Produção Científica
Artigo em Revista
Adding Prior Information in FWI through Relative Entropy Full waveform inversion is an advantageous technique for obtaining highresolution subsurface information. In the petroleum industry, mainly in reservoir characterisation, it is common to use information from wells as previous information to decrease the ambiguity of the obtained results. For this, we propose adding a relative entropy term to the formalism of the full waveform inversion. In this context, entropy will be just a nomenclature for regularisation and will have the role of helping the converge to the global minimum. The application of entropy in inverse problems usually involves formulating the problem, so that it is possible to use statistical concepts. To avoid this step, we propose a deterministic application to the full waveform inversion. We will discuss some aspects of relative entropy and show three different ways of using them to add prior information through entropy in the inverse problem. We use a dynamic weighting scheme to add prior information through entropy. The idea is that the prior information can help to find the path of the global minimum at the beginning of the inversion process. In all cases, the prior information can be incorporated very quickly into the full waveform inversion and lead the inversion to the desired solution. When we include the logarithmic weighting that constitutes entropy to the inverse problem, we will suppress the lowintensity ripples and sharpen the point events. Thus, the addition of entropy relative to full waveform inversion can provide a result with better resolution. In regions where salt is present in the BP 2004 model, we obtained a significant improvement by adding prior information through the relative entropy for synthetic data. We will show that the prior information added through entropy in fullwaveform inversion formalism will prove to be a way to avoid local minimums. 

Artigo em Revista
Structural and sedimentary discontinuities control the generation of karst dissolution cavities in a carbonate sequence, Potiguar Basin, Brazil Epigenetic karstic systems in carbonate rocks commonly result from progressive dissolution by acidic meteoric waters over thousands to millions of years. The generation of secondary porosity and permeability improvement due to dissolution in carbonate reservoirs of geofluids (e.g., groundwater, hydrocarbons, and CO2) can profoundly impact reservoir storage capacity and subsurface fluid flow. This study investigates the control of structural discontinuities such as stylolites, fractures, and primary sedimentary discontinuities on the generation of multiscale karst dissolution cavities by epigenetic fluid percolation in a Late Cretaceous carbonate sequence (JandaÃra Formation) in the Potiguar Basin, Northeastern Brazil. The study relies on micro and macroscale nalyses such as stratigraphic logs, field structural investigations, rock strength data collected in the field (Schmidt hammer), microtomographic and drone images, thin section analyses, porosity and permeability laboratory measurements. The results show that bedperpendicular stratabound and nonstratabound stylolites and fractures can be enlarged due to meteoric water percolation until they merge and form a single channel system that crosscuts all sedimentary multilayers. Bedparallel stylolites are ubiquitous in carbonate sequences overprinting bed interfaces and layers. Where not dissolved, bedparallel stylolites have low porosity and permeability and thus can act as barriers to vertical fluid flow. Where dissolved, such stylolites can contribute to horizontal fluid flow and form channel porosity. The results of this study led to a formulation of a conceptual model of rock dissolution along structural and sedimentary discontinuities that affects carbonate rock successions in the subsurface. 

Artigo em Revista
Imageguided ray tracing and its applications Eikonal solvers have important applications in seismic data processing and inversion, the socalled imageguided methods. To this day, in imageguided applications, the solution of the eikonal equation is implemented using partialdifferentialequation solvers, such as fastmarching or fastsweeping methods. We have found that alternatively, one can numerically integrate the dynamic Hamiltonian system defined by the imageguided eikonal equation and reconstruct the solution with imageguided rays. We evaluate interesting applications of imageguided ray tracing to seismic data processing, demonstrating the use of the resulting rays in imageguided interpolation and smoothing, welllog interpolation, image flattening, and residualmoveout picking. Some of these applications make use of properties of the raytracing system that are not directly obtained by eikonal solvers, such as ray position, ray density, wavefront curvature, and ray curvature. These ray properties open space for a different set of applications of the imageguided eikonal equation, beyond the original motivation of accelerating the construction of minimum distance tables. We stress that imageguided ray tracing is an embarrassingly parallel problem that makes its implementation highly efficient on massively parallel platforms. Imageguided ray tracing is advantageous for most applications involving the tracking of seismic events and imagingguided interpolation. Our numerical experiments using synthetic and real data sets indicate the efficiency and robustness of imageguided rays for the selected applications. 

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. 
