (for instance, Lode-Mamone and Golfo Aranci) that are considered the intrusive counterparts of middle-Ordovician metavolcanics rocks outcropping in the Nappe Zone. Thus, the studied ortogneiss bodies, even lacking radiometric data, can be considered as belonging to the same magmatic cycle.