Análise e síntese de antenas e superfícies seletivas de frequência utilizando computação evolucionária e inteligência de enxames

The frequency selective surfaces, or FSS (Frequency Selective Surfaces), are structures consisting of periodic arrays of conductive elements, called patches, which are usually very thin and they are printed on dielectric layers, or by openings perforated on very thin metallic surfaces, for applications in bands of microwave and millimeter waves. These structures are often used in aircraft, missiles, satellites, radomes, antennae reflector, high gain antennas and microwave ovens, for example. The use of these structures has as main objective filter frequency bands that can be broadcast or rejection, depending on the specificity of the required application. In turn, the modern communication systems such as GSM (Global System for Mobile Communications), RFID (Radio Frequency Identification), Bluetooth, Wi-Fi and WiMAX, whose services are highly demanded by society, have required the development of antennas having, as its main features, and low cost profile, and reduced dimensions and weight. In this context, the microstrip antenna is presented as an excellent choice for communications systems today, because (in addition to meeting the requirements mentioned intrinsically) planar structures are easy to manufacture and integration with other components in microwave circuits. Consequently, the analysis and synthesis of these devices mainly, due to the high possibility of shapes, size and frequency of its elements has been carried out by full-wave models, such as the finite element method, the method of moments and finite difference time domain. However, these methods require an accurate despite great computational effort. In this context, computational intelligence (CI) has been used successfully in the design and optimization of microwave planar structures, as an auxiliary tool and very appropriate, given the complexity of the geometry of the antennas and the FSS considered. The computational intelligence is inspired by natural phenomena such as learning, perception and decision, using techniques such as artificial neural networks, fuzzy logic, fractal geometry and evolutionary computation. This work makes a study of application of computational intelligence using meta-heuristics such as genetic algorithms and swarm intelligence optimization of antennas and frequency selective surfaces. Genetic algorithms are computational search methods based on the theory of natural selection proposed by Darwin and genetics used to solve complex problems, eg, problems where the search space grows with the size of the problem. The particle swarm optimization characteristics including the use of intelligence collectively being applied to optimization problems in many areas of research. The main objective of this work is the use of computational intelligence, the analysis and synthesis of antennas and FSS. We considered the structures of a microstrip planar monopole, ring type, and a cross-dipole FSS. We developed algorithms and optimization results obtained for optimized geometries of antennas and FSS considered. To validate results were designed, constructed and measured several prototypes. The measured results showed excellent agreement with the simulated. Moreover, the results obtained in this study were compared to those simulated using a commercial software has been also observed an excellent agreement. Specifically, the efficiency of techniques used were CI evidenced by simulated and measured, aiming at optimizing the bandwidth of an antenna for wideband operation or UWB (Ultra Wideband), using a genetic algorithm and optimizing the bandwidth, by specifying the length of the air gap between two frequency selective surfaces, using an optimization algorithm particle swarm

Uma contribuição ao estudo das categorias internas e de sua proliferação em redes ARTMAP

ART networks present some advantages: online learning; convergence in a few epochs of training; incremental learning, etc. Even though, some problems exist, such as: categories proliferation, sensitivity to the presentation order of training patterns, the choice of a good vigilance parameter, etc. Among the problems, the most important is the category proliferation that is probably the most critical. This problem makes the network create too many categories, consuming resources to store unnecessarily a large number of categories, impacting negatively or even making the processing time unfeasible, without contributing to the quality of the representation problem, i. e., in many cases, the excessive amount of categories generated by ART networks makes the quality of generation inferior to the one it could reach. Another factor that leads to the category proliferation of ART networks is the difficulty of approximating regions that have non-rectangular geometry, causing a generalization inferior to the one obtained by other methods of classification. From the observation of these problems, three methodologies were proposed, being two of them focused on using a most flexible geometry than the one used by traditional ART networks, which minimize the problem of categories proliferation. The third methodology minimizes the problem of the presentation order of training patterns. To validate these new approaches, many tests were performed, where these results demonstrate that these new methodologies can improve the quality of generalization for ART networks

Mapeamento com Sonar Usando Grade de Ocupação baseado em Modelagem Probabilística

