Produção Científica

**Artigo em Revista**

SoluÃ§Ãµes de Problemas envolvendo EquaÃ§Ãµes Diferenciais Sujeitas a IncertezasEste trabalho objetiva analisar, atravÃ©s de alguns exemplos, a influÃªncia de se considerar aleatoriedades na soluÃ§Ã£o de equaÃ§Ãµes diferenciais com dados e/ou parÃ¢metros aleatÃ³rios. Um comparativo das mÃ©dias das soluÃ§Ãµes das equaÃ§Ãµes estocÃ¡sticas com as soluÃ§Ãµes das equaÃ§Ãµes determinÃsticas simplificadas, nas quais substituÃmos os parÃ¢metros aleatÃ³rios por suas mÃ©dias, Ã© apresentado. Estes exemplos mostram que a mÃ©dia da soluÃ§Ã£o, que normalmente Ã© uma informaÃ§Ã£o relevante em aplicaÃ§Ãµes, pode ser qualitativamente diferente da aproximaÃ§Ã£o obtida pela soluÃ§Ã£o de uma equaÃ§Ã£o diferencial determinÃstica na qual substituÃmos os parÃ¢metros aleatÃ³rios por suas mÃ©dias. |

**Artigo em Revista**

A spaceâ€“time multiscale method for computing statistical moments in strongly heterogeneous poroelastic media of evolving scalesA new multiscale procedure is proposed to compute flow in compressible heterogeneous porous media with geology characterized by power-law covariance structure. At the fine scale, the deformable medium is modeled by the partially coupled formulation of poroelasticity with Youngâ€™s modulus and permeability treated as stationary random fields represented by their Karhunenâ€“LoÃ¨ve decompositions. The framework underlying the multiscale procedure is based on mapping these random parameters to an auxiliary domain and constructing a family of equivalent stochastic processes at different length scales characterized by the same ensemble mean and covariance function. The poromechanical variables inherit a spaceâ€“time version of the scaling relations of the random input parameters which allows for constructing a set of multiscale solutions of the same governing equations posed at different space and time scales. A notable feature of the multiscale method proposed herein is the feasibility of solving both the poroelastic model and the Fredholm integral equation for the eigenpairs of the Karhunenâ€“LoÃ¨ve expansion in an auxiliary domain with much lower computational effort and then derive the long term behavior at a coarser scale from a straightforward rescaling of the auxiliary solution. Within the framework of the finite element approximation, in conjunction with the Monte Carlo algorithm, numerical simulations of fluid withdrawal and injection problems in a heterogeneous poroelastic reservoir are performed to illustrate the potential of the method in drastically reducing the computational burden in the computation of the statistical moments of the poromechanical unknowns in large-scale simulations. |

**Artigo em Revista**

A Numerical Comparison Between Quasi-MonteCarlo and Sparse Grid Stochastic Collocation MethodsQuasi-Monte Carlo methods and stochastic collocation methods based on sparse grids have become popular with solving stochastic partial differential equations.These methods use deterministic points for multi-dimensional integration or interpolation without suffering from the curse of dimensionality. It is not evident which method is best, specially on random models of physical phenomena. We numerically study the error of quasi-Monte Carlo and sparse gridmethods in the context of groundwater flow in heterogeneous media. In particular, we consider the dependence of the variance error on the stochastic dimension and the number of samples/collocation points for steady flow problems in which the hydraulic conductivity is a lognormal process. The suitability of each technique is identified in terms of computational cost and error tolerance. |

**Artigo em Revista**

Effect of Element Distortion on the Numerical Dispersion of Spectral Element MethodsSpectral element methods are well established in the field of wave propagation,in particular because they inherit the flexibility of finite element methods and have low numerical dispersion error. The latter is experimentally acknowledged, but has been theoretically shown only in limited cases, such as Cartesian meshes. It is well known that a finite element mesh can contain distorted elements that generate numerical errors for very large distortions. In the present work, we study the effect of element distortion on the numerical dispersion error and determine the distortion range in which an accurate solution is obtained for a given error tolerance. We also discuss a double-grid calculation of the spectral element matrices that preserves accuracy in deformed geometries. |

**Dissertação de Mestrado**

Filtragem adaptativa SVD de volumes sÃsmicos 3D para realÃ§ar refletores e estruturas geolÃ³gicas.Washington Oliveira Martins. Filtragem adaptativa SVD de volumes sÃsmicos 3D para realÃ§ar refletores e estruturas geolÃ³gicas. 2012. DissertaÃ§Ã£o (Mestrado em GeofÃsica) - Universidade Federal da Bahia, . Orientador: Milton JosÃ© Porsani. |

