Produção Científica
Artigo em Revista
Computational cost comparison between nodal and vector finite elements in the modeling of controlled source electromagnetic data using a direct solver The Finite Element method can be implemented to model geophysical electromagnetic data using one of two methodologies called Nodal and Vector Finite Elements. This paper presents a comparison between the two approaches, emphasizing memory usage and processing time, when simulating Marine Controlled Source Electromagnetic (MCSEM) data in threedimensional models. The study is carried out using unstructured meshes and a direct solver. Computational cost information from both methodologies are gathered from four different 3D models, each emphasizing a different aspect of the problem. The results indicate that the Vector Finite Element methodology requires less memory and processing time to calculate the same data using the same mesh. Although the nodal method generates a smaller linear system than the vector method, the vector coefficient matrix is significantly more sparse than the nodal one. The greater sparsity makes the vector approach more computationally efficient, requiring less memory and running in less time than the nodal method to generate results with the same level of accuracy. 

Artigo em Revista
Anisotropic Born scattering for the qP scalar wavefield using a lowrank symbol approximation We have developed a procedure to derive lowrank evolution operators in the mixed spacewavenumber domain for modeling the qP Bornscattered wavefield at perturbations of an anisotropic medium under the pseudoacoustic approximation. To approximate the full wavefield, this scattered field is then added to the reference wavefield obtained with the corresponding lowrank evolution operator in the background medium. Being built upon a Hamiltonian formulation using the dispersion relation for qPwaves, this procedure avoids pseudoSwave artifacts and provides a unified approach for linearizing anisotropic pseudoacoustic evolution operators. Therefore, it is immediately applicable to any arbitrary class of anisotropy. As an additional asset, the scattering operators explicitly contain the sensitivity kernels of the Bornscattered wavefield with respect to the anisotropic medium parameters. This enables direct access to important information such as its offset dependence or directional characteristics as a function of the individual parameter perturbations. For our numerical tests, we specify the operators for a mildly anisotropic tilted transversely isotropic (TTI) medium. We validate our implementation in a simple model with weak contrasts and simulate reflection data in the BP TTI model to indicate that the procedure works in a more realistic scenario. The Bornscattering results indicate that our procedure is applicable to strongly heterogeneous anisotropic media. Moreover, we use the analytical capabilities of the kernels by means of sensitivity tests to demonstrate that using two different medium parameterizations leads to different results. The mathematical formulation of the method is such that it allows for an immediate application to leastsquares migration in pseudoacoustic anisotropic media. 

Artigo em Revista
The Generalized Cross Validation Method for the Selection of Regularization Parameter in Geophysical Diffraction Tomography Inverse problems are usually illposed in such a way that it is necessary to use some method to reduce their deficiencies. For this purpose, we use the regularization by derivative matrices, known as Tikhonov regularization. There is a crucial problem in regularization, which is the selection of the regularization parameter Î». In this work, we use generalized cross validation (GCV) as a tool for the selection of Î». GCV is used here for an application in geophysical diffraction tomography, where the objective is to obtain the 2D velocity distribution from the measured values of the scattered acoustic field. The results are compared to those obtained using Lcurve, and also Ï´curve, which is an extension of Lcurve. We present several simulation results with synthetic data, and in general the results using GCV are equal or eventually better than the other two approaches. 

Artigo em Revista
Signal timeâ€“frequency representation and decomposition using partial fractions The Ztransform of a complex time signal (or the analytic signal of a real signal) is equal to the Ztransform of a prediction error divided by the Ztransform of the rediction error operator. This inverse is decomposed into a sum of partial fractions, which are used to obtain impulse response operators formed by noncausal filters that complexconjugate symmetric coefficients. The time components are obtained by convolving the filters with the original signal, and the peak frequencies, corresponding to the poles of the prediction error operator, are used for mapping the time components into frequency components. For nonstationary signals, this decomposition is done in sliding time windows, and the signal component values, in the middle of each window, are attributed to the peak value of its frequency response that corresponds to the pole of this partial fraction component. The result is an exact, but nonunique, timeâ€“frequency representation of the input signal. A sparse signal decomposition can be obtained by summing along the frequency axis in patches with similar characteristics in the timeâ€“frequency domain. The peak amplitude frequency of each new time component is obtained by computing a scalar prediction error operator in sliding time windows, resulting in a sparse timeâ€“frequency representation. In both cases, the result is a timeâ€“frequency matrix where an estimate of the frequency content of the input signal can be obtained by summation over the time variable. The performance of the new method is demonstrated with excellent results on a synthetic time signal, the LIGO gravitational wave signal and seismic field data. 

Artigo em Revista
A combined method using singular spectrum analysis and instantaneous frequency for the groundroll filtering The noise attenuation is a fundamental step in seismic data processing, especially when groundroll suppression remains a challenge. Rankreduction methods have become quite popular in recent decades, as they promote significant improvements in the quality of data, highlighting reflections in seismograms. We present a methodology for groundroll filtering, which combines the application of a recursiveiterative singular spectrum analysis method, in the time domain, as a particular way to decompose seismic data, with the computation of the average instantaneous frequency of the signal components. This combination allows for a precise estimation and filtering of the groundroll noise. The frequency values are used for determining, in each component, the lowfrequency parts associated with the ground roll. For every single component, the ground roll is attenuated by zeroing, and stacking the data components, where the average instantaneous frequency values match the groundroll bandwidth of frequency. Also, in order to enhance the lateral coherence of the reflectors,we present an extension of the recursiveiterative algorithm for a multichannel case. The multichannel algorithm is applicable on a shot, or common midpoint family of seismic traces, after the normal moveout correction. The numerical results using real data show the effectiveness of the proposed methodology for groundroll attenuation and for improving the velocity analysis. 

Artigo em Revista
Potencial de exploraÃ§Ã£o de nÃ£oconvencionais  Bahia. A Bahia, com seu pioneirismo e histÃ³ria de sucesso na produÃ§Ã£o comercial de petrÃ³leo na Bacia do RecÃ´ncavo, possui significativo potencial exploratÃ³rio. Embora as atividades de exploraÃ§Ã£o e produÃ§Ã£o estejam em declÃnio, devido ao baixo fator de recuperaÃ§Ã£o de poÃ§os em campos produtores e ao desinvestimento da Petrobras na exploraÃ§Ã£o em Ã¡reas terrestre, desperta interesse o potencial de gÃ¡s associado aos folhelhos da FormaÃ§Ã£o Candeias, que sÃ£o rochas geradora+reservatÃ³rio de gÃ¡s, pois possuem valores elevados de carbono orgÃ¢nico total e maturaÃ§Ã£o tÃ©rmica adequada. A localizaÃ§Ã£o privilegiada da Bacia do RecÃ´ncavo, em relaÃ§Ã£o aos centros consumidores, aumenta a importÃ¢ncia dos reservatÃ³rios de baixa permeabilidade no cenÃ¡rio de E&P do estado. Neste capÃtulo, serÃ¡ apresentado o contexto geolÃ³gico das Ã¡reas terrestres potenciais para exploraÃ§Ã£o em reservatÃ³rios nÃ£o convencionais, com maior Ãªnfase na Bacia do RecÃ´ncavo. SerÃ¡ dado destaque, ainda, Ã importÃ¢ncia e ao potencial dos dados geofÃsicos disponÃveis no BDEP/ ANP20, Ã s contribuiÃ§Ãµes da UFBA na formaÃ§Ã£o de recursos humanos para a E&P e Ã importÃ¢ncia do reprocessamento de dados sÃsmicos e da interpretaÃ§Ã£o sismoestratigrÃ¡fica na investigaÃ§Ã£o do potencial de shale gas do Estado da Bahia. 

Artigo em Revista
Prestack seismic data reconstruction and denoising by orientationdependent tensor decomposition Multidimensional seismic data reconstruction and denoising can be achieved by assuming noiseless and complete data as lowrank matrices or tensors in the frequencyspace domain. We have adopted a simple and effective approach to interpolate prestack seismic data that explores the lowrank property of multidimensional signals. The orientationdependent tensor decomposition represents an alternative to multilinear algebraic schemes. Our method does not need to perform any explicit matricization, only requiring calculation of the socalled covariance matrix for one of the spatial dimensions. The elements of such a matrix are the inner products between the lower dimensional tensors in a convenient direction. The eigenvalue decomposition of the covariance matrix provides the eigenvectors for the reducedrank approximation of the data tensor. This approximation is used for recovery and denoising, iteratively replacing the missing values. Synthetic and field data examples illustrate the methodâ€™s effectiveness for denoising and interpolating 4D and 5D seismic data with randomly missing traces. 

Artigo em Revista
Time evolution of the firstorder linear acoustic/elastic wave equation using Lie product formula and Taylor expansion We propose a new numerical solution to the firstorder linear acoustic/elastic wave equation. This numerical solution is based on the analytic solution of the linear acoustic/elastic wave equation and uses the Lie product formula, where the time evolution operator of the analytic solution is written as a product of exponential matrices where each exponential matrix term is then approximated by Taylor series expansion. Initially, we check the proposed approach numerically and then demonstrate that it is more accurate to apply a Taylor expansion for the exponential function identity rather than the exponential function itself. The numerical solution formulated employs a recursive procedure and also incorporates the split perfectly matched layer boundary condition. Thus, our scheme can be used to extrapolate wavefields in a stable manner with even larger timesteps than traditional finitedifference schemes. This new numerical solution is examined through the comparison of the solution of full acoustic wave equation using the Chebyshev expansion approach for the matrix exponential term. Moreover, to demonstrate the efficiency and applicability of our proposed solution, seismic modelling results of three geological models are presented and the processing time for each model is compared with the computing time taking by the Chebyshev expansion method. We also present the result of seismic modelling using the scheme based in Lie product formula and Taylor series expansion for the firstorder linear elastic wave equation in vertical transversely isotropic and tilted transversely isotropic media as well. Finally, a poststack migration results are also shown using the proposed method. 

Artigo em Revista
Potencial gerador e maturidade tÃ©rmica dos folhelhos da FormaÃ§Ã£o Barreirinha, borda sul da Bacia do Amazonas, Brasil Este trabalho tem como objetivo avaliar o potencial gerador e o efeito da intrusiva Ãgnea bÃ¡sica na maturidade tÃ©rmica das amostras com base no estudo de geoquÃmica orgÃ¢nica e palinologia. Foram estudadas 15 amostras de rocha coletadas em um afloramento da FormaÃ§Ã£o Barreirinha, borda sul da Bacia do Amazonas. Nesse afloramento foi observada uma soleira de basalto que pode ter influenciado os dados geoquÃmicos das amostras localizadas no topo do perfil. Os teores de Carbono orgÃ¢nico total (COT; 0,04â€“2,06%) e os resultados da pirÃ³lise RockEval indicam a presenÃ§a de querogÃªnio predominantemente dos tipos II e III, potencial gerador de hidrocarbonetos (S2; 0,04â€“3,00 mg HC/g rocha) variando de pobre a mÃ©dio, baixa concentraÃ§Ã£o de hidrocarbonetos livres (S1; 0,01â€“0,25 mg HC/g rocha) e uma variaÃ§Ã£o na maturidade termal (TmÃ¡x: 359â€“605Â°C). A razÃ£o aquÃ¡ticoterrestre (RAT; 0,08â€“1,16) indica a predominÃ¢ncia de deposiÃ§Ã£o de matÃ©ria orgÃ¢nica algÃ¡lica, e as razÃµes dos biomarcadores saturados [Hopanos/esteranos; gamacerano/(gamacerano + C30 hopano); TTP/(TTP + DIA); e esteranos C27C28C29] indicam um paleoambiente marinho com contribuiÃ§Ã£o variÃ¡vel de componentes terrestres, devido as oscilaÃ§Ãµes do nÃvel do mar ocorridas durante o Devoniano Superior. A razÃ£o entre os isoprenÃ³ides Pristano e Fitano (P/F: 1,6â€“7,1) apontam ambiente subÃ³xico. Os resultados da cromatografia gasosa e das razÃµes de biomarcadores saturados dos extratos orgÃ¢nicos [Ts/(Ts + Tm); C29 Î±Î²Î²/(Î±Î²Î² + Î±Î±Î±); C29 S/(C29 S + C29R)] indicam a variaÃ§Ã£o na maturidade tÃ©rmica ao longo do afloramento, e sugerem a geraÃ§Ã£o e migraÃ§Ã£o de Ã³leo e gÃ¡s, e/ou a degradaÃ§Ã£o termal de alguns biomarcadores saturados. 

Artigo em Revista
Some problems related to nonlinear 3Dmagnetoelasticity We consider some direct and inverse problems associated with the vibration of an elastic conductive body governed by the LamÃ© and Maxwell equations coupled through the nonlinear magnetoelastic effect. First, we prove the existence and uniqueness result for a mixed initialboundary value problem. Uniqueness is proved under additional assumptions on the smoothness of the solution. Second, we prove the solvability of an inverse problem, which consists of identifying the unknown scalar function Î±(t) in the elastic force Î±(t)Î²(x, t) acting on the body when some additional measurement is available. 
