Produção Científica

**Artigo em Revista**

Analysis of Eshelby-Cheng’s model in anisotropic porous cracked medium: An ultrasonic physical modeling approachMany effective medium theories are designed to describe the macroscopic properties of a medium (the rock, or reservoir in this case) in terms of the properties of its constituents (the background matrix of the rock and the inclusions, for our scenario). A very well known effective medium theory is the Eshelby-Cheng model, which was studied by us in previous work, being tested for the case where the background medium was weakly-anisotropic and porous. The analysis was done testing elastic velocities and Thomsen parameters - as a function of crack density for fixed values of aspect ratio - predicted by the model with data acquired from synthetic rock samples. In this work, we aim to complete the analysis of the Eshelby-Cheng model capabilities when applied to rocks with porous and vertical transversely isotropic (VTI) backgrounds, testing the model for the elastic velocities as functions of aspect ratio - for fixed values of crack density - against experimental data. The data used to test the model were obtained from 17 synthetic rock samples, one uncracked and 16 cracked, the latter divided into four groups of four samples each, each group with cracks having the same aspect ratio, but with the samples having different crack densities. In these samples, ultrasonic pulse transmission measurements were performed to obtain the experimental velocities used to test the model. As was not possible to acquire data for velocity as a function of aspect ratio for fixed values of crack density, we performed interpolations of the experimental data to estimate these velocities. Eshelby-Cheng model effective velocities and Thomsen parameters were calculated using three formulations proposed for the crack porosity: one proposed by Thomsen, the second one proposed in our previous work (which depends only on the crack density) and the third one proposed in this work (which depends on the crack porosity and the aspect ratio, just like Thomsen’s proposal). The comparisons between elastic velocities and Thomsen parameters - as function of crack aspect ratio, for fixed values of crack density - predicted by the model and estimated from the data via interpolation showed that the third formulation produced better fittings (lower root-mean-square errors) between model and experimental data for all ranges of aspect ratio and crack density. |

**Artigo em Revista**

Tectonic Control and Crustal Thickness of the Basement Adjacent to the Sergipe-Alagoas BasinThis work used gravimetric and magnetic data to investigate the Sergipano Belt that occupies the Southern Borborema Province, Brazil. The main objective was to interpret tectonic relationships between the geological domains, crustal lateral variation of the physical properties and the behavior of the Moho relief. The gravity and magnetic inversion was performed to determine the physical properties magnetic susceptibility and density contrast to delineate the geometry of the true source. The regional gravity anomaly was used to obtain solutions depth of the interface crust-mantle in which it was necessary to know the initial model of the crustal thickness and density contrast. The geophysical measures was used to delineate the initially crustal thickness and compared to the results based on a compilation of data published in the literature mainly derived from seismic database such as deep seismic refraction experiments. These magnetic sources have signals with different amplitudes that originate from different geometric sources, situated at different depths and with different magnetic properties. As to the crustal thickness results, we found that the southern region of the Sergipano Belt has a crustal (34-35 km) and mantle uplift, mainly in the Girau do Ponciano Dome. The Rio Coruripe domain as well as the PEAL Terrain has a thicker crust (38-40 km), with magnetic and gravimetric sources that reach from 15 to 20 km deep marked in sections. |

**Artigo em Revista**

A robust interactive estimation of the regularization parameterWe have developed a new and robust method (in the sense of it being applicable to a wide range of situations) to estimate the regularization parameter μ in a regularized inverse problem. For each tentative value of μ, we perturb the observations with J sequences of pseudorandom noise and we track down the instability effect on the solutions. Then, we define a quantitative measure ρ(μ) of the solution instability consisting of the largest value among the Chebyshev norms of the vectors obtained by the differences between all pairs of the perturbed solutions. Despite being quantitative, ρ(μ) cannot be used directly to estimate the best value of μ (the smallest value that stabilizes the solution) because, in practice, instability may depend on the particular and specific interests of the interpreter. Then, we determine that the interpreter, at each iteration of a bisection method, visually compares, in the (x, y, z) space, the pair p^i and p^j of the solutions most distant from each other and associated with the current ρ(μ). From this comparison, the interpreter decides if the current μ produces stable solutions. Because the bisection method can be applied only to monotonic functions (or segments of monotonic functions) and because ρ(μ) has a theoretical monotonic behavior that can be corrupted, in practice by a poor experiment design, the set of values of ρ(μ) can be used as a quality control of the experiments in the proposed bisection method to estimate the best value of μ. Because the premises necessary to apply the proposed method are very weak, the method is robust in the sense of having broad applicability. We have determined part of this potential by applying the proposed method to gravity, seismic, and magnetotelluric synthetic data, using two different interpretation models and different types of pseudorandom noise. |

**Artigo em Revista**

Modeling the wave propagation in viscoacoustic media: An efficient spectral approach in time and space domainWe present an efficient and accurate modeling approach for wave propagation in anelastic media, based on a fractional spatial differential operator. The problem is solved with the Fourier pseudo-spectral method in the spatial domain and the REM (rapid expansion method) in the time domain, which, unlike the finite-difference and pseudo-spectral methods, offers spectral accuracy. To show the accuracy of the scheme, an analytical solution in a homogeneous anelastic medium is computed and compared with the numerical solution. We present an example of wave propagation at a reservoir scale and show the efficiency of the algorithm against the conventional finite-difference scheme. The new method, being spectral in the time and space simultaneously, offers a highly accurate and efficient solution for wave propagation in attenuating media. |

**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+ε1)+ 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 time–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 time–frequency representation. By interpretation of the time signals and their time–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 time–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 Parnaíba basin - BrazilThe Parnaíba 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, 1400 km long and 20 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 Parnaíba 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 João 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. |