Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2016-06-23T21:42:48Z No. of bitstreams: 1 TiagoCavalcantiDaRocha_DISSERT.pdf: 2006470 bytes, checksum: 040fe0cabeb92d020f46f16a7d13eca9 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2016-06-28T21:30:50Z (GMT) No. of bitstreams: 1 TiagoCavalcantiDaRocha_DISSERT.pdf: 2006470 bytes, checksum: 040fe0cabeb92d020f46f16a7d13eca9 (MD5) / Made available in DSpace on 2016-06-28T21:30:50Z (GMT). No. of bitstreams: 1 TiagoCavalcantiDaRocha_DISSERT.pdf: 2006470 bytes, checksum: 040fe0cabeb92d020f46f16a7d13eca9 (MD5) 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.