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Previous issue date: 2016-02-01 / Na ?rea do petr?leo os dados s?smicos geralmente s?o irregulares e esparsamente amostrados ao longo das coordenadas espaciais em raz?o de obst?culos na coloca??o dos geofones. M?todos de Fourier s?o eficientes se os dados de entrada est?o em uma grade de amostragem regular. Entretanto, quando o m?todo de Fourier ? aplicado a um conjunto de dados amostrados irregularmente, a ortogonalidade entre as componentes de Fourier deixam de existir e a energia de uma componente de Fourier pode ?vazar? para outros componentes, fen?meno chamado de ?vazamento espectral?. O objetivo da pesquisa desta disserta??o ? estudar a representa??o espectral de dados amostrados irregularmente. Em particular, ser? apresentada a estrutura b?sica da representa??o da transformada de Fourier n?o igualmente espa?ada (NDFT - nonuniform discrete Fourier transform), estudo de suas propriedades e demonstra??o do seu potencial no processamento do sinal s?smico. Para isso, estudamos a transformada de Fourier r?pida (FFT? - fast Fourier transform) e a transformada de Fourier r?pida n?o igualmente espa?ada (NFFT - nonuniform fast Fourier transform) que calculam rapidamente a transformada de Fourier discreta (DFT - discrete Fourier transform) e a NDFT, respectivamente. Comparamos a recupera??o do sinal usando a FFT, NDFT e NFFT. Abordamos a interpola??o do tra?o s?smico usando a transformada de Fourier anti-vazamento (ALFT - antileakage Fourier transform) para superar o problema do vazamento espectral causado pela amostragem irregular. As aplica??es a dados sint?ticos e dados reais mostraram que o m?todo ALFT funciona bem em dados s?smicos de geologia complexa, sofre pouco com a amostragem espacial irregular dos dados e os efeitos de borda e ? robusto e est?vel com dados com ru?do. Entretanto, n?o ? t?o eficiente quanto o FFT e sua reconstru??o n?o ? t?o boa no caso de preenchimento irregular de grandes buracos na aquisi??o. / In the oil prospection research seismic data are usually irregular and sparsely sampled along
the spatial coordinates due to obstacles in placement of geophones. Fourier methods provide a
way to make the regularization of seismic data which are efficient if the input data is sampled
on a regular grid. However, when these methods are applied to a set of irregularly sampled
data, the orthogonality among the Fourier components is broken and the energy of a Fourier
component may "leak" to other components, a phenomenon called "spectral leakage". The
objective of this research is to study the spectral representation of irregularly sampled data
method. In particular, it will be presented the basic structure of representation of the NDFT
(nonuniform discrete Fourier transform), study their properties and demonstrate its potential
in the processing of the seismic signal. In this way we study the FFT (fast Fourier transform)
and the NFFT (nonuniform fast Fourier transform) which rapidly calculate the DFT (discrete
Fourier transform) and NDFT. We compare the recovery of the signal using the FFT, DFT
and NFFT. We approach the interpolation of seismic trace using the ALFT (antileakage
Fourier transform) to overcome the problem of spectral leakage caused by uneven sampling.
Applications to synthetic and real data showed that ALFT method works well on complex
geology seismic data and suffers little with irregular spatial sampling of the data and edge
effects, in addition it is robust and stable with noisy data. However, it is not as efficient as the
FFT and its reconstruction is not as good in the case of irregular filling with large holes in the
acquisition.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/20815 |
| Date | 01 February 2016 |
| Creators | Rocha, Tiago Cavalcanti da |
| Contributors | 00405663404, http://lattes.cnpq.br/7151949476055522, Silva, Luciano Rodrigues da, 07416407400, http://lattes.cnpq.br/5182830756789229, R?go, H?nio Henrique Arag?o, 78598834491, http://lattes.cnpq.br/3002951945786094, Freitas, Joaquim Elias de, 00588750425, http://lattes.cnpq.br/6051109030233375, Corso, Gilberto, Lucena, Liacir dos Santos |
| Publisher | Universidade Federal do Rio Grande do Norte, PROGRAMA DE P?S-GRADUA??O EM CI?NCIA E ENGENHARIA DE PETR?LEO, UFRN, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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