In this work, we propose a probabilistic mapping method with the mapped environment represented through a modified occupancy grid. The main idea of the proposed method is to allow a mobile robot to construct in a systematic and incremental way the geometry of the underlying space, obtaining at the end a complete environment map. As a consequence, the robot can move in the environment in a safe way, based on a confidence value of data obtained from its perceptive system. The map is represented in a coherent way, according to its sensory data, being these noisy or not, that comes from exterior and proprioceptive sensors of the robot. Characteristic noise incorporated in the data from these sensors are treated by probabilistic modeling in such a way that their effects can be visible in the final result of the mapping process. The results of performed experiments indicate the viability of the methodology and its applicability in the area of autonomous mobile robotics, thus being an contribution to the field

Desenvolvimento de monopolos quase-espirais para aplicações em sistemas UWB

This work is the analysis of a structure of the microstrip antenna designed for application in ultra wide band systems (Ultra Wideband - UWB). This is a prospective analytical study where they tested the changes in the geometry of the antenna, observing their suitability to the proposed objectives. It is known that the UWB antenna must operate in a range of at least 500 MHz, and answer a fractional bandwidth greater than or equal to 25%. It is also desirable that the antenna meets the specifications of track determined by FCC - Federal Communication Commission, which regulates the system in 2002 designating the UWB bandwidth of 7.5 GHz, a range that varies from 3.1 GHz to 10, 6 GHz. by setting the maximum power spectral density of operation in -41.3 dB / MHz, and defining the fractional bandwidth by 20%. The study starts of a structure of geometry in the form of stylized @, which evolves through changes in its form, in simulated commercial software CST MICROWAVE STUDIO, version 5.3.1, and then tested using the ANSOFT HFSS, version 9. These variations, based on observations of publications available from literature referring to the microstrip monopole planar antennas. As a result it is proposed an antenna, called Monopole Antenna Planar Spiral Almost Rectangular for applications in UWB systems - AMQEUWB, which presents simulated and measured results satisfactory, consistent with the objectives of the study. Some proposals for future work are mentioned

Uma proposta de FSS fractal com geometria simplificada

Frequency Selective Surfaces (FSS) are periodic structures in one or two dimensions that act as spatial filters, can be formed by elements of type conductors patches or apertures, functioning as filters band-stop or band-pass respectively. The interest in the study of FSS has grown through the years, because such structures meet specific requirements as low-cost, reduced dimensions and weighs, beyond the possibility to integrate with other microwave circuits. The most varied applications for such structures have been investigated, as for example, radomes, antennas systems for airplanes, electromagnetic filters for reflective antennas, absorbers structures, etc. Several methods have been used for the analysis of FSS, among them, the Wave Method (WCIP). Are various shapes of elements that can be used in FSS, as for example, fractal type, which presents a relative geometric complexity. This work has as main objective to propose a simplification geometric procedure a fractal FSS, from the analysis of influence of details (gaps) of geometry of the same in behavior of the resonance frequency. Complementarily is shown a simple method to adjust the frequency resonance through analysis of a FSS, which uses a square basic cell, in which are inserted two reentrance and dimensions these reentrance are varied, making it possible to adjust the frequency. For this, the structures are analyzed numerically, using WCIP, and later are characterized experimentally comparing the results obtained. For the two cases is evaluated, the influence of electric and magnetic fields, the latter through the electric current density vector. Is realized a bibliographic study about the theme and are presented suggestions for the continuation of this work

Desenvolvimento de métodos construtivos e de novos materiais empregados na confecção de cartuchos de próteses de membros inferiores

The manufacture of prostheses for lower limb amputees (transfemural and transtibial) requires the preparation of a cartridge with appropriate and custom fit to the profile of each patient. The traditional process to the patients, mainly in public hospitals in Brazil, begins with the completion of a form where types of equipment, plugins, measures, levels of amputation etc. are identified. Currently, such work is carried out manually using a common metric tape and caliper of wood to take the measures of the stump, featuring a very rudimentary, and with a high degree of uncertainty geometry of the final product. To address this problem, it was necessary to act in two simultaneously and correlated directions. Originally, it was developed an integrated tool for viewing 3D CAD for transfemoral types of prostheses and transtibial called OrtoCAD I. At the same time, it was necessary to design and build a reader Mechanical equipment (sort of three-dimensional scanner simplified) able to obtain, automatically and with accuracy, the geometric information of either of the stump or the healthy leg. The methodology includes the application of concepts of reverse engineering to computationally generate the representation of the stump and/or the reverse image of the healthy member. The materials used in the manufacturing of prostheses nor always obey to a technical scientific criteria, because, if by one way it meets the criteria of resistance, by the other, it brings serious problems mainly due to excess of weight. This causes to the user various disorders due to lack of conformity. That problem was addressed with the creation of a hybrid composite material for the manufacture of cartridges of prostheses. Using the Reader Fitter and OrtoCAD, the new composite material, which aggregates the mechanical properties of strength and rigidity on important parameters such as low weight and low cost, it can be defined in its better way. Besides, it brings a reduction of up steps in the current processes of manufacturing or even the feasibility of using new processes, in the industries, in order to obtain the prostheses. In this sense, the hybridization of the composite with the combination of natural and synthetic fibers can be a viable solution to the challenges offered above

