Produção Científica
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 tĂ©rmica dos folhelhos da FormaĂ§ĂŁo Barreirinha, borda sul da Bacia do Amazonas, Brasil Este trabalho tem como objetivo avaliar o potencial gerador e o efeito da intrusiva Ăgnea bĂˇsica na maturidade tĂ©rmica das amostras com base no estudo de geoquĂmica orgĂ˘nica e palinologia. Foram estudadas 15 amostras de rocha coletadas em um afloramento da FormaĂ§ĂŁo Barreirinha, borda sul da Bacia do Amazonas. Nesse afloramento foi observada uma soleira de basalto que pode ter influenciado os dados geoquĂmicos das amostras localizadas no topo do perfil. Os teores de Carbono orgĂ˘nico total (COT; 0,04â€“2,06%) e os resultados da pirĂłlise RockEval indicam a presenĂ§a de querogĂŞnio predominantemente dos tipos II e III, potencial gerador de hidrocarbonetos (S2; 0,04â€“3,00 mg HC/g rocha) variando de pobre a mĂ©dio, baixa concentraĂ§ĂŁo de hidrocarbonetos livres (S1; 0,01â€“0,25 mg HC/g rocha) e uma variaĂ§ĂŁo na maturidade termal (TmĂˇx: 359â€“605Â°C). A razĂŁo aquĂˇticoterrestre (RAT; 0,08â€“1,16) indica a predominĂ˘ncia de deposiĂ§ĂŁo de matĂ©ria orgĂ˘nica algĂˇlica, e as razĂµes dos biomarcadores saturados [Hopanos/esteranos; gamacerano/(gamacerano + C30 hopano); TTP/(TTP + DIA); e esteranos C27C28C29] indicam um paleoambiente marinho com contribuiĂ§ĂŁo variĂˇvel de componentes terrestres, devido as oscilaĂ§Ăµes do nĂvel do mar ocorridas durante o Devoniano Superior. A razĂŁo entre os isoprenĂłides Pristano e Fitano (P/F: 1,6â€“7,1) apontam ambiente subĂłxico. Os resultados da cromatografia gasosa e das razĂµes de biomarcadores saturados dos extratos orgĂ˘nicos [Ts/(Ts + Tm); C29 Î±Î˛Î˛/(Î±Î˛Î˛ + Î±Î±Î±); C29 S/(C29 S + C29R)] indicam a variaĂ§ĂŁo na maturidade tĂ©rmica ao longo do afloramento, e sugerem a geraĂ§ĂŁo e migraĂ§ĂŁo de Ăłleo e gĂˇs, e/ou a degradaĂ§ĂŁo 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 LamĂ© 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)Î˛(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 Biotâ€™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. 

Artigo em Revista
NUMERICAL SIMULATION OF SEISMIC WAVES IN POROUS MEDIA This work presents a mathematical algorithm for modeling the propagation of poroelastic waves. We have shown how the classical Biot equations can be put into Ursinâ€™s form in a planelayered 3D porous medium. Using this form, we have derived explicit formulas that can be used as the basis of an efficient computational algorithm. To validate the algorithm, numerical simulations were performed using both the poroelastic and equivalent elastic models. The results obtained confirmed the proposed algorithmâ€™s reliability, identifying the main wave events in both lowfrequency and highfrequency regimes in the reservoir and laboratory scales, respectively. We have also illustrated the influence of some physical parameters on the attenuation and dispersion of the slow wave. 

Artigo em Revista
An application of the Marchenko internal multiple elimination scheme formulated as a leastsquares problem Images produced by migration of seismic data related to complex geology are often contaminated by artifacts due to the presence of internal multiple reflections. These reflections are created when the seismic wave is reflected more than once in a sourcereceiver path and can be interpreted as the main coherent noise in seismic data. Several schemes have been developed to predict and subtract internal multiple reflections from measured data, such as the Marchenko multiple elimination (MME) scheme that eliminates the referred events without requiring a subsurface model or an adaptive subtraction approach. The MME scheme is datadriven, can remove or attenuate most of these internal multiples, and was originally based on the Neumann series solution of Marchenkoâ€™s projected equations. However, the Neumann series approximate solution is conditioned to a convergence criterion. We reformulate the MME as a leastsquares problem (LSMME) in such a way that it can provide an alternative that avoids a convergence condition as required in the Neumann series approach. To demonstrate the LSMME scheme performance, we apply it to 2D numerical examples and compare the results with those obtained by the conventional MME scheme. In addition, we evaluate the successful application of our method through the generation of indepth seismic images, by applying reverse time migration (RTM) to the original data set and to those obtained through MME and LSMME schemes. From the RTM results, we found that the application of both schemes on seismic data allows the construction of seismic images free of artifacts related to internal multiple events. 

