Produção Científica

**Apresentação**

Numerical integration in the Calculation of the 2.5-D Response of a Very Large LoopValdelÃrio da Silva e Silva, CÃcero RÃ©gis, Allen Q. Howard Jr., Universidade Federal do ParÃ¡ and National Institute of Science and Technology of Petroleum Geophysics SUMMARY This work presents the details of a procedure for the numerical integration of Hankel transforms in the calculation of the electromagnetic fields generated by a large horizontal loop over a 2D earth. The method performs the integration by deforming the integration path into the complex plane and applying Cauchyâ€™s theorem on a modified version of the integrand. The modification is the replacement of the Bessel functions J0 and J1 by the Hankel functions H(1) 0 and H(1) 1 . The integration on a path going up the complex plane allows us to take advantage of the vanishing properties of the Hankel functions, so that we can calculate on very small segments, instead of the infinite line of the original improper integrals. We have applied the method to calculate the fields of very large loops, at distances and depths which are prohibitive for the traditional numerical integration methods. |

**Apresentação**

Separate P- and SV-wave equations for VTI mediaReynam C. Pestana, CPGG/UFBA and INCT-GP/CNPQ, BjÃ¸rn Ursin, Norwegian University of Science and Technology (NTNU) and Paul L. Stoffa, University of Texas at Austin, Institute for Geophysics SUMMARY In isotropic media we use the scalar acoustic wave equation to perform reverse time migration (RTM) of the recorded pressure wavefield data. In anisotropic media P- and SV-waves are coupled and the elastic wave equation should be used for RTM. However, an acoustic anisotropic wave equation is often used instead. This results in significant shear wave energy in both modeling and RTM. To avoid this undesired SV-wave energy, we propose a different approach to separate P- and SV-wave components for vertical transversely isotropic (VTI) media. We derive independent pseudo-differential wave equations for each mode. The derived equations for P- and SV-waves are stable and reduce to the isotropic case. The equations presented here can be effectively used to model and migrate seismic data in VTI media where |e âˆ’d| is small. The SV-wave equation we develop is now well-posed and triplications in the SV wavefront are removed resulting in stable wave propagation. We show modeling and RTM results using the derived pure P-wave mode in complex VTI media and use the rapid expansion method (REM) to propagate the wavefields in time. |

**Apresentação**

A experiÃªncia nos programas pioneiros de pesquisa e formaÃ§Ã£o de mestres e doutores em geofÃsica para exploraÃ§Ã£o de petrÃ³leo em parceria com a PETROBRAS, o CNPq e a FINEP, na UFBA e na UFPAConferÃªncia apresentada no 1Âº Workshop do INCT-GP pelo Prof. Carlos Alberto Dias (PhD - LENEP / UENF). |

**Artigo em Revista**

A fast modified parabolic radon transform.We propose a fast and efficient frequency-domain implementation of a modified parabolic Radon transform (modified PRT) based on a singular value decomposition (SVD) with applications to multiple removal. The problem is transformed into a complex linear system involving a single operator after merging the curvature-frequency parameters into a new variable. A complex SVD is applied to this operator and the forward transform is computed by means of a complex back-substitution that is frequency independent. The new transform offers a wider curvature range at signal frequencies than the other PRT implementations, allowing the mapping in the transform domain of low-frequency events with important residual moveouts (long period multiples). The method is capable of resolving multiple energy from primaries when they interfere in a small time interval, a situation where most frequency-domain methods fail to discriminate the different wave types. Additionally, the method resists better to amplitude variations with offset (AVO) effects in the data than does the iteratively reweighted least-squares (IRLS) method.The proposed method was successfully applied to a deep-water seismic line in the Gulf of Mexico to attenuate water-bottom multiples and subsequent peg-legs originating from multiple paths in the water column. Combining the suggested method with the surface-related multiple elimination (SRME) has led to the best attenuation results in removing residual multiple energy in the stack. Â©2011 Society of Exploration Geophysicists |

**Artigo em Revista**

Total variation regularization for depth-to-basement estimate: Part 1 â€” Mathematical details and applicationsWe have developed an inversion approach that estimates the basement relief of a fault-bounded sedimentary basin. The sedimentary pack is approximated by a grid of 3D or 2D vertical prisms juxtaposed in the horizontal directions of a right-handed coordinate system. The prisms' thicknesses represent the depths to the basement and are the parameters to be estimated from the gravity data. To obtain depth-to-basement estimates, we introduce the total variation (TV) regularization as a stabilizing function. This approach lets us estimate a nonsmooth basement relief because it does not penalize sharp features of the solution. We have deduced a compact matrix form of the gradient vector and the Hessian matrix of the approximation to the TV function that allows a regularized Gauss-Newton minimization approach. Because the Hessian matrix of the approximation to the TV function is ill conditioned, we have modified this Hessian matrix to improve its condition and to accelerate the convergence of the Gauss-Newton algorithm. Tests conducted with synthetic data show that the inversion method can delineate discontinuous basements presenting large slips or sequences of small-slip step faults. Tests on field data from the Almada Basin, Brazil, and from the San Jacinto Graben, California, U.S.A., confirm the potential of the method in detecting and locating in-depth normal faults in the basement relief of a sedimentary basin. Â©2011 Society of Exploration Geophysicists |

**Artigo em Revista**

Total variation regularization for depth-to-basement estimate: Part 2 â€” Physicogeologic meaning and comparisons with previous inversion methodsWe applied the mathematical basis of the total variation (TV) regularization to analyze the physicogeologic meaning of the TV method and compared it with previous gravity inversion methods (weighted smoothness and entropic Regularization) to estimate discontinuous basements. In the second part, we analyze the physicogeologic meaning of the TV method and compare it with previous gravity inversion methods (weighted smoothness and entropic regularization) to estimate discontinuous basements. Presenting a mathematical review of these methods, we show that minimizing the TV stabilizing function favors discontinuous solutions because a smooth solution, to honor the data, must oscillate, and the presence of these oscillations increases the value of the TV stabilizing function. These three methods are applied to synthetic data produced by a simulated 2D graben bordered by step faults. TV regularization and weighted smoothness are also applied to the real anomaly of Steptoe Valley, Nevada, U.S.A. In all applications, the three methods perform similarly. TV regularization, however, has the advantage, compared with weighted smoothness, of requiring no a priori information about the maximum depth of the basin. As compared with entropic regularization, TV regularization is much simpler to use because it requires, in general, the tuning of just one regularization parameter. Â©2011 Society of Exploration Geophysicists |

**Artigo em Revista**

Partitioned least-squares operator for large-scale geophysical inversion Geophysics 75, R121, 2010Least-squares (LS) problems are encountered in many geophysical estimation and data analysis problems where a large number of observations (data) are combined to determine a model (some aspect of the earth structure). Examples of least squares in seismic exploration include several data processing algorithms, theoretically accurate LS migration, inversion for reservoir parameters, and background velocity estimation. A frequently encountered problem is that the volume of data in 3D is so large that the matrices required for the LS solution cannot be stored within the memory of a single computer. A new technique is described for parallel computation of the LS operator that is based on a partitioned-matrix algorithm. The classical LS method for solution of block-Toeplitz systems of normal equation (NE) to the general case of block-Hermitian and non-Toeplitz systems of NE. is generalized. Specifically, a solution of a block-Hermitian system of NE is shown that may be obtained recursively by linearly combining the solutions of lesser order that are related to the forward and backward subsystems of equations. This results in an efficient parallel algorithm in which each partitioned system can be evaluated independently. The application of the algorithm to the problem of 3D plane wave transformation is demonstrated. Â©2010 Society of Exploration Geophysicists |

**Apresentação**

Ground-roll attenuation based on SVD filteringWe present a singular value decomposition (SVD) filtering method for attenuation of the ground roll. Before the SVD computation, the normal move-out (NMO) correction is applied to the seismograms, with the purpose of flattening the reflections. SVD is performed on a small number of traces in a sliding window. The output trace is the central trace of the first few eigenimages. These contains mostly horizontally aligned signals, and other noise in the data will be suppressed. The new method preserves the character and frequency content of the horizontal reflections and attenuates all other type of events. We illustrate the method using land seismic data of the Tacutu basin, located in the north-east part of Brazil. The results show that the proposed method is effective and is able to reveal reflections masked by the ground-roll. Â©2009 Society of Exploration Geophysicists |

**Artigo em Revista**

Simultaneous 3D depth-to-basement and density-contrast estimates using gravity data and depth control at few pointsWe have developed a gravity-inversion method for simultaneously estimating the 3D basement relief of a sedimentary basin and the parameters defining a presumed parabolic decay of the density contrast with depth in a sedimentary pack, assuming prior knowledge about the basement depth at a few points. The sedimentary pack is approximated by a grid of 3D vertical prisms juxtaposed in both horizontal directions of a right-handed coordinate system. The prisms' thicknesses represent the depths to the basement and are the parameters to be estimated from the gravity data. To estimate the parameters defining the parabolic decay of the density contrast with depth and to produce stable depth-to-basement estimates, we imposed smoothness on the basement depths and proximity between estimated and known depths at boreholes. We applied our method to synthetic data from a simulated complex 3D basement relief with two sedimentary sections having distinct parabolic laws describing the density-contrast variation with depth. The results provide good estimates of the true parameters of the parabolic law of density-contrast decay with depth and of the basement relief. Inverting the gravity data from the onshore and part of the shallow offshore Almada Basin on Brazil's northeastern coast shows good correlation with known structural features. |

