Produção Científica

**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. |

**Artigo em Revista**

Seismic processing applied to shale-gas reservoir characterization in Reconcavo basinThis paper is intended to present all the steps used in the seismic processing to characterize and interpret the 2D seismic line 0026-RL-1624, located between Dom JoÃ£o and Candeias fields, from the perspective of nonconventional reservoirs. It includes a new SVD (Singular Value Decomposition) method used to attenuate the ground-roll and direct wave, which had a very dispersive form in the shot domain, causing several problems in the visualization of reflections and, consequently, in the raw stacked data as well. It was later applied seismic attributes in order to have a better precision in mapping geological structures of interest and also interpret the main horizons present in the log well data. During the development of this work, the processing step were entirely performed by both Seismic Unix and SeisSpace/Promax, software developed by Landmark/Halliburton. |

**Artigo em Revista**

Up/down acoustic wavefield decomposition using a single propagation and its application in reverse time migrationThe separation of up- and downgoing wavefields is an important technique in the processing of multicomponent recorded data, propagating wavefields, and reverse time migration (RTM). Most of the previous methods for separating up/down propagating wavefields can be grouped according to their implementation strategy: a requirement to save time steps to perform Fourier transform over time or construction of the analytical wavefield through a solution of the wave equation twice (one for the source and another for the Hilbert-transformed source), in which both strategies have a high computational cost. For computing the analytical wavefield, we are proposing an alternative method based on the first-order partial equation in time and by just solving the wave equation once. Our strategy improves the computation of wavefield separation, and it can bring the causal imaging condition into practice. For time extrapolation, we are using the rapid expansion method to compute the wavefield and its first-order time derivative and then we can compute the analytical wavefield. By computing the analytical wavefield, we can, therefore, separate the wavefield into up- and downgoing components for each time step in an explicit way. Applications to synthetic models indicate that our method allows performing the wavefield decomposition similarly to the conventional method, as well as a potential application for the 3D case. For RTM applications, we can now use the causal imaging condition for several synthetic examples. Acoustic RTM up/down decomposition demonstrates that it can successfully remove the low-frequency noise, which is common in the typical crosscorrelation imaging condition, and it is usually removed by applying a Laplacian filter. Moreover, our method is efficient in terms of computational time when compared to RTM using an analytical wavefield computed by two propagations, and it is a little more costly than conventional RTM using the crosscorrelation imaging condition. |

**Artigo em Revista**

Time-stepping wave-equation solution for seismic modeling using a multiple-angle formula and the Taylor expansionWe have developed an analytical solution for wave equations using a multiple-angle formula. The new solution based on the multiple-angle expansion allows us to generate a family of solutions for the acoustic-wave equation, which may be combined with Taylor-series, Chebyshev, Hermite, and Legendre polynomial expansions or any other expansion for the cosine function and used for seismic modeling, reverse time migration, and inverse problems. Extension of this method to the solution of elastic and anisotropic wave equations is also straightforward. We also derive a criterion using the stability and dispersion relations to determine the order of the solution for a given time step and, thus, obtaining stable wavefields free of numerical dispersion. Afterward, numerical tests are performed using complex 2D velocity models to evaluate the effectiveness and robustness of our method, combined with second- or fourth-order Taylor approximations. Our multiple-angle approach is stable and provides reliable seismic modeling results for larger times steps than those usually used by conventional finite-difference methods. Moreover, multiple-angle schemes using a second-order Taylor approximation for each cosine term have a lower computational cost than the mixed wavenumber-space rapid expansion method. |

**Artigo em Revista**

Basement fabric controls rift nucleation and postrift basin inversion in the continental margin of NE BrazilIn passive continental margins, the brittle reactivation of shear zones and their role in the deformation and deposition of sedimentary basins are still a matter of debate. In this research, we investigated the role of the brittle reactivation of Precambrian shear zones in the nucleation of rift and postrift faults in the onshore portion of the Sergipe-Alagoas and Pernambuco basins in northeastern Brazil. We combine and interpret a dataset of aeromagnetic and topographic data, associated with reflection seismic and borehole data, to analyze the evolution of a portion of the Atlantic continental margin of Brazil. Our results indicate that in the crystalline basement, the magnetic lineaments are correlated with ductile structures as shear zones, and the continuity of these lineaments in the Sergipe-Alagoas and Pernambuco basins is interpreted as the shear zones below the sedimentary cover of these basins. We document the following phases of the brittle reactivation of basement shear zones: (1) the opening of the South Atlantic Ocean in the Early Cretaceous under an extensional stress regime and (2) tectonic inversion induced by the Mid-Atlantic Ridge push and the Andean Cordillera rise in the Neogene-Quaternary under a predominantly strike-slip stress regime. During the rift phase, the brittle reactivation of the shear zones controlled the locations and architectures of the rifts. These structures acted as zones of weakness and were reactivated as normal faults. The brittle reactivation of shear zones was still active during the postrift phase and was responsible for the development of compressional structures. The reverse faulting and related folding pattern indicate tectonic inversion in the Late Cretaceous-Cenozoic. The structures formed during the postrift phase under a strike-slip regime are consistent with the present-day stress field, indicating that tectonic inversion is an active phase of the Brazilian margin. |

