Differential geometry of intersection curves in R(4) of three implicit surfaces

We present algorithms for computing the differential geometry properties of intersection Curves of three implicit surfaces in R(4), using the implicit function theorem and generalizing the method of X. Ye and T. Maekawa for 4-dimension. We derive t, n, b(1), b(2) vectors and curvatures (k(1), k(2), k(3)) for transversal intersections of the intersection problem. (C) 2008 Elsevier B.V. All rights reserved.

Utilizando mapas de conectividade fuzzy no desenvolvimento de algoritmos reparadores de imagens binárias 3D

A 3D binary image is considered well-composed if, and only if, the union of the faces shared by the foreground and background voxels of the image is a surface in R3. Wellcomposed images have some desirable topological properties, which allow us to simplify and optimize algorithms that are widely used in computer graphics, computer vision and image processing. These advantages have fostered the development of algorithms to repair bi-dimensional (2D) and three-dimensional (3D) images that are not well-composed. These algorithms are known as repairing algorithms. In this dissertation, we propose two repairing algorithms, one randomized and one deterministic. Both algorithms are capable of making topological repairs in 3D binary images, producing well-composed images similar to the original images. The key idea behind both algorithms is to iteratively change the assigned color of some points in the input image from 0 (background)to 1 (foreground) until the image becomes well-composed. The points whose colors are changed by the algorithms are chosen according to their values in the fuzzy connectivity map resulting from the image segmentation process. The use of the fuzzy connectivity map ensures that a subset of points chosen by the algorithm at any given iteration is the one with the least affinity with the background among all possible choices

Caracterização geométrica e parametrização de depósitos transacionais recentes e sua aplicação na modelagem de reservatórios petrolíferos

In this beginning of the XXI century, the Geology moves for new ways that demand a capacity to work with different information and new tools. It is within this context that the analog characterization has important in the prediction and understanding the lateral changes in the geometry and facies distribution. In the present work was developed a methodology for integration the geological and geophysical data in transitional recent deposits, the modeling of petroliferous reservoirs, the volume calculation and the uncertainties associate with this volume. For this purpose it was carried planialtimetric and geophysics (Ground Penetrating Radar) surveys in three areas of the Parnaíba River. With this information, it was possible to visualize the overlap of different estuary channels and make the delimitation of the channel geometry (width and thickness). For three-dimensional visualization and modeling were used two of the main reservoirs modeling software. These studies were performed with the collected parameters and the data of two reservoirs. The first was created with the Potiguar Basin wells data existents in the literature and corresponding to Açu IV unit. In the second case was used a real database of the Northern Sea. In the procedures of reservoirs modeling different workflows were created and generated five study cases with their volume calculation. Afterwards an analysis was realized to quantify the uncertainties in the geological modeling and their influence in the volume. This analysis was oriented to test the generating see and the analogous data use in the model construction

Processamento e interpretação de dados 2D e 3D de GPR :aplicações no imageamento de feições kársticas e estruturas de dissolução no campo de petróleo de Fazenda Belém-CE