Simulação computacional da interação fluido-estrutura em bombas de cavidades progressivas

The pumping through progressing cavities system has been more and more employed in the petroleum industry. This occurs because of its capacity of elevation of highly viscous oils or fluids with great concentration of sand or other solid particles. A Progressing Cavity Pump (PCP) consists, basically, of a rotor - a metallic device similar to an eccentric screw, and a stator - a steel tube internally covered by a double helix, which may be rigid or deformable/elastomeric. In general, it is submitted to a combination of well pressure with the pressure generated by the pumping process itself. In elastomeric PCPs, this combined effort compresses the stator and generates, or enlarges, the clearance existing between the rotor and the stator, thus reducing the closing effect between their cavities. Such opening of the sealing region produces what is known as fluid slip or slippage, reducing the efficiency of the PCP pumping system. Therefore, this research aims to develop a transient three-dimensional computational model that, based on single-lobe PCP kinematics, is able to simulate the fluid-structure interaction that occurs in the interior of metallic and elastomeric PCPs. The main goal is to evaluate the dynamic characteristics of PCP s efficiency based on detailed and instantaneous information of velocity, pressure and deformation fields in their interior. To reach these goals (development and use of the model), it was also necessary the development of a methodology for generation of dynamic, mobile and deformable, computational meshes representing fluid and structural regions of a PCP. This additional intermediary step has been characterized as the biggest challenge for the elaboration and running of the computational model due to the complex kinematic and critical geometry of this type of pump (different helix angles between rotor and stator as well as large length scale aspect ratios). The processes of dynamic generation of meshes and of simultaneous evaluation of the deformations suffered by the elastomer are fulfilled through subroutines written in Fortan 90 language that dynamically interact with the CFX/ANSYS fluid dynamic software. Since a structural elastic linear model is employed to evaluate elastomer deformations, it is not necessary to use any CAE package for structural analysis. However, an initial proposal for dynamic simulation using hyperelastic models through ANSYS software is also presented in this research. Validation of the results produced with the present methodology (mesh generation, flow simulation in metallic PCPs and simulation of fluid-structure interaction in elastomeric PCPs) is obtained through comparison with experimental results reported by the literature. It is expected that the development and application of such a computational model may provide better details of the dynamics of the flow within metallic and elastomeric PCPs, so that better control systems may be implemented in the artificial elevation area by PCP

A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

Um estudo sobre o ensino-aprendizagem das demonstrações matemáticas

Demonstrations are fundamental instruments for Mathematics and, as such, are frequently used by mathematicians, math teachers and students. In fact, demonstrations are part of every Mathematics teaching environment, because Mathematics considers something true when it can be demonstrated. This is in contrast to other fields of knowledge that employ observation and experimentation to validate truth. This dissertation presents a study of the teaching and learning of demonstrations in Mathematics, describing a Teaching Module applied in a course on the Theory of Numbers offered by the Mathematics Department of the Universidade Federal do Rio Grande do Norte for mathematics majors. The objective of the dissertation was to propose and test a Teaching Module that can serve as a model for teaching demonstrations. The Teaching Module consisted of the following five steps: the application of a survey to determine the students‟ profiles and their previous knowledge of mathematical language and techniques of demonstration; the analysis of a series of dialogues containing arguments in everyday language; the investigation and analysis of the structure of some important techniques of demonstration; a written assessment; and, finally, an interview to further verify the principal results of the Teaching Module. The analysis of the data obtained though the classroom activities, written assessments and interviews led to the conclusion that there was a significant amount of assimilation of the issue at the level of relational understanding, (SKEMP, 1980). These instruments verified that the students attained considerable improvement in their use of mathematical language and of the techniques of demonstration presented. Thus, the evidence supports the conclusion that the proposed Teaching Module is an effective means for the teaching/learning of mathematical demonstration and, as such, provides a methodological guide which may lay the foundations for a new approach to this important subject