Artigo em Revista
3D reverse time migration using a wavefield domain dynamic approach 3D Reversetime migration (RTM) is a powerful technique for imaging complex geologic structures. This approach requires a significant computational effort, demanding a high amount of memory for storing the source's wavefields, consequently leading to a high cost to perform the imaging condition. Thus, this work aims to reduce these problems by introducing a dynamic approach (DA) that considers the sparsity of the wavefield in the first periods of propagation. The RTM combined with the DA (RTMDA) approximates the computational domain to the propagation domain, which is the region delimited by the wavefront. In practical terms, the computational domain expands together with the wavefront, reflecting in a very significant economy of memory and reduction of processing time when compared to the conventional RTM, which we denominate as a static approach (RTMSA). To reduce the sparsity of the wavefields in the first periods of propagation, we have built an empirical 3D filter that maps each timestep of the wavefield and gives the coordinates to approximate the computational domain to the propagation domain. We compare both approaches using the 3D SEG/EAGE Salt model and demonstrate that the RTMDA is more efficient than the RTMSA in terms of memory consumption and computational time, preserving the quality of the seismic image. 

Artigo em Revista
Influence of Bubblepoint Pressure on the Gas Formation in an Oil Reservoir Under Water Injection To evaluate the oil recovering in a reservoir producing at the bubblepoint pressure, we performed numerical simulations using a sandbox model and a black oil approach for the reservoir, and the toolkit CFD software OpenFOAM. A new solver treats the threephase dynamics of the oil watergas in the reservoir. The calculation includes four cases with different pressures of the injection and production wells to explore the free gas formation. Our results show that even keeping constant the pressure unbalance between the injection and production wells, we observe different dynamics. There is no gas formation and a typical production profile results if the bottomhole pressure is just above the bubblepoint in the injection and production wells. In case only the production well bottomhole pressure is just below the bubblepoint, we see no gas formation near the injection well and oscillatory gas formation around the production well. We see a triphasic flow along with the whole domain if both bottom hole pressures are just below the bubblepoint. However, if the bottomhole pressure in both wells goes further below, the gas flow rate no more oscillates and the gas formation becomes continuous. We have also treated a special case to analyze the influence of gravity on the triphasic flow. Here we observed the gravity segregation to be not significant. 

Artigo em Revista
Interferometric redatuming by deconvolution and correlationbased focusing Seismic interferometry is a method used to calculate wavefields for sources and receivers that are located where only sources or only receivers are available. There are correlation or deconvolutionbased interferometric methods that can be used to reposition the seismic array from the earthâ€™s surface to an arbitrary datum at depth. Based on the oneway reciprocity theorems of convolution and correlation type, we have determined that interferometric redatuming can be achieved in a deconvolutiononly procedure in three steps. The first two steps consist of separately retrieving, for sources at the earthâ€™s surface, the downward and upwardpropagating Greenâ€™s functions at receivers at the datum, which are then used in the third step to reposition the sources to the datum. For the involved deconvolutions, transmitted and backscattered wavefields need to be modeled with a velocity model between the acquisition and datum levels. Our numerical experiments demonstrate that the method can help to reduce nonphysical events and other artifacts that commonly arise in purely correlationbased procedures. If a highquality overburdenvelocity model is available, it correctly accounts for inhomogeneities in the overburden medium. Because the methodâ€™s sensitivity to the velocity model is mainly introduced by backscattering at overburden heterogeneities, a smooth model is sufficient when overburden scattering is weak. 
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