In Fazenda Belém oil field (Potiguar Basin, Ceará State, Brazil) occur frequently sinkholes and sudden terrain collapses associated to an unconsolidated sedimentary cap covering the Jandaíra karst. This research was carried out in order to understand the mechanisms of generation of these collapses. The main tool used was Ground Penetrating Radar (GPR). This work is developed twofold: one aspect concerns methodology improvements in GPR data processing whilst another aspect concerns the geological study of the Jandaíra karst. This second aspect was strongly supported both by the analysis of outcropping karst structures (in another regions of Potiguar Basin) and by the interpretation of radargrams from the subsurface karst in Fazenda Belém. It was designed and tested an adequate flux to process GPR data which was adapted from an usual flux to process seismic data. The changes were introduced to take into account important differences between GPR and Reflection Seismic methods, in particular: poor coupling between source and ground, mixed phase of the wavelet, low signal-to-noise ratio, monochannel acquisition, and high influence of wave propagation effects, notably dispersion. High frequency components of the GPR pulse suffer more pronounced effects of attenuation than low frequency components resulting in resolution losses in radargrams. In Fazenda Belém, there is a stronger need of an suitable flux to process GPR data because both the presence of a very high level of aerial events and the complexity of the imaged subsurface karst structures. The key point of the processing flux was an improvement in the correction of the attenuation effects on the GPR pulse based on their influence on the amplitude and phase spectra of GPR signals. In low and moderate losses dielectric media the propagated signal suffers significant changes only in its amplitude spectrum; that is, the phase spectrum of the propagated signal remains practically unaltered for the usual travel time ranges. Based on this fact, it is shown using real data that the judicious application of the well known tools of time gain and spectral balancing can efficiently correct the attenuation effects. The proposed approach can be applied in heterogeneous media and it does not require the precise knowledge of the attenuation parameters of the media. As an additional benefit, the judicious application of spectral balancing promotes a partial deconvolution of the data without changing its phase. In other words, the spectral balancing acts in a similar way to a zero phase deconvolution. In GPR data the resolution increase obtained with spectral balancing is greater than those obtained with spike and predictive deconvolutions. The evolution of the Jandaíra karst in Potiguar Basin is associated to at least three events of subaerial exposition of the carbonatic plataform during the Turonian, Santonian, and Campanian. In Fazenda Belém region, during the mid Miocene, the Jandaíra karst was covered by continental siliciclastic sediments. These sediments partially filled the void space associated to the dissolution structures and fractures. Therefore, the development of the karst in this region was attenuated in comparison to other places in Potiguar Basin where this karst is exposed. In Fazenda Belém, the generation of sinkholes and terrain collapses are controlled mainly by: (i) the presence of an unconsolidated sedimentary cap which is thick enough to cover completely the karst but with sediment volume lower than the available space associated to the dissolution structures in the karst; (ii) the existence of important structural of SW-NE and NW-SE alignments which promote a localized increase in the hydraulic connectivity allowing the channeling of underground water, thus facilitating the carbonatic dissolution; and (iii) the existence of a hydraulic barrier to the groundwater flow, associated to the Açu-4 Unity. The terrain collapse mechanisms in Fazenda Belém occur according to the following temporal evolution. The meteoric water infiltrates through the unconsolidated sedimentary cap and promotes its remobilization to the void space associated with the dissolution structures in Jandaíra Formation. This remobilization is initiated at the base of the sedimentary cap where the flow increases its abrasion due to a change from laminar to turbulent flow regime when the underground water flow reaches the open karst structures. The remobilized sediments progressively fill from bottom to top the void karst space. So, the void space is continuously migrated upwards ultimately reaching the surface and causing the sudden observed terrain collapses. This phenomenon is particularly active during the raining season, when the water table that normally is located in the karst may be temporarily located in the unconsolidated sedimentary cap

Uso do GPR na geração de modelos estáticos 3D para o planejamento de lavra de minerais pesados depositados em dunas eólicas

This project was developed as a partnership between the Laboratory of Stratigraphical Analyses of the Geology Department of UFRN and the company Millennium Inorganic Chemicals Mineração Ltda. This company is located in the north end of the paraiban coast, in the municipal district of Mataraca. Millennium has as main prospected product, heavy minerals as ilmenita, rutilo and zircon presents in the sands of the dunes. These dunes are predominantly inactive, and overlap the superior portion of Barreiras Formation rocks. The mining happens with the use of a dredge that is emerged at an artificial lake on the dunes. This dredge removes sand dunes of the bottom lake (after it disassembles of the lake borders with water jets) and directs for the concentration plant, through piping where the minerals are then separate. The present work consisted in the acquisition external geometries of the dunes, where in the end a 3D Static Model could be set up of these sedimentary deposits with emphasis in the behavior of the structural top of Barreiras Formation rocks (inferior limit of the deposit). The knowledge of this surface is important in the phase of the plowing planning for the company, because a calculation mistake can do with that the dredge works too close of this limit, taking the risk that fragments can cause obstruction in the dredge generating a financial damage so much in the equipment repair as for the stopped days production. During the field stages (accomplished in 2006 and 2007) topographical techniques risings were used with Total Station and Geodesic GPS as well as shallow geophysical acquisitions with GPR (Ground Penetrating Radar). It was acquired almost 10,4km of topography and 10km of profiles GPR. The Geodesic GPS was used for the data geopositioning and topographical rising of a traverse line with 630m of extension in the stage of 2007. The GPR was shown a reliable method, ecologically clean, fast acquisition and with a low cost in relation to traditional methods as surveys. The main advantage of this equipment is obtain a continuous information to superior surface Barreiras Formation rocks. The static models 3D were elaborated starting from the obtained data being used two specific softwares for visualization 3D: GoCAD 2.0.8 and Datamine. The visualization 3D allows a better understanding of the Barreiras surface behavior as well as it makes possible the execution of several types of measurements, favoring like calculations and allowing that procedures used for mineral extraction is used with larger safety

