Produção Científica
Artigo em Revista
An identification problem related to the Biot system. In this paper, we study the propagation of elastic waves in porous media governed by the Biot equations in the low frequency range. We prove the existence and uniqueness result both for the direct problem and the inverse one, which consists in identifying the unknown scalar function f(t) in the body density force f(t) 
Artigo em Revista
Prony Filtering of Seismic Data Prony filtering is a method of seismic data processing which can be used to solve various geological and production tasks, involving an analysis of target horizons characteristics and a prediction of possible productive zones. This method is based on decomposing the observed seismic signals by exponentially damped cosines at shorttime intervals. As a result, a discrete Prony spectrum including values of four parameters (amplitude, damping factor, frequency, phase) can be created. This decomposition occurs at many shorttime intervals moving along an observed trace. The combined Prony spectrum of the trace can be used to create images of the trace through a selection of some values of the parameters. These images created for all traces of a seismic section provide an opportunity for locating zones of frequencydependent anomalous scattering and absorption of seismic energy. Subsequently, the zones can be correlated with target seismic horizons. Analysis and interpretation of these zones may promote understanding of the target horizons features and help to connect these features with the presence of possible reservoirs. 
Artigo em Revista
An identification problem related to the Biot system In this paper, we study the propagation of elastic waves in porous media governed by the Biot equations in the low frequency range. We prove the existence and uniqueness result both for the direct problem and the inverse one, which consists in identifying the unknown scalar function f(t) in the body density force f(t) 
Artigo em Revista
On an initial boundary value problem in nonlinear 3Dmagnetoelasticity We prove existence and uniqueness of a weak solution to an initial boundary value problem, related to the Maxwell and LamÃ© systems nonlinearly coupled through the socalled magnetoelastic effect. Uniqueness is proved under additional assumptions on the smoothness of the solution. 
Artigo em Revista
DIRECT PROBLEMS FOR POROELASTIC WAVES WITH FRACTIONAL DERIVATIVES We prove the uniqueness and continuous dependence on the data of a weak solution to a problem for poroelastic waves with fractional derivatives both in unbounded and bounded time intervals and in all space dimensions. 
Artigo em Revista
3D SEISMIC MODELING AND DEPTH MIGRATION COMBINING THE EXTRAPOLATION OF UPGOING AND DOWNGOING WAVEFIELDS The 3D acoustic wave equation is generally solved using finite difference schemes on the mesh which defines the velocity model. However, when numerical solution of the wave equation is done by finite difference schemes, attention should be taken with respect to dispersion and numerical stability. To overcome these problems, one alternative is to solve the wave equation in the Fourier domain. This approach is stabler and makes possible to separate the full wave equation in its unidirectional equations. Thus, the full wave equation is decoupled in two first order differential equations, namely two equations related to the vertical component: upgoing (Z) and downgoing (+Z) unidirectional equations. Among the solution methods, we can highlight the SplitStepPlusInterpolation (SSPSPI). This method has been proven to be quite adequate for migration problems in 3D media, providing satisfactory results at low computational cost. In this work, 3D seismic modeling is implemented using Huygensâ€™ principle and an equivalent simulation of the full wave equation solution is obtained by properly applying the solutions of the two uncoupled equations. In this procedure, a point source wavefield located at the surface is extrapolated downward recursively until the last depth level in the velocity field is reached. A second extrapolation is done in order to extrapolate the wavefield upwards, from the last depth level to the surface level, and at each depth level the previously stored wavefield (saved during the downgoing step) is convolved with a reflectivity model in order to simulate secondary sources. To perform depth prestack migration of 3D datasets, the decoupled wave equations were used and the same process described for seismic modeling is applied for the propagation of sources and receivers wavefields. Thus, depth migrated images are obtained using appropriate image conditions: the upgoing and downgoing wavefields of sources and receivers are correlated and the migrated images are formed. The seismic modeling and migration methods using upgoing and downgoing wavefields were tested on simple 3D models. Tests showed that the addition of upgoing wavefield in seismic migration, provide better result and highlight steep deep reflectors which do not appear in the results using only downgoing wavefields. 
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Q factor estimation from the amplitude spectrum of the timeâ€“frequency transform of stacked reflection seismic data Attenuation is one factor that degrades the quality of reflection seismic subsurface imaging. It causes a progressive decrease in the seismic pulse energy and is also responsible for limiting seismic resolution. Currently, many methods exist for inverse Q filtering,which can be used to correct these effects to some extent; however, but all of these methods require the value of the Q factor to be known, and this information is rarely available. In this paper we present and evaluate three different strategies to derive the Q factor from the timeâ€“frequency amplitude spectrum of the seismic trace. They are based in the analyses of the amplitude decay trend curves that can be measured along time, along frequency or along a compound variable obtained from the timeâ€“frequency product. Some difficulties are highlighted, such as the impossibility to use short time window intervals that prevents the method from providing a precise map of the Q factor value of the subsurface layers. However, the Q factor estimation made in thisway can be used to guide the parameterization of attenuation correction by means of inverse Q filtering applied to a stacked seismic section; this is demonstrated in a real data example. 
Artigo em Revista
Reduction of crosstalk in blendedshot migration When migrating more than one shot at the same time, the nonlinearity of the imaging condition causes the final image to contain socalled crosstalk, i.e., the results of the interference of wavefields associated with different sources. We studied various ideas of using weights in the imaging condition, called encoding, for the reduction of crosstalk. We combined the ideas of random phase and/or amplitude encoding and random alteration of the sign with additional multiplication with powers of the imaginary unit. This procedure moved part of the crosstalk to the imaginary part of the resulting image, leaving the desired crosscorrelation in the real part. In this way, the final image is less impaired. Our results indicated that with a combination of these weights, the crosstalk can be reduced by a factor of four as compared with unencoded shot blending. Moreover, we evaluated the selection procedure of sources contributing to each group of shots. We compared random choice with a deterministic procedure, in which the random numbers were exchanged for numbers similar to those of a Costