Produção Científica

**Artigo em Revista**

Estimation of the seismic wavelet through homomorphic deconvolution and well log data: application on well-to-seismic tie procedureWavelet estimation and well-tie procedures are important tasks in seismic processing and interpretation. Deconvolutional statistical methods to estimate the proper wavelet, in general, are based on the assumptions of the classical convolutional model, which implies a random process reflectivity and a minimum-phase wavelet. The homomorphic deconvolution, however, does not take these premises into account. In this work, we propose an approach to estimate the seismic wavelet using the advantages of the homomorphic deconvolution and the deterministic estimation of the wavelet, which uses both seismic and well log data. The feasibility of this approach is verified on well-to-seismic tie from a real data set from Viking Graben Field, North Sea, Norway. The results show that the wavelet estimated through this methodology produced a higher quality well tie when compared to methods of estimation of the wavelet that consider the classical assumptions of the convolutional model. |

**Artigo em Revista**

Fast estimation of prestack Common Reflection Surface parameters.We present a method for fast estimation of finite offset common reflection surface parameters. Firstly, the derivatives with respect to offset are derived from the velocity guide. Secondly, we apply structure tensors to extract the derivatives with respect to midpoint from stacked common offset sections. Finally, the mixed derivative is estimated using a oneāparametric semblance search. The proposed method is compared to the global fiveāparametric semblance search and the pragmatic sequential twoāparametric semblance search on one synthetic and one real data set. The experiments show that the proposed method is more robust against noise than the pragmatic search and have comparable robustness with the global search. The proposed method smoothes parameter estimates in a local window, and the window size is set to give the best tradeāoff between detail and robustness. Since the proposed method is dependent on a velocity guide, the quality of the other parameter estimates may be influenced by any inaccuracies in the guide. The main advantage of the proposed method is the computational efficiency. When compared with a gridded implementation of the semblance search, the proposed method is 10 and 400 times faster than the pragmatic and global search. Alternative search strategies significantly reduce the computational cost of the global search. However, since more than 99% of the computational cost of the proposed method comes from the semblance search to estimate the mixed derivative, it is expected that such techniques also reduce the computational cost for the proposed method. |

**Artigo em Revista**

Stretch-free generalized normal moveout correction.The effective application of normal moveout correction processes mainly depends on four factors: the chosen traveltime approximation, the stretching associated with the given traveltime, crossing events and phase changes, the last two being inherent to the seismic data. In this context, we conduct a quantitative analysis on stretching considering a general traveltime expression depending on halfāoffset and midpoint coordinates. Through this analysis, we propose a mathematically proven procedure to eliminate stretching, which can be applied to any traveltime approximation. The proposed method is applied to synthetic and real data sets, considering different traveltime approximations and achieved complete elimination of stretching. |

**Artigo em Revista**

Gravity and Magnetic Modeling Sergipano Belt, Brazil: 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**

Density log correction for borehole effects and its impact on well-to-seismic tie: Application on a North Sea data setReservoir characterization requires accurate elastic logs. It is necessary to guarantee that the logging tool is stable during the drilling process to avoid compromising the measurements of the physical properties in the formation in the vicinity of the well. Irregularities along the borehole may happen, especially if the drilling device is passing through unconsolidated formations. This affects the signals recorded by the logging tool, and the measurements may be more impacted by the drilling mud than by the formation. The caliper log indicates the change in the diameter of the borehole with depth and can be used as an indicator of the quality of other logs whose data have been degraded by the enlargement or shrinkage of the borehole wall. Damaged well-log data, particularly density and velocity profiles, affect the quality and accuracy of the well-to-seismic tie. To investigate the effects of borehole enlargement on the well-to-seismic tie, an analysis of density log correction was performed. This approach uses Dollās geometric factor to correct the density log for wellbore enlargement using the caliper readings. Because the wavelet is an important factor on the well tie, we tested our methodology with statistical and deterministic wavelet estimations. For both cases, the results using the real data set from the Viking Graben field ā North Sea indicated up to a 7% improvement on the correlation between the real and synthetic seismic traces for well-to-seismic tie when the density correction was made. |

**Artigo em Revista**

Analysis of Eshelby-Chengās 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 Thomsenās 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 Ī¼ in a regularized inverse problem. For each tentative value of Ī¼, 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 Ļ(Ī¼) 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, Ļ(Ī¼) cannot be used directly to estimate the best value of Ī¼ (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 Ļ(Ī¼). From this comparison, the interpreter decides if the current Ī¼ produces stable solutions. Because the bisection method can be applied only to monotonic functions (or segments of monotonic functions) and because Ļ(Ī¼) has a theoretical monotonic behavior that can be corrupted, in practice by a poor experiment design, the set of values of Ļ(Ī¼) can be used as a quality control of the experiments in the proposed bisection method to estimate the best value of Ī¼. 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. |

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