Dobramentos distensionais e a geometria da falha de Baixa Grande, Graben de Umbuzeiro, Bacia Potiguar (RN)

In spite of significant study and exploration of Potiguar Basin, easternmost Brazilian equatorial margin, by the oil industry, its still provides an interesting discussion about its origin and the mechanisms of hydrocarbon trapping. The mapping and interpretation of 3D seismic reflection data of Baixa Grande Fault, SW portion of Umbuzeiro Graben, points as responsible for basin architecture configuration an extensional deformational process. The fault geometry is the most important deformation boundary condition of the rift stata. The development of flat-ramp geometries is responsible for the formation of important extensional anticline folds, many of then hydrocarbon traps in this basin segment. The dominant extensional deformation in the studied area, marked by the development of normal faults developments, associated with structures indicative of obliquity suggests variations on the former regime of Potiguar Basin through a multiphase process. The changes in structural trend permits the generation of local transpression and transtension zones, which results in a complex deformation pattern displayed by the Potiguar basin sin-rift strata. Sismostratigraphic and log analysis show that the Baixa Grande Fault acts as listric growing fault at the sedimentation onset. The generation of a relay ramp between Baixa Grande Fault and Carnaubais Fault was probably responsible for the balance between subsidence and sedimentary influx taxes, inhibiting its growing behaviour. The sismosequences analysis s indicates that the extensional folds generation its diachronic, and then the folds can be both syn- and post-depositional

Estruturação do grupo Serra Grande região de Santana do Acaraú- CE e a reativação do lineamento Sobral Pedro II, integração com dados geofísicos

The study area is located in the NW portion of the Ceará state nearby the city of Santana do Acaraú. Geologically it lies along the Sobral-Pedro II lineament which limits the domains of Ceará Central and Noroeste do Ceará, both belonging to the Borborema Province.The object of study was a NE trending 30km long siliciclastic body (sandstone and conglomerate) bounded by transcurrent dextral faults. The sediments are correlated to the Ipú Formation (Serra Grande Group) from the Parnaiba basin, which age is thought to be Siluro-Devonian. Existing structural data shown that bedding has higher but variable dips (70-45) near the borders faults and much lower to subhorizontal inward the body. The brittle deformation was related to a reactivation, in lower crustal level, of the Sobral-Pedro II lineament (Destro (1987, 1999; Galvão, 2002).The study presented here was focused in applying geophysicals methods (gravimetry and seismic) to determine the geometry of the sandstone/conglomeratic body and together with the structural data, to propose a model to explain its deformation. The residual anomalies maps indicate the presence of two main graben-like structures. The sedimentary pile width was estimated from 2D gravimetric models to be about 500-600 meters. The 3D gravimetric model stressed the two maximum width regions where a good correlation is observed between the isopach geometry and the centripetal strike/dip pattern displayed by the sediments bedding. Two main directions (N-S and E-W) of block moving are interpreted from the distribution pattern of the maximum width regions of the sedimentary rock

Caracterização macro, meso e microscópica das estruturas frágeis do corpo arenítico conglomerático da região de Santana do Acaraú (CE) e seu embasamento circundante