Condições de energia de hawking e ellis e a equação de raychaudhuri

In the Einstein s theory of General Relativity the field equations relate the geometry of space-time with the content of matter and energy, sources of the gravitational field. This content is described by a second order tensor, known as energy-momentum tensor. On the other hand, the energy-momentum tensors that have physical meaning are not specified by this theory. In the 700s, Hawking and Ellis set a couple of conditions, considered feasible from a physical point of view, in order to limit the arbitrariness of these tensors. These conditions, which became known as Hawking-Ellis energy conditions, play important roles in the gravitation scenario. They are widely used as powerful tools for analysis; from the demonstration of important theorems concerning to the behavior of gravitational fields and geometries associated, the gravity quantum behavior, to the analysis of cosmological models. In this dissertation we present a rigorous deduction of the several energy conditions currently in vogue in the scientific literature, such as: the Null Energy Condition (NEC), Weak Energy Condition (WEC), the Strong Energy Condition (SEC), the Dominant Energy Condition (DEC) and Null Dominant Energy Condition (NDEC). Bearing in mind the most trivial applications in Cosmology and Gravitation, the deductions were initially made for an energy-momentum tensor of a generalized perfect fluid and then extended to scalar fields with minimal and non-minimal coupling to the gravitational field. We also present a study about the possible violations of some of these energy conditions. Aiming the study of the single nature of some exact solutions of Einstein s General Relativity, in 1955 the Indian physicist Raychaudhuri derived an equation that is today considered fundamental to the study of the gravitational attraction of matter, which became known as the Raychaudhuri equation. This famous equation is fundamental for to understanding of gravitational attraction in Astrophysics and Cosmology and for the comprehension of the singularity theorems, such as, the Hawking and Penrose theorem about the singularity of the gravitational collapse. In this dissertation we derive the Raychaudhuri equation, the Frobenius theorem and the Focusing theorem for congruences time-like and null congruences of a pseudo-riemannian manifold. We discuss the geometric and physical meaning of this equation, its connections with the energy conditions, and some of its several aplications.

Polaritons de exciton em super-redes semicondutoras

In this work we study the spectrum (bulk and surface modes) of exciton-polaritons in infinite and semi-infinite binary superlattices (such as, ···ABABA···), where the semiconductor medium (A), whose dielectric function depends on the frequency and the wavevector, alternating with a standard dielectric medium B. Here the medium A will be modeled by a nitride III-V semiconductor whose main characteristic is a wide-direct energy gap Eg. In particular, we consider the numerical values of gallium nitride (GaN) with a crystal structure wurtzite type. The transfer-matrix formalism is used to find the exciton-polariton dispersion relation. The results are obtained for both s (TE mode: transverse electric) and p (TM mode: transverse magnetic) polarizations, using three diferent kind of additional boundary conditions (ABC1, 2 e 3) besides the standard Maxwell's boundary conditions. Moreover, we investigate the behavior of the exciton-polariton modes for diferent ratios of the thickness of the two alternating materials forming the superlattice. The spectrums shows a confinement of the exciton-polariton modes due to the geometry of the superlattice. The method of Attenuated Total Reflection (ATR) and Raman scattering are the most adequate for probing this excitations

Fermion localization on a split brane

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estruturas tectônicas cenozóicas na porção leste da Bacia Potiguar - RN

