Processo de difusão com agregação e reorganização espontânea em uma rede 2D

Difusive processes are extremely common in Nature. Many complex systems, such as microbial colonies, colloidal aggregates, difusion of fluids, and migration of populations, involve a large number of similar units that form fractal structures. A new model of difusive agregation was proposed recently by Filoche and Sapoval [68]. Based on their work, we develop a model called Difusion with Aggregation and Spontaneous Reorganization . This model consists of a set of particles with excluded volume interactions, which perform random walks on a square lattice. Initially, the lattice is occupied with a density p = N/L2 of particles occupying distinct, randomly chosen positions. One of the particles is selected at random as the active particle. This particle executes a random walk until it visits a site occupied by another particle, j. When this happens, the active particle is rejected back to its previous position (neighboring particle j), and a new active particle is selected at random from the set of N particles. Following an initial transient, the system attains a stationary regime. In this work we study the stationary regime, focusing on scaling properties of the particle distribution, as characterized by the pair correlation function ø(r). The latter is calculated by averaging over a long sequence of configurations generated in the stationary regime, using systems of size 50, 75, 100, 150, . . . , 700. The pair correlation function exhibits distinct behaviors in three diferent density ranges, which we term subcritical, critical, and supercritical. We show that in the subcritical regime, the particle distribution is characterized by a fractal dimension. We also analyze the decay of temporal correlations

Remoção de ruídos sísmicos utilizando transformada de wavelet 1D e 2D com software em desenvolvimento

In the Hydrocarbon exploration activities, the great enigma is the location of the deposits. Great efforts are undertaken in an attempt to better identify them, locate them and at the same time, enhance cost-effectiveness relationship of extraction of oil. Seismic methods are the most widely used because they are indirect, i.e., probing the subsurface layers without invading them. Seismogram is the representation of the Earth s interior and its structures through a conveniently disposed arrangement of the data obtained by seismic reflection. A major problem in this representation is the intensity and variety of present noise in the seismogram, as the surface bearing noise that contaminates the relevant signals, and may mask the desired information, brought by waves scattered in deeper regions of the geological layers. It was developed a tool to suppress these noises based on wavelet transform 1D and 2D. The Java language program makes the separation of seismic images considering the directions (horizontal, vertical, mixed or local) and bands of wavelengths that form these images, using the Daubechies Wavelets, Auto-resolution and Tensor Product of wavelet bases. Besides, it was developed the option in a single image, using the tensor product of two-dimensional wavelets or one-wavelet tensor product by identities. In the latter case, we have the wavelet decomposition in a two dimensional signal in a single direction. This decomposition has allowed to lengthen a certain direction the two-dimensional Wavelets, correcting the effects of scales by applying Auto-resolutions. In other words, it has been improved the treatment of a seismic image using 1D wavelet and 2D wavelet at different stages of Auto-resolution. It was also implemented improvements in the display of images associated with breakdowns in each Auto-resolution, facilitating the choices of images with the signals of interest for image reconstruction without noise. The program was tested with real data and the results were good

Fractais e Percolação na Recuperação de Petróleo

The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points

Fractais e percolação na recuperação de Petróleo

The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points. In oil recovery terminology, the given single point can be mapped to an injection well (injector) and the multiple other points to production wells (producers). In the previously standard case of one injection well and one production well separated by Euclidean distance r, the distribution of shortest paths l, P(l|r), shows a power-law behavior with exponent gl = 2.14 in 2D. Here we analyze the situation of one injector and an array A of producers. Symmetric arrays of producers lead to one peak in the distribution P(l|A), the probability that the shortest path between the injector and any of the producers is l, while the asymmetric configurations lead to several peaks in the distribution. We analyze configurations in which the injector is outside and inside the set of producers. The peak in P(l|A) for the symmetric arrays decays faster than for the standard case. For very long paths all the studied arrays exhibit a power-law behavior with exponent g ∼= gl.

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