**Tese de Doutorado**

Dorian Caraballo Ledesma. DeconvoluÃ§Ã£o de dados sÃsmicos de reflexÃ£o utilizando mudanÃ§a de fase do filtro de Wiener-Levinson. 2011.Dorian Caraballo Ledesma. DeconvoluÃ§Ã£o de dados sÃsmicos de reflexÃ£o utilizando mudanÃ§a de fase do filtro de Wiener-Levinson. 2011. Tese (Doutorado em GeofÃsica) - Universidade Federal da Bahia, CoordenaÃ§Ã£o de AperfeiÃ§oamento de Pessoal de NÃvel Superior. Orientador: Milton JosÃ© Porsani. |

**Dissertação de Mestrado**

Processamento de Dados SÃsmicos com Grandes Afastamentos: Dados SintÃ©ticos e Linha SÃsmica do Campo de Tenerife, ColÃ´mbia.Francisco Ortega Gamboa. Processamento de Dados SÃsmicos com Grandes Afastamentos: Dados SintÃ©ticos e Linha SÃsmica do Campo de Tenerife, ColÃ´mbia. 2012. DissertaÃ§Ã£o (Mestrado em GeofÃsica) - Universidade Federal da Bahia, CoordenaÃ§Ã£o de AperfeiÃ§oamento de Pessoal de NÃvel Superior. Orientador: Amin Bassrei. |

**Apresentação**

GÃªBR: a free seismic processing interfaceThere are many programs for processing seismic data that are freely available and widespread, for example Seismic Un*x, Madagascar, FreeUSP, and SEPlib, among others. All these packages consist of packages of command-line-oriented programs that are designed to be used in sequence; the data conceptually flow in a pipeline through one program after another. Each program is generally controlled by its own set of command-line options. To take full advantage of such a toolkit, the user must have considerable knowledge beyond general geophysical expertise: shell scripting, process submission and management, and batch queue processing, to name a few. While these skills are useful, they should not be a requirement for seismic data processing. A suitable graphical user interface could take care of these computational details, allowing the user to focus on the central problem of processing seismic data. This is particularly important during training courses, where the limited duration of the does not leave time for learning skills that are not essential to the material being taught. A graphical user interface may also boost the uptake of a new program, by making it more accessible to users and allowing its easy integration with other programs available within the same interface. These principles have guided the development of GÃªBR, a graphical user interface to control commandline programs for seismic processing. It permits users to build complex processing flows from predefined modules known as menus. Menus describing new programs can be easily added to the interface, extending its capabilities. GÃªBR is also designed to be simple, in the sense that a couple of hours is enough to introduce the core features of the interface, to allow the user to start working with the seismic data. |

**Apresentação**

Minimum-delay seismic trace decomposition and SVD filtering for seismic reflection enhancementSpiking deconvolution corrects for the effect of the seismic wavelet, assumed to be minimum delay, by applying an inverse filter to the seismic trace to get an estimate of reflectivity. In order to compensate for propagation and absorption effects one may use time-varying deconvolution where a different inverse filter is computed and applied for each output sample position. We modify this procedure by estimating a minimum-delay wavelet for each time-sample position of the seismic trace. This gives a decomposition of the seismic trace as a sum of minimum-delay wavelets, each multiplied by a reflectivity coefficient. The reflectivity estimation is a single-trace process which is sensitive to non-white noise, and it does not take into account lateral continuity of reflections. We therefore have developed a new data processing strategy by combining it with adaptive SVD filtering. The SVD filtering process is applied to the data in two steps. First, in a sliding spatial window on NMO-corrected CMP or common shot gathers. Next, after local dip estimation and correction, on local patches in common-offset panels. After the SVD filtering, we apply the new reflectivity estimation procedure. The SVD filtering removes noise and improves lateral continuity while the reflectivity estimation increases the high-frequency content in the data and improves vertical resolution. The new data processing strategy was successfully applied to land seismic data from North-east in Brazil. Improvements in data quality are evident in prestack data panels, velocity analysis and the stacked section. |

**Apresentação**

Migration velocity analysis using residual diffraction moveout in the pre/post-stack depth domainDiffraction events contain direct information on the medium velocity. In this work, we develop a method for migration velocity improvement and diffraction localization based on a moveout analysis of over or undermigrated diffraction events in the depth domain. The method uses an arbitrary initial velocity model as input. It provides an update to the velocity model and diffraction locations in the depth domain as a result. The algorithm is based on the focusing of remigration velocity rays from incorrectly migrated diffraction curves. These velocity rays are constructed from a ray-tracing like approach applied to the image-wave equation for velocity continuation. After picking the diffraction events in the migrated domain, the method has a very low computational cost, and the diffraction points are located automatically. We demonstrate the feasibility of our methods using a synthetic data example. |

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