This thesis encompasses the integration of geological, geophysical, and seismological data in the east part of the Potiguar basin, northeastern Brazil. The northeastern region is located in South American passive margin, which exhibits important areas that present neotectonic activity. The definition of the chronology of events, geometry of structures generated by these events, and definition of which structures have been reactivated is a necessary task in the region. The aims of this thesis are the following: (1) to identify the geometry and kinematics of neotectonic faults in the east part of the Potiguar basin; (2) to date the tectonic events related to these structures and related them to paleoseismicity in the region; (3) to present evolutional models that could explain evolution of Neogene structures; (4) and to investigate the origin of the reactivation process, mainly the type of related structure associated with faulting. The main type of data used comprised structural field data, well and resistivity data, remote sensing imagery, chronology of sediments, morphotectonic analysis, x-ray analysis, seismological and aeromagnetic data. Paleostress analysis indicates that at least two tectonic stress fields occurred in the study area: NSoriented compression and EW-oriented extension from the late Campanian to the early Miocene and EW-oriented compression and NS-oriented extension from the early Miocene to the Holocene. These stress fields reactivated NE-SW- and NW-SE-trending faults. Both set of faults exhibit right-lateral strike-slip kinematics, associated with a minor normal component. It was possible to determine the en echelon geometry of the Samambaia fault, which is ~63 km long, 13 km deep, presents NE-SW trend and strong dip to NW. Sedimentfilled faults in granite rocks yielded Optically Stimulated Luminescence (OSL) and Single-Aliquot Regeneration (SAR) ages at 8.000 - 9.000, 11.000 - 15.000, 16.000 - 24.000, 37.000 - 45.500, 53.609 - 67.959 e 83.000 - 84.000 yr BP. The analysis of the ductile fabric in the João Câmara area indicate that the regional foliation is NE-SW-oriented (032o - 042o), which coincides with the orientation of the epicenters and Si-rich veins. The collective evidence points to reactivation of preexisting structures. Paleoseismological data suggest paleoseismic activity much higher than the one indicated by the short historical and instrumental record

Evolução tectono-estrutural do Campo de Xaréu (Sub-bacia de Mundaú, Bacia do Ceará - NE do Brasil: abordagem multiescala e pluriferramental

The Xaréu Oil Field, located in the center-southern portion of the Mundaú Sub-Basin (eastern portion of the Ceará Basin), is characterized by a main Iramework of NW-trending and NE-dipping faults. The faults in the Xaréu Oil Field, among which the Xaréu Fautt stands out, are arranged according to an extensional-listriclan, rooted on a detachment surface corresponding to the Mundaú Fault, the border fautt of Mundaú Sub-Basin. During the tectonic-structural evolution of the Xaréu Oil Field and the Mundaú Sub-Basin, the Mundaú Fault played a crucial role on the control of the geometry of both compartments. The main carbonatic unit in the Xaréu Oil Field, named the Trairí Member(Paracuru Formation of Late Aptian to Early Albian age), contains the largest oil volume in the field, concentrated in structurally-controlled accumulations. The Trairí Member is composed by a variety of carbonatic rocks (massive, bedded or laminated calcilutites, ostracodites, calcarenites and carbonatic rudites, all of them presenting variable degrees of dolomitization). The carbonatic rocks are interbedded into thick packages of black shales and marls, besides local beds of siliciclastic conglomerates, sandstones, siltnes and argillites. From the spatial association and the genetic relationships between the carbonatic and siliciclastic units, it is possible to group them in three lithofacies associations (Marginal Plain, Ramp and Lacustrine Interior) that, together, were developed in a lacustrine system associated to a marginal sabkha. Structural studies based on drill coresthat sample the Trairí Member in the Xaréu Oil Field allowed to characterize two generations of meso- to microscale structures: the D1 group presents a typical hydroplastic character, being characterized by intra/interstratal to oblique-bedding shear zones. The hydroplastic character related to these structures allowed to infer their development at an early-lithilication stage of the Trairí Member, leading to infer an Early Cretaceous age to them. The second group of structures identified in the drill cores, nominated D2 and ascribed to a Neogene age, presents a strictly brttle character, being typilied by normal faults and slickenfibers of re-crystallized clayminerals, ali olthem displaying variable orientations. Although the present faults in the Xaréu Oil Field (and, consequently, in the Mundaú Sub-Basin) were classically relerred as struetures of essentially normal displacement, the kinematics analysis of the meso-to microscaie D1 struetures in the drill cores led to deline oblique displacements (normal with a clockwise strike-slip component) to these faults, indicating a main tectonic transport to ENE. These oblique movements would be responsible for the installation of a transtensive context in the Mundaú Sub-Basin, as part of the transcurrent to translormant opening of the Atlantic Equatorial Margin. The balancing of four struetural cross-sections ofthe Xaréu Oil Field indicates that the Mundaú Fault was responsible for more than 50% of the total stretching (ß factor) registered during the Early Aptian. At the initial stages of the "rifting", during Early Aptianuntil the Holocene, the Mundaú Sub-Basin (and consequently the Xaréu Oil Fleld) accumulated a total stretching between 1.21 and 1.23; in other words, the crust in this segment of the Atlantic Equatorial Margin was subjeeted to an elongation of about 20%. From estimates of oblique displacements related to the faults, it ws possible to construct diagrams that allow the determination of stretching factors related to these displacements. Using these diagrams and assuming the sense 01 dominant teetonictransport towards ENE, it was possible to calculate the real stretching lactors related to the oblique movement 0 of the faults in the Mundaú Sub-Basin. which reached actual values between 1.28 and 1.42. ln addnion to the tectonic-structural studies in the Xaréu Oil Field, the interpretation of remote sensing products, coupled wnh characterization of terrain analogues in seleeted areas along the northern Ceará State (continental margins of the Ceará and Potiguar basins), provided addnional data and constraints about the teetonic-structural evolution of the oil lield. The work at the analogue sites was particularly effective in the recognition and mapping, in semidetail scale, several generations of struetures originated under a brittle regime. Ali the obtained information (from the Xaréu Oil Field, the remote sensor data and the terrain analogues) were jointly interpreted, culminating with the proposnion of an evolutionary model lor this segment of the Atlantic Equatorial Margin; this model that can be applied to the whole Margin, as well. This segmentof the Atlantic Equatorial Margin was delormedin an early E-W (when considered lhe present-day position of the South American Plate) transcurrent to transform regime with dextral kinematics, started Irom, at least, the Early Aptian, which left its record in several outcrops along the continental margin of the Ceará State and specilically in the Xaréu off Field. The continuous operation of the regime, through the Albian and later periods, led to the definitive separation between the South American and African plates, with the formation of oceanic lithosphere between the two continental blocks, due to the emplacement off spreading centers. This process involved the subsequent transition of the transcurrent to a translorm dextral regime, creating lhe Equatorial Atlantic Oceano With the separation between the South American and African plates already completed and the increasing separation between lhe continental masses, other tecton ic mechanisms began to act during the Cenozoic (even though the Cretaceous tectonic regime lasted until the Neogene), like an E-W compressive stress líeld (related to the spreading olthe oceanic floor along lhe M id-Atlantic Ridge and to the compression of the Andean Chain) effective Irom the Late Cretaceous, and a state of general extension olthe horizontal surface (due to the thermal uplift ofthe central portion of Borborema Province), effective during the Neogene. The overlap of these mechanisms during the Cenozoic led to the imprint of a complex tectonic framework, which apparently influenced the migration and entrapment 01 hydrocarbon in the Ceará Basin

Proposta metodológica para o imageamento, caracterização, parametrização e geração de modelos virtuais de afloramentos

The aim of this work was to describe the methodological procedures that were mandatory to develop a 3D digital imaging of the external and internal geometry of the analogue outcrops from reservoirs and to build a Virtual Outcrop Model (VOM). The imaging process of the external geometry was acquired by using the Laser Scanner, the Geodesic GPS and the Total Station procedures. On the other hand, the imaging of the internal geometry was evaluated by GPR (Ground Penetrating Radar).The produced VOMs were adapted with much more detailed data with addition of the geological data and the gamma ray and permeability profiles. As a model for the use of the methodological procedures used on this work, the adapted VOM, two outcrops, located at the east part of the Parnaiba Basin, were selected. On the first one, rocks from the aeolian deposit of the Piaui Formation (Neo-carboniferous) and tidal flat deposits from the Pedra de Fogo Formation (Permian), which arises in a large outcrops located between Floriano and Teresina (Piauí), are present. The second area, located at the National Park of Sete Cidades, also at the Piauí, presents rocks from the Cabeças Formation deposited in fluvial-deltaic systems during the Late Devonian. From the data of the adapted VOMs it was possible to identify lines, surfaces and 3D geometry, and therefore, quantify the geometry of interest. Among the found parameterization values, a table containing the thickness and width, obtained in canal and lobes deposits at the outcrop Paredão and Biblioteca were the more relevant ones. In fact, this table can be used as an input for stochastic simulation of reservoirs. An example of the direct use of such table and their predicted radargrams was the identification of the bounding surface at the aeolian sites from the Piauí Formation. In spite of such radargrams supply only bi-dimensional data, the acquired lines followed of a mesh profile were used to add a third dimension to the imaging of the internal geometry. This phenomenon appears to be valid for all studied outcrops. As a conclusion, the tool here presented can became a new methodology in which the advantages of the digital imaging acquired from the Laser Scanner (precision, accuracy and speed of acquisition) were combined with the Total Station procedure (precision) using the classical digital photomosaic technique