The structural framework of the sedimentary basins usually plays an important role in oil prospects and reservoirs. Geometry, interconectivity and density of the brittle features developed during basin evolution could change the permo-porous character of the rocks involved in generation, migration and entrapment of fluid flow. Once the structural characterization of the reservois using only sub-surface data is not an easy task, many studies are focused in analogous outcrops trying to understand the main processes by which brittle tectonic is archieved. In the Santana do Acaraú region (Ceará state, NE Brazil) a pack of conglomeratic sandstone (here named CAC) has its geometry controlled mainly by NE trending faults, interpreted as related to reactivation of a precambrian Sobral Pedro II Lineament (LSP-II). Geological mapping of the CAC showed a major NE-SW trending synform developed before its complete lithification during a dextral transpression. This region was then selected to be studied in details in order of constrain the cretaceous deformation and so help the understanding the deformation of the basins along the brazilian equatorial margin. In order to characterize the brittle deformation in different scales, I study some attributes of the fractures and faults such as orientation, density, kinematic, opening, etc., through scanlines in satellite images, outcrops and thin sections. The study of the satellite images showed three main directions of the macrostructures, N-S, NE-SW and E-W. Two of theses features (N-S and E-W) are in aggreement with previous geophysical data. A bimodal pattern of the lineaments in the CAC´s basement rocks has been evidenciated by the NE and NW sets of structures obtained in the meso and microscale data. Besides the main dextral transpression two others later events, developed when the sediments were complety lithified, were recognized in the area. The interplay among theses events is responsible for the compartimentation of the CAC in several blocks along within some structural elements display diferents orientations. Based on the variation in the S0 orientation, the CAC can be subdivided in several domains. Dispite of the variations in orientations of the fractures/faults in the diferents domains, theses features, in the meso and microscopic scale, are concentrated in two sets (based on their trend) in all domains which show similar orientation of the S0 surface. Thus the S0 orientation was used to group the domains in three major sets: i) The first one is that where S0 is E-W oriented: the fractures are oriented mainly NE with the development of a secondary NW trending; ii) S0 trending NE: the fractures are concentrated mainly along the trend NW with a secondary concentration along the NE trend; iii) The third set, where S0 is NS the main fractures are NE and the secondary concentration is NW. Another analized parameter was the fault/fracture length. This attribute was studied in diferent scales trying to detect the upscale relationship. A terrain digital model (TDM) was built with the brittlel elements supperposed. This model enhanced a 3D visualization of the area as well as the spatial distribution of the fault/fractures. Finally, I believe that a better undertanding of the brittle tectonic affecting both CAC and its nearby basement will help the future interpretations of the tectonic envolved in the development of the sedimentary basins of the brazilian equatorial margin and their oil reservoirs and prospects, as for instance the Xaréu field in the Ceará basin, which subsurface data could be correlated with the surface ones

Aplicação da modelagem estrutural computacional direta na análise da geometria de falhas: exemplo da falha de Baixa Grande (Bacia Potiguar - NE do Brasil)

The Baixa grande fault is located on the edge of the S-SW Potiguar Rift. It limits the south part of Umbuzeiro Graben and the Apodi Graben. Although a number of studies have associated the complex deformation styles in the hanging wall of the Baixa Grande Fault with geometry and displacement variations, none have applied the modern computational techniques such as geometrical and kinematic validations to address this problem. This work proposes a geometric analysis of the Baixa Fault using seismic interpretation. The interpretation was made on 3D seismic data of the Baixa Grande fault using the software OpendTect (dGB Earth Sciences). It was also used direct structural modeling, such as Analog Direct Modeling know as Folding Vectors and, 2D and 3D Direct Computational Modeling. The Folding Vectors Modeling presented great similarity with the conventional structural seismic interpretations of the Baixa Grande Fault, thus, the conventional interpretation was validated geometrically. The 2D direct computational modeling was made on some sections of the 3D data of the Baixa Grande Fault on software Move (Midland Valley Ltd) using the horizon modeling tool. The modeling confirms the influence of fault geometry on the hanging wall. The Baixa Grande Fault ramp-flat-ramp geometry generates synform on the concave segments of the fault and antiform in the convex segments. On the fault region that does not have segments angle change, the beds are dislocated without deformation, and on the listric faults occur rollover. On the direct 3D computational modeling, structural attributes were obtained as horizons on the hanging wall of the main fault, after the simulation of several levels of deformation along the fault. The occurrence of structures that indicates shortening in this modeling, also indicates that the antiforms on the Baixa Grande Fault were influenced by fault geometry

Proposta metodológica para o imageamento digital e modelagem virtual 3d de um bloco de rochas travertinas

In this paper we present the methodological procedures involved in the digital imaging in mesoscale of a block of travertines rock of quaternary age, originating from the city of Acquasanta, located in the Apennines, Italy. This rocky block, called T-Block, was stored in the courtyard of the Laboratório Experimental Petróleo "Kelsen Valente" (LabPetro), of Universidade Estadual de Campinas (UNICAMP), so that from it were performed Scientific studies, mainly for research groups universities and research centers working in brazilian areas of reservoir characterization and 3D digital imaging. The purpose of this work is the development of a Model Solid Digital, from the use of non-invasive techniques of digital 3D imaging of internal and external surfaces of the T-Block. For the imaging of the external surfaces technology has been used LIDAR (Light Detection and Range) and the imaging surface Interior was done using Ground Penetrating Radar (GPR), moreover, profiles were obtained with a Gamma Ray Gamae-spectômetro laptop. The goal of 3D digital imaging involved the identification and parameterization of surface geological and sedimentary facies that could represent heterogeneities depositional mesoscale, based on study of a block rocky with dimensions of approximately 1.60 m x 1.60 m x 2.70 m. The data acquired by means of terrestrial laser scanner made available georeferenced spatial information of the surface of the block (X, Y, Z), and varying the intensity values of the return laser beam and high resolution RGB data (3 mm x 3 mm), total points acquired 28,505,106. This information was used as an aid in the interpretation of radargrams and are ready to be displayed in rooms virtual reality. With the GPR was obtained 15 profiles of 2.3 m and 2 3D grids, each with 24 sections horizontal of 1.3 and 14 m vertical sections of 2.3 m, both the Antenna 900 MHz to about 2600 MHz antenna. Finally, the use of GPR associated with Laser Scanner enabled the identification and 3D mapping of 3 different radarfácies which were correlated with three sedimentary facies as had been defined at the outset. The 6 profiles showed gamma a low amplitude variation in the values of radioactivity. This is likely due to the fact of the sedimentary layers profiled have the same mineralogical composition, being composed by carbonate sediments, with no clay in siliciclastic pellitic layers or other mineral carrier elements radioactive

