Produção Científica

**Artigo em Revista**

Perfectly matched layer boundary conditions for the second-order acoustic wave equation solved by the rapid expansion methodWe derive a governing second-order acoustic wave equation in the time domain with a perfectly matched layer absorbing boundary condition for general inhomogeneous media. Besides, a new scheme to solve the perfectly matched layer equation for absorbing reflections from the model boundaries based on the rapid expansion method is proposed. The suggested scheme can be easily applied to a wide class of wave equations and numerical methods for seismic modelling. The absorbing boundary condition method is formulated based on the split perfectly matched layer method and we employ the rapid expansion method to solve the derived new perfectly matched layer equation. The use of the rapid expansion method allows us to extrapolate wavefields with a time step larger than the ones commonly used by traditional finite-difference schemes in a stable way and free of dispersion noise. Furthermore, in order to demonstrate the efficiency and applicability of the proposed perfectly matched layer scheme,numerical modelling examples are also presented. The numerical results obtained with the put forward perfectly matched layer scheme are compared with results from traditional attenuation absorbing boundary conditions and enlarged models as well. The analysis of the numerical results indicates that the proposed perfectly matched layer scheme is significantly effective and more efficient in absorbing spurious reflections. from the model boundaries. |

**Artigo em Revista**

NEW ITERATIVE AND MULTIFREQUENCY APPROACHES IN GEOPHYSICAL DIFFRACTION TOMOGRAPHYSeismic tomography is used in reservoir geophysics as an important method for high-resolution imaging. The classical Born approach, which is used in single-frequency diffraction tomography under the condition of weak scattering, is limited by the requirement to know the background velocity in advance. We propose tomographic inversion approaches within matrix formalism and the Born approximation conditions. These approaches are iterative (in the sense that the background velocity field is updated at each iteration) and do not require knowledge of the true background velocity. In the first approach, a single-frequency that is kept constant is used. In the second approach, several frequencies are also kept constant and are used simultaneously. In the third approach, in addition to the background velocity, the working frequency is also updated. Finally, in the last approach, the multiple frequencies used simultaneously are updated throughout the iteration. The proposed approaches were tested on a synthetic model containing a dipping layer and a paleochannel, with cross-well acquisition geometry, and the data were contaminated with Gaussian noise. When compared to the standard, single-frequency non-iterative approach, the iterative process with the use of multiple frequencies generated results with smaller RMS errors for model parameter, velocity and data.Keywords: seismic inversion, seismic tomography, wave numerical modeling, reservoir characterization. |

**Artigo em Revista**

Inversion of Bottom Hole Temperatures for Gradient Determination by the Damped Least Squares Method for Noise AttenuationThis study consists in obtain the 1-D distribution of the geothermal gradient from the inversion of Bottom Hole Temperature (BHT) data. Before the inversion procedure, Horner correction method was used to determine the correct formation temperature. The inversion was performed in a synthetic model based on real data from Pineview Field (Utah, USA), in this case, to obtain geothermal gradients from nine formations using BHT data from 32 wells. The Z matrix of the geothermal problem contains the elements zi j, i.e., the thickness of the i-th layer logged in the j-th well. The least squares method was used, and, because of the occurrence of noise, damping was required. The numerical implementation of the inversion, i.e., the determination of the inverse operator (ZtZ)+ or (ZtZ+Îµ1)+ was performed by singular value decomposition. Initial inversions did not produce satisfactory results, but they significantly improved with the introduction of damping. The improvement of the results is quantitatively explained by the fact that the condition number of the matrix to be inverted greatly reduced with the use of the damping. In turn, damping requires the choice of an optimal parameter, and the L-curve was used for this purpose. |

**Artigo em Revista**

Signal decomposition and timeâ€“frequency representation using iterative singular spectrum analysisThe application of the singular value decomposition method (SVD) for filtering of seismic data has become common in recent decades, as it promotes significant improvements of the signal-to-noise ratio, highlighting reflections in seismograms. One particular way to apply SVD in a single (or multivariate) time-series is the singular spectrum analysis (SSA) method, normally applied on constant-frequency slices in one or many spatial dimensions. We demonstrate that SSA method applied in the time domain corresponds to filtering the time-series with a symmetric zero-phase filters, which are the autocorrelations of the eigenvectors of the data covariance matrix, preserving the phase of the original data. In this paper, we explore the SSA method in the time domain, and we propose a new recursive-iterative SSA (RI-SSA) algorithm, which uses only the first eigenvector of the data covariance matrix to decompose a discrete time-series into signal components. From the analytic signal of each component we compute a timeâ€“frequency representation. By interpretation of the time signals and their timeâ€“frequency representations, groups with similar features are summed to produce a smaller number of signal components. The resulting RI-SSA signal decomposition is exact and phase-preserving, but non-unique. Applications to land seismic data for ground-roll removal and to two synthetic signals for timeâ€“frequency analysis give good results. |

**Artigo em Revista**

Deep structures seismic enhancement using singular spectral analysis in time and frequency domain: Application in the regional transect of ParnaÃba basin - BrazilThe ParnaÃba basin is located in the Northeast of Brazil and it started in the Archaean. In a project involving Global Geophysical Services Incorporated and BP Energy do Brasil, a 2D seismic data, 1400â€¯km long and 20â€¯s of two-way travel time was acquired. Because of the acquisition characteristics and large volume of data it was necessary to develop a powerful filtering flow, in order to enhance the signal-to-noise ratio, particularly for deep structures, such as the Moho Discontinuity. For that matter, we have used a two-step recursive-adaptive singular spectral analysis (RA-SSA) to enhance the signal-to-noise ratio. First, we applied the RA-SSA in the t-x domain, along the time variable, for every seismic trace, to attenuate uncorrelated noise, and to enhance the low frequency content of the data. Second, the data was moved to the f-x domain, by means of the Fourier Transform of every single trace, and the RI-SSA method was applied for every frequency, along the x variable, to enhance the correlation of the reflectors between neighboring seismic traces. The filtered results, shown on common offset and CMP gather and on stacked data, show how successful the method was in enhancing the reflectors. We introduce a processing flow capable of enhancing the final stacked image quality, in order to map the Moho Discontinuity and interpret the transect to obtain a better understanding of the ParnaÃba basin formation. |

**Material Didático**

SimulaÃ§Ã£o por Linhas de Corrente da InjeÃ§Ã£o de Bancos de PolÃmero. Uma Abordagem SemianalÃtica |

**Material Didático**

Perfilagem geofÃsica em poÃ§o aberto - fundamentos bÃ¡sicos com Ãªnfase em petrÃ³leo |

**Material Didático**

Conceitos da AnÃ¡lise Espectral de Sinais em GeofÃsica |

**Material Didático**

Inverse Problems of Mathematical Physics |

**Material Didático**

Estratigrafia de SequÃªncias - HistÃ³rico, princÃpios e aplicaÃ§Ãµes. |

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