Parâmetro de regularização em problemas inversos: estudo numérico com a transformada de Radon

In general, an inverse problem corresponds to find a value of an element x in a suitable vector space, given a vector y measuring it, in some sense. When we discretize the problem, it usually boils down to solve an equation system f(x) = y, where f : U Rm ! Rn represents the step function in any domain U of the appropriate Rm. As a general rule, we arrive to an ill-posed problem. The resolution of inverse problems has been widely researched along the last decades, because many problems in science and industry consist in determining unknowns that we try to know, by observing its effects under certain indirect measures. Our general subject of this dissertation is the choice of Tykhonov´s regulaziration parameter of a poorly conditioned linear problem, as we are going to discuss on chapter 1 of this dissertation, focusing on the three most popular methods in nowadays literature of the area. Our more specific focus in this dissertation consists in the simulations reported on chapter 2, aiming to compare the performance of the three methods in the recuperation of images measured with the Radon transform, perturbed by the addition of gaussian i.i.d. noise. We choosed a difference operator as regularizer of the problem. The contribution we try to make, in this dissertation, mainly consists on the discussion of numerical simulations we execute, as is exposed in Chapter 2. We understand that the meaning of this dissertation lays much more on the questions which it raises than on saying something definitive about the subject. Partly, for beeing based on numerical experiments with no new mathematical results associated to it, partly for being about numerical experiments made with a single operator. On the other hand, we got some observations which seemed to us interesting on the simulations performed, considered the literature of the area. In special, we highlight observations we resume, at the conclusion of this work, about the different vocations of methods like GCV and L-curve and, also, about the optimal parameters tendency observed in the L-curve method of grouping themselves in a small gap, strongly correlated with the behavior of the generalized singular value decomposition curve of the involved operators, under reasonably broad regularity conditions in the images to be recovered

Análise de terrenos na porção setentrional da Província Borborema, NE do Brasil: integração de dados geológicos e gravimétricos

It is presently assumed that the Borborema Province resulted from a complex collisional process associated with the convergent movement of plates, possibly involving amalgamation and accretion of microplates. This process was consolidated at the end of the Brasiliano event. It is investigated the possible limits for the tectonostratigraphic terranes in the northern portion of the province based on an integrated study of geological and gravity data. The study area comprises the portion of the Borborema Province located north of the Patos Lineament, limited by longitudes 33º00 W and 43º29 44"W and latitudes 1º36 S and 8º00 S. A revision of the regional geology allowed to identify areas presenting contrasting geological attributes, possibly representing different terranes whose limits are always shear zones of Brasiliano-age. The Sobral-Pedro II shear zone is the only one undoubtedly presenting geological attributes of sutures zones. The other shear zones are very likely associated with a geodinymic context of accretion, involving oblique collisions (docking), transcurrent and/or transforming sutures, and deep intracrustal shear zones. The gravity data contributed as a tool to identify strong lateral contrasts of density inside the upper crust possibly associated with crustal blocks tectonically juxtaposed. The dominant long wavelength anomaly in the Bouguer anomaly map is an expressive gradient, grossly parallel to the continental margin, caused by density variation across the crust-mantle interface in the transition from the continental crust to the oceanic crust originated by the separation between South America and Africa. Medium to small wavelength anomalies are due to intracrustal heterogeneities such as different Precambrian crustal blocks, Brasiliano-age granites and Mesozoic sedimentary basins. A regional-residual separation of the Bouguer anomaly map was performed in order to enhance in the residual map the effect due to intracrustal heterogeneities. The methodology used for this separation was a robust polinomial fitting. The inversion of residual gravity field resulted in a density contrast map (Δρ), in an equivalent layer that provided more accurated anomalies contours and consolidated the model which the sources of residual anomalies are located in the upper part of the present crust. Based on the coincidence of gravity lineaments in the residual map and Brasiliano shear zones, and using additional geological information, the following shear zones are proposed as limits between terranes: Patos shear zone, Sobral-Pedro II shear zone, Picuí-João Câmara shear zone, Remígio-Pocinhos shear zone, Senador Pompeu shear zone, Tauá shear zone, and Portalegre shear zone. Based on the geological/geophysical information it is attributed a higher level of confidence to the first three proposed limits(Patos, Sobral Pedro II, and Picuí-João Câmara shear zones). From west to east, these shear zones individualize the following terranes: Northwest of Ceará terrane, Central Ceará terrane, Tauá terrane, Orós-Jaguaribe terrane, Seridó terrane, and São José de Campestre terrane. In our study, the Rio Piranhas and Patos terranes are questioned because their previously proposed limits do not present good geological and gravimetric evidences. On the other hand, the previously proposed Cearense terrane is now subdivided into Central Ceará and Tauá terranes. Two residual gravity profiles located in the Seridó belt were interpreted using 2 ½ D direct gravity modeling. The main result of the modeling process is that all anomalies, with the exception of one, can be explained by outcroppring bodies, therefore restricted to the upper part of the present crust

Estudo do potencial da técnica de nanossísmica para o monitoramento de hidrofraturamento em reservatórios de hidrocarbonetos

Hydraulic fracturing is an operation in which pressurised fluid is injected in the geological formation surrounding the producing well to create new permeable paths for hydrocarbons. The injection of such fluids in the reservoir induces seismic events. The measurement of this reservoir stimulation can be made by location these induced microseismic events. However, microseismic monitoring is an expensive operation because the acquisition and data interpretation system using in this monitoring rely on high signal-to-noise ratios (SNR). In general, the sensors are deployed in a monitoring well near the treated well and can make a microseismic monitoring quite an expensive operation. In this dissertation we propose the application of a new method for recording and location of microseismic events called nanoseismic monitoring (Joswig, 2006). In this new method, a continuous recording is performed and the interpreter can separate events from noise using sonograms. This new method also allows the location of seismic sources even when P and S phases onsets are not clear like in situations of 0 dB SNR. The clear technical advantage of this new method is also economically advantageous since the sensors can potentially be installed on the surface rather than in observation well. In this dissertation field tests with controlled sources were made. In the first test small explosives using fire works at 28 m (slant distances) were detected yealding magnitudes between -2.4 ≤ ML ≤ -1.6.. In a second test, we monitored perforation shots in a producing oil field. In this second test, one perforation shot was located with slant distances of 861 m and magnitude 2.4 ML. Data from the tests allow us to say that the method has potential to be used in the oil industry to monitor hydrofracture

Dinâmica costeira entre as praias de Areia Preta e do Forte, Natal/RN

The coastal zone has been studied worldwide with a focus on the coastal erosion. In the present days, much of the world's coastlines are being affected by erosion, which causes great damage to the economy. This work had as study case the beaches of Areia Preta, Artistas, Meio and Forte located in Natal in Rio Grande do Norte. It shows as result the monitoring of the beach strip that makes possible to obtain quantitative and qualitative data, allows the study of the coastal dynamics of the beaches and the Recovery Project of the Areia Preta beach interference on adjacent beaches. This research was guided by the integrated analysis method on the systemic perspective. The pratical procedures adopted were: bibliographic research; fieldwork during eleven months (environmental characterization, collection of hydrodynamic data, topographic leveling, collection of sediments) and; sedimentological analysis of samples collected. By monitoring of the points A, B, C, D and E we were able to find the occurrence of the coastal erosion on their biggest part except by the C and D profiles. It was noted the need for the government to complete the hydraulic fill, as it made only 60% of the landfill planed. It was found that the spikes built on the beach of Areia Preta are preventing the natural transport of sediments that the longshore performs towards South-North. This interference is causing the lack of sediment on the beaches of Forte and Meio and their coastal erosion in consequence