**Artigo em Revista**

A multiscale approach to full-waveform inversion using a sequence of time-domain misfit functionsMost of the approaches designed to avoid cycle skipping in full-waveform inversion (FWI) involve calculating a sequence of inversions in a multiscale fashion. We have adopted an alternative strategy, which is inverting a sequence of different misfit functions in the time domain. This is an implicit multiscale approach in the sense that the used misfit functions are sensitive to different wavelengths, but all of the inversion steps use the same modeling algorithm and the same model grid. In the first and third inversion steps, the transmitted (early arrivals) and reflected (late arrivals) components of the wavefield envelopes are respectively fitted. The second step promotes a smooth transition between the first and third steps, by using the envelope of the complete waveform. Because fitting just the envelope of the reflected waves has a minor effect on the misfit function of the whole data set, the phases of the reflected waves are mostly fitted in the fourth step, which is based on the waveform misfit function preserving only the late arrivals. The third and fourth steps are of crucial importance to fit the reflected events. We test the sequential inversion approach with the Marmousi model using data sets with different frequencies, obtaining better estimates of the velocity field than those obtained with the classic FWI. The solutions obtained with classic FWI and sequential inversion approach degrade with a progressively higher peak frequency data set, but the classic FWI solution degrades more rapidly. |

**Artigo em Revista**

3D Seismic survey design using mixed-radix based algorithm inversionThe determination of three-dimensional geometry and acquisition parameters, the seismic acquisition survey design, is constantly subject of studies in obtaining data with the highest seismic quality, operational efficiency and cost minimization. In this paper, we propose a methodology for inverting geometry parameters of threedimensional orthogonal land seismic surveys based on a direct search method using a mixed-radix based algorithm. In this algorithm, the search space is discretized on a mixed-radix base, which depends on the extreme values and the search resolution of each parameter. We will show how to reparametrize the orthogonal acquisition geometry elements in order to obtain the independents and integers parameters that are necessary to construct the mixed-radix base. For the optimization purpose, we define an objective function to contemplate target parameters associated with the elements of the acquisition geometry directly related to the geophysical and operationa constraints. Taking in account that the mathematical functions and the objective function we define for the problem have no significant computational cost, all model space parameters are fast and efficiently tested. We applied the algorithm, using as input data, provided by a one-line roll orthogonal reference geometry, assuming a pair of geological objectives as shallow and deep targets. All selected models that meet both the proposed objectives and the constraints are organized by decreasing order of fitness so that with the mixed-radix inversion algorithm we found not only the best model, but also a set of suitable models. Likewise, with the best set of geometries, it is possible to establish a direct comparison between them, analysing their adherence to the technical and operational requirements according to the availability and degree of detail of each one. We show the top 10 best results as a table, allowing a direct comparison between all aspects of these geometries, and we summarize the results showing graphically the fitness of all selected geometries and the inverted geometry elements for the 1000 best geometries. These graphical displays provide a direct way to understand how each model behaves as the fitness decreases. The algorithm is very flexible and its application can be extended to any environment and type of acquisition geometry, and in any phase study of an area be it regional, exploratory or development. Key words: 3D seismic survey design, Geophysical inversion, Mixed-radix representation, Optimization. |

**Artigo em Revista**

Colored and linear inversions to relative acoustic impedanceAcoustic impedance (AI) is a widely used seismic attribute in stratigraphic interpretation. Because of the frequency-band-limited nature of seismic data, seismic amplitude inversion cannot determine AI itself, but it can only provide an estimate of its variations, the relative AI (RAI). We have revisited and compared two alternative methods to transform stacked seismic data into RAI. One is colored inversion (CI), which requires well-log information, and the other is linear inversion (LI), which requires knowledge of the seismic source wavelet. We start by formulating the two approaches in a theoretically comparable manner. This allows us to conclude that both procedures are theoretically equivalent. We proceed to check whether the use of the CI results as the initial solution for LI can improve the RAI estimation. In our experiments, combining CI and LI cannot provide superior RAI results to those produced by each approach applied individually. Then, we analyze the LI performance with two distinct solvers for the associated linear system. Moreover, we investigate the sensitivity of both methods regarding the frequency content present in synthetic data. The numerical tests using the Marmousi2 model demonstrate that the CI and LI techniques can provide an RAI estimate of similar accuracy. A field-data example confirms the analysis using synthetic-data experiments. Our investigations confirm the theoretical and practical similarities of CI and LI regardless of the numerical strategy used in LI. An important result of our tests is that an increase in the low-frequency gap in the data leads to slightly deteriorated CI quality. In this case, LI required more iterations for the conjugate-gradient least-squares solver, but the final results were not much affected. Both methodologies provided interesting RAI profiles compared with well-log data, at low computational cost and with a simple parameterization. |