**Dissertação de Mestrado**

AtenuaÃ§Ã£o de reflexÃ£o mÃºltipla do fundo marinho utilizando deconvoluÃ§Ã£o preditiva adaptativaA atenuaÃ§Ã£o das reflexÃµes mÃºltiplas de curto, mÃ©dio ou longo perÃodos em dados sÃsmicos marÃtimos represnta um grande e importante problema do procesamento de dados sÃsmicos enfrentado pela indÃºstria do petrÃ³leo.Tais reflexÃµes mÃºltiplas estÃ£o presntes nos dados sÃmicos adquirdos sobre lÃ¢mina de Ã¡gua e prejudicam sobremaneira oprocesamento dos dados e qualidafefinal da imagem sÃmica. O mÃ©todo de deconvoluÃ§Ã£o preditiva de Wiener-Levinson (WL) visa a prediÃ§Ã£o e subtraÃ§Ã£o desses eventos periÃ³dicos.Os filtros preditvos sÃ£o obtidos com o mÃ©todo dos mÃnimos quadrados e implicitamente utilzam a premissa usual de que os dados sÃsmicos possuem valores de amplitude nula fora da jqnela de tempo considerada. Desta forma os filtros de WL perdem eficÃ¡cia na prediÃ§Ã£o do evento periÃ³dico penalizando o resultado final da atenuaÃ§Ã£o da mÃºltipla. Outro fator limitante do sucesso da deconvoluÃ§Ã£o preditva de WL Ã© a ausÃªncia de periodicidade das reflexÃµesmÃºltiplas ao longo do traÃ§o sÃmico. A perfeita periodicidade ocorre apenas em registros de incidÃªncia normal, quando os traÃ§o sÃ£o de afastamento nulo entre fonte-receptor, o que faz a deconvoluÃ§Ã£o preditiva de WL nÃ£oser tÃ£o eficaz. Na presente dissertaÃ§Ã£o foi investigada a aplicaÃ§Ã£o do mÃ©todo de deconvoluÃ§Ã£o preditiva utilzando o algoritmo de Morf modificado (prediÃ§Ã£o unitÃ¡ria L = 1 para prediÃ§Ã£o arbitrÃ¡ia L > 1), que nÃ£o faz consideraÃ§Ãµes quanto Ã s amplitudes das amostras fora da janela especificada. Este algoritmo Ã© apropriado para trabalhar no interior de janelas do traÃ§o sÃmicos sem que o filtro perca sua eficÃ¡cia de predizer e, consequentemente, atenuar a reflexÃ£o mÃºltipla. Utilzando o algoritmo de Morf modificado sobre janelas deslizantes de tempo foi definido um procedimento que denominou-se de deconvoluÃ§Ã£o adaptativa de Morf modicada (DAMM). Este mÃ©todo foi comparado com resultados obtidos com o mÃ©todo de deconvoluÃ§Ã£o adaptativa de WL(DAWL). Resultados com dados sintÃ©ticos e reais demonstrarama eficÃ¡cia e superioridade da DAMM na atenuaÃ§Ã£o de reflexÃµes mÃºltiplas. O emprego do mÃ©todo sobre dados reais da Bacia do Jequitinhonha mostraram que o mÃ©todo DAMM atenuou as mÃºltiplas de maneira mais efetiva que o mÃ©todo DAWL. Os grandes problemas e dificuldades que sÃ£o encontrados na atenuaÃ§Ã£o das reflexÃµes mÃºltiplas de curto perÃodo na parte de lÃ¢mica d'Ã¡gua rasa da plataforma continental e as mÃºltiplas de mÃ©dio perÃodo na regiÃ£o da quebra da talude foram resolvidos satisfatoriamente com o mÃ©todo DAMM. Os resultados com a DAMM sÃ£o considerados bons, inclusive na comparaÃ§Ã£o com resultados obtidos com o mÃ©todo SRME, bastante utilizaod na indÃºstria do petrÃ³leo. Os resultados promissores obtidos sugerem o emprego da DAMM no processamento sÃsmico bem como a extensÃ£o do mÃ©todo DAMM para a forma multicanal, esperando-se assim tornar o mÃ©todo ainda mais robusto e eficaz. |

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