Caracterização de reservatórios siliciclásticos neoaptianos: um estudo do membro carmópolis no campo de Camorim, sub-bacia de Sergipe, Brasil

The Camorim Oilfield, discovered in 1970 in the shallow water domain of the Sergipe Sub-basin, produces hydrocarbons from the Carmópolis Member of the Muribeca Formation, the main reservoir interval, interpreted as siliciclastics deposited in an alluvial-fluvial-deltaic context during a late rifting phase of Neoaptian age, in the Sergipe-Alagoas Basin. The structural setting of the field defines different production blocks, being associated to the evolution of the Atalaia High during the rift stage and subsequent reactivations, encompassing NE-SW trending major normal faults and NWEW trending secondary faults. The complexity of this field is related to the strong facies variation due to the interaction between continental and coastal depositional environments, coupled with strata juxtaposition along fault blocks. This study aims to geologically characterize its reservoirs, to provide new insights to well drilling locations in order to increase the recovery factor of the field. Facies analysis based on drill cores and geophysical logs and the 3D interpretation of a seismic volume, provide a high resolution stratigraphic analysis approach to be applied in this geodynamic transitional context between the rift and drift evolutionary stages of the basin. The objective was to define spatial and time relations between production zones and the preferential directions of fluid flow, using isochore maps that represent the external geometry of the deposits and facies distribution maps to characterize the internal heterogeneities of these intervals, identified in a 4th order stratigraphic zoning. This work methodology, integrated in a 3D geological modelling process, will help to optimize well drilling and hydrocarbons production. This methodology may be applied in other reservoirs in tectonic and depositional contexts similar to the one observed at Camorim, for example, the oil fields in the Aracaju High, Sergipe Sub-basin, which together represent the largest volume of oil in place in onshore Brazilian basins

Gel de plaquetas: arcabouço 3D para cultura celular

INTRODUÇÃO: O reparo tissular é o objetivo final da cirurgia. A cultura celular requer arcabouço mecânico que dê suporte ao crescimento celular e difusão dos nutrientes. O uso do plasma rico em plaquetas (PRP) como um arcabouço 3D possui diversas vantagens: é material biológico, de fácil absorção pós-transplante, rico em fatores de crescimento, em especial PDGF- ββ e TGF-β que estimula síntese de matriz extracelular na cartilagem. OBJETIVO: Desenvolver arcabouço 3D à base de PRP. MATERIAIS E MÉTODOS: Duas formas foram idealizadas: Sphere e Carpet. Condições estéreis foram utilizadas. O gel de plaquetas permaneceu em cultura celular, observado diariamente em microscópio invertido. RESULTADOS: Ambos arcabouços obtiveram sucesso, com aspectos positivos e negativos. DISCUSSÃO: A forma Sphere não aderiu ao plástico. Observou-se retração do gel e investigação ao microscópio dificultada devido às áreas opacas no campo visual. A forma Carpet não aderiu ao plástico e apresentou-se translúcida. O tempo de estudo foi de 20 dias. CONCLUSÕES: A produção de um arcabouço 3D PRP foi um sucesso, e trata-se de uma alternativa que necessita ser mais utilizado e investigado para que se consolide em uma rota eficiente e confiável na tecnologia de engenharia tissular, particularmente em cultura de tecido cartilaginoso.

3D reconstruction and scanning electron microscopy of salivary glands of the millipede Rhinocricus padbergi (Verhoef, 1938) (Diplopoda: Spirobolida)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)