Produção Científica

**Apresentação**

3D complex PadÃ© FFD migration: A comparison of splitting techniquesJessÃ© C. Costa, DÃ©bora Mondini, JÃ¶rg Schleicher, and AmÃ©lia Novais SEG Expanded Abstracts 30, 4420-4424 (2011) SUMMARY Three-dimensional wave-equation migration techniques are quite expensive because of the huge matrices that need to be inverted. Many techniques have been proposed to reduce this cost by splitting the 3D problem into a sequence of 2D problems. We compare the performance of splitting techniques for stable 3D Fourier Finite-Difference (FFD) migration techniques in terms of image quality and computational cost. The FFD methods are complex Pade FFD and FFD plus interpolation, and the compared splitting techniques are two and fourway splitting as well as alternating four-way splitting, i.e., splitting into the coordinate directions at one depth and the diagonal directions at the next level. From numerical examples in homogeneous and inhomogeneous media, we conclude that alternate four-way splitting yields results of the same quality as full four-way splitting at the cost of two-way splitting. |

**Apresentação**

Diffraction imaging point of common-offset gather: GPR data exampleJ. J. S. de Figueiredo, F. Oliveira, E. Esmi, L. Freitas, S. Green, A. Novais, and J. Schleicher SEG Expanded Abstracts 30, 4399-4403 (2011) SUMMARY Hydrocarbon traps are generally located beneath complex geological structures. Such areas contain many seismic diffractors that carry detailed structure information in the order of the seismic wavelength. Therefore, the development of computational resources capable of detecting diffractor points with a good resolution is desirable, but has been a challenge in the area of seismic processing. In this work, we present a method for the detection of diffractor points in the common-offset gathers domain. In our approach, the diffraction imaging is based on the diffraction operator, which can be used in both the time and depth domains, in accordance with the complexity of the area. This method, which does not require any knowledge apart from the migration velocity field (i.e., rms velocities or interval velocities) applies pattern recognition to the amplitudes along the diffraction operator. Numerical examples using synthetic and real data demonstrate the feasibility of the technique. |

**Apresentação**

Coherence measures in automatic time migration velocity analysisJonathas S. Maciel, JessÃ© C. Costa (UFPA & INCT-GP, Brazil) and JÃ¶rg Schleicher (Unicamp & INCT-GP, Brazil) SUMMARY Time-migration velocity analysis can be carried out automatically by evaluating the coherence of the migrated seismic events in the common-image gathers (CIGs). The performance of gradient methods for automatic time-migration velocity analysis depends on the coherence measures used in the objective function. We compare the results of four different coherence measures, being conventional semblance, differential semblance, an extended differential semblance using more neighboring traces, and the product of the latter with conventional semblance. In our numerical experiments, the objective functions based on conventional semblance and on the product of conventional semblance with extended differential semblance provided the best velocity models, as evaluated by the flatness of the resulting common-image gathers. The method can be easily extended to anisotropic media. |

**Apresentação**

Design of all-pass operators using a genetic algorithm for mixed phase deconvolutionDorian Caraballo L. CPGG/UFBA and Milton J. Porsani, CPGG/IGEO/UFBA and INCT-GP/CNPQ SUMMARY This paper present a new approach for mixed phase deconvolution. We investigate the use of arbitrary subsets of roots, distributed outside of the unit circle, to estimated mixed-phase inverse filter and wavelets. All pass filters are used to change the phase of the minimum phase filter. The influence of numbers of roots and its distributions was studied in order the obtain a optimum inverse mixed-phase filter. The optimization process to obtain the best inverse filter is performed by using a genetic algorithm. We have used the varimax norm as the object function to measure the simplicity of the deconvolved seismic trace. The method was tested using synthetic and real seismic data. |

**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 |

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