Chebychev semi-discretizations for both ordinary and partial differential equations are explored. The Helmholtz, heat, Schrӧdinger and 15° migration equations are investigated. The Galerkin, pseudospectral and tau projection operators are employed, while the Crank-Nicolson scheme is used for the integration of the time (depth) dependence. The performance of the Chebychev scheme is contrasted with the performance of the finite difference scheme for Dirichlet and Neumann boundary conditions. Comparisons between all finite difference, Fourier and Chebychev migration algorithms are drawn as well. Chebychev expansions suffer from neither the artificial dispersion dispersion of finite difference approximations nor the demand for a periodic boundary structure of Fourier expansions. Thus, it is shown that finite difference schemes require at least one order of magnitude more points in order to match the accuracy level of the Chebychev schemes. In addition, the Chebychev migration algorithm is shown to be free of the wraparound problem, inherent in migration procedures based on Fourier transform. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

"July 2004" / Bibliography: leaves 215-230. / viii, 230 leaves : ill., maps ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, School of Chemistry and Physics, Discipline of Physics, 2004

Orientadores: Joerg Dietrich Wilhelm Schleicher, Maria Amelia Novais Schleicher / Tese (doutorado - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T12:49:36Z (GMT). No. of bitstreams: 1 Pila_MatheusFabiano_D.pdf: 9692582 bytes, checksum: 422912b9753d685de0277a6d91cf8f0a (MD5) Previous issue date: 2011 / Resumo: Entende-se por datum a superfície onde estão posicionados os pares fonte-receptor usados na aquisição sísmica. Este datum pode ser plano ou irregular e sua profundidade pode variar. O objetivo da redatumação é transformar o dado sísmico adquirido na superfície original em um dado simulado adquirido em outra superfície. Obtém-se assim um novo dado, como se tivesse sido adquirido em uma superfície de geometria e profundidade diferentes. A vantagem deste processo seria eliminar a propagação indesejada da onda sísmica em camadas com forte variação na velocidade. A transformação correta das amplitudes, do dado na superfície original para os dados no novo datum, é de importância fundamental. Um dado com esta propriedade poderia ser usado em diversos processos que necessitam de um dado com amplitude verdadeira, possibilitando melhor caracterização de possíveis reservatórios, por exemplo. Um destes processos seria a migração Kirchhoff em amplitude verdadeira. Na literatura, existem trabalhos que discutem e comprovam que uma transformação de configuração em amplitude verdadeira pode ser obtida encadeando os processos de migração e demigração com funções peso. Nesta tese, nós estendemos este resultado e derivamos um operador de redatumação em amplitude verdadeira, ao considerar que neste encadeamento podemos também mudar a profundidade dos pares fonte-receptor, tanto no dado sísmico de entrada quanto no simulado de saída. Processos Kirchhoff como este dependem de um bom modelo de velocidades para poder calcular as correções de tempo de trânsito de cada traço. Ao longo deste trabalho, foi possível verificar como a cinemática da redatumação independe da velocidade abaixo do novo datum. Esta velocidade afeta apenas a função peso que corrige as amplitudes. No entanto, após alguns testes foi possível verificar que pequenas incertezas inseridas nesta variável produzem pouco erro relativo na amplitude final / Abstract: The surface where the source-receiver pairs used in the seismic aquisition are positioned is called a datum. This datum can be flat or irregular and the depth may vary. The main goal of redatuming is to transform the seismic data acquired on the original surface into simulated data as if acquired on another datum. The advantage of this process is that it can eliminate undesired seismic wave propagation in layers with strong velocity variation or strong topography. The correct amplitude transformation, from the original surface data to the new datum, is of fundamental importance if the data are to be used in subsequent true-amplitude processes that allow better characterization of potential reservoirs, for example. One of these processes is the true-amplitude migration. In the literature, there are studies that argue and prove that a true-amplitude configuration transform can be obtained by chaining the weighted migration and demigration integral operators. In this thesis, we extend this result and derive a true-amplitude redatuming operator. For this purpuse, we consider that in this chaining procedure, we can also change the depth of the source-receiver pairs, either in the input or simulated output configuration. Kirchhoff processes like this one depend on a good velocity model in order to calculate traveltime corrections for each trace. Throughout this work, we demonstrated that the kinematics of redatuming is independent of the velocity below the new datum. This velocity affects only the weight function that corrects the amplitudes. However, our numerical tests indicated that small uncertainties inserted in this variable resulted in little relative error in the final amplitude / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

[Truncated abstract] A number of controlled and natural seismic sources are utilised to model the Pwave velocity structure of the southwest of the Yilgarn Craton, Western Australia. The Yilgarn Craton is one of the largest pieces of Archaean crust in the world and is known for its gold and nickel deposits in the east and intraplate seismicity in the west. The aim of the project is to link 2D and 3D models of variations in seismic velocity with the local seismicity and geology. A new set of seismic refraction data, acquired in 25 overlapping deployments between 2002 and 2005, has been processed, picked and analysed using forward modelling. The data comprise two perpendicular traverses of three-component recordings of various delay-fired blasts from local commercial quarries. The data were processed using a variety of techniques. Tests were carried out on a number of data enhancement and picking procedures in order to determine the best method for enhancement of delay-fired data. A new method for automatic phase recognition is presented, where the maximum of the derivative of the rectilinearity of a trace is taken as the first break. Complete shot gathers with first break picks for each seismic source are compiled from the overlapping deployments. ... The starting 3D model was based on the models produced by 2D forward modelling. 14 iterations were carried out and the best-fit 3D model was achieved at the 10th iteration. It is 35% better then the current model used to locate earthquakes in this region. The resultant velocity block model was used to iii construct a density block model. A relative gravity map of the southwest of Yilgarn Craton was made. The results of 2D forward modelling, 3D tomography and forward gravity modelling have been compared and it was found that the HVZ is present in all models. Such a zone has been previously seen on a single seismic refraction profile, but it is the first time, this zone has been mapped in 3D. The gravity high produced by the zone coincides with the gravity high observed in reality. There is strong evidence that suggests that the HVZ forms part of the Archaean terrane boundary within the Yilgarn Craton. The distribution of the local seismicity was then discussed in the framework of the new 3D velocity model. A hypothesis, that the primary control on the seismicity in the study area is rotation of the major horizontal stress orientation, is presented. It is also argued that the secondary control on seismicity in the SWSZ is accommodation of movements along major faults.

Orientadores: João Marcos Travassos Romano, Leonardo Tomazeli Duarte / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-23T23:21:46Z (GMT). No. of bitstreams: 1 Zanetti_RicardoAntonio_M.pdf: 21586747 bytes, checksum: 452b3dadea31fa37e922d925b45c10be (MD5) Previous issue date: 2013 / Resumo: : O Resumo poderá ser visualizado no texto completo da tese digital / Abstract: : The complete Abstract is available with the full electronic / Mestrado / Telecomunicações e Telemática / Mestre em Engenharia Elétrica