Produção Científica
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 λ. In this work, we use generalized cross validation (GCV) as a tool for the selection of λ. 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 ϴcurve, 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 time–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, time–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 time–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 time–frequency representation. In both cases, the result is a time–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 exploração de nãoconvencionais  Bahia. A Bahia, com seu pioneirismo e história de sucesso na produção comercial de petróleo na Bacia do Recôncavo, possui significativo potencial exploratório. Embora as atividades de exploração e produção estejam em declínio, devido ao baixo fator de recuperação de poços em campos produtores e ao desinvestimento da Petrobras na exploração em áreas terrestre, desperta interesse o potencial de gás associado aos folhelhos da Formação Candeias, que são rochas geradora+reservatório de gás, pois possuem valores elevados de carbono orgânico total e maturação térmica adequada. A localização privilegiada da Bacia do Recôncavo, em relação aos centros consumidores, aumenta a importância dos reservatórios de baixa permeabilidade no cenário de E&P do estado. Neste capítulo, será apresentado o contexto geológico das áreas terrestres potenciais para exploração em reservatórios não convencionais, com maior ênfase na Bacia do Recôncavo. Será dado destaque, ainda, à importância e ao potencial dos dados geofísicos disponíveis no BDEP/ ANP20, às contribuições da UFBA na formação de recursos humanos para a E&P e à importância do reprocessamento de dados sísmicos e da interpretação sismoestratigráfica na investigação 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 method’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 térmica dos folhelhos da Formação Barreirinha, borda sul da Bacia do Amazonas, Brasil Este trabalho tem como objetivo avaliar o potencial gerador e o efeito da intrusiva ígnea básica na maturidade térmica das amostras com base no estudo de geoquímica orgânica e palinologia. Foram estudadas 15 amostras de rocha coletadas em um afloramento da Formação Barreirinha, borda sul da Bacia do Amazonas. Nesse afloramento foi observada uma soleira de basalto que pode ter influenciado os dados geoquímicos das amostras localizadas no topo do perfil. Os teores de Carbono orgânico total (COT; 0,04–2,06%) e os resultados da pirólise RockEval indicam a presença de querogênio predominantemente dos tipos II e III, potencial gerador de hidrocarbonetos (S2; 0,04–3,00 mg HC/g rocha) variando de pobre a médio, baixa concentração de hidrocarbonetos livres (S1; 0,01–0,25 mg HC/g rocha) e uma variação na maturidade termal (Tmáx: 359–605°C). A razão aquáticoterrestre (RAT; 0,08–1,16) indica a predominância de deposição de matéria orgânica algálica, e as razões dos biomarcadores saturados [Hopanos/esteranos; gamacerano/(gamacerano + C30 hopano); TTP/(TTP + DIA); e esteranos C27C28C29] indicam um paleoambiente marinho com contribuição variável de componentes terrestres, devido as oscilações do nível do mar ocorridas durante o Devoniano Superior. A razão entre os isoprenóides Pristano e Fitano (P/F: 1,6–7,1) apontam ambiente subóxico. Os resultados da cromatografia gasosa e das razões de biomarcadores saturados dos extratos orgânicos [Ts/(Ts + Tm); C29 αββ/(αββ + ααα); C29 S/(C29 S + C29R)] indicam a variação na maturidade térmica ao longo do afloramento, e sugerem a geração e migração de óleo e gás, e/ou a degradação 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 Lamé 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 α(t) in the elastic force α(t)β(x, t) acting on the body when some additional measurement is available. 

Artigo em Revista
AN ANALYTICAL SOLUTION OF THE SATURATED AND INCOMPRESSIBLE POROELASTIC MODEL FOR TRANSIENT WAVE PROPAGATION A transient wave propagation model is provided as a consequence of a new theory of porous media and wave propagation in saturated poroelastic media. This theory, in the linear case, becomes to be equivalent to the theory proposed by de Boer, R., Ehlers, W. & Liu, Z. in 1993. It leads to a model for the 1D porous saturated column problem, which after the appropriate establishment of boundary and initial conditions, can be solved analytically with the aid of the Laplace transform concerning time. Numerical experiments are performed to illustrate the behavior of constituents displacement fields. The theory results in having an inertial effect on the motion of solid constituents as commonly expected. However, in contrast to Biot’s theory, is not introduced by the present theory the relative acceleration as an interactive force between solid and fluid constituents to account for the apparent inertial effect. 

Artigo em Revista
Computation of Acoustic Velocity of Natural Gases With an Alternative Heat Capacity Ratio Equation and Application to Seismic Modeling We investigate three formulations for computing acoustic velocity of natural gas and derive an equation for the heat capacity ratio, which plays a central role in these formulations. The first formulation is a compilation of fundamental equations available in the engineering literature, referred to as the DASH formulation. The second formulation is a development from the first, in which we use the derived equation for the heat capacity ratio (modified DASH). The third formulation is a mainstream method implemented in Geoscience (BW formulation). All three formulations stem from virial Equations of State that take preponderance in the exploration stage, when the detailed fluid composition is unknown and compositional methods are frequently inapplicable. We test the formulations on an extensive experimental data set of acoustic velocity of natural gases and compare the resulting accuracies. Both DASH and modified DASH formulations provide significantly higher accuracy when compared to the BW formulation. Additionally, the modified DASH, as we derive in this work, has the highest accuracy at pressures above 7000 psi, a condition typically encountered in the Brazilian presalt reservoirs. In a final step, we investigate how these different formulations and corresponding accuracies in velocity computation may affect seismic modeling, using a single interface model between a dense gas reservoir and a sealing rock. A direct comparison of amplitude versus offset modeling using our modified DASH formulation and the BW formulation shows up to 50% difference in amplitude calculation in a sensitivity exercise, especially at the longer offsets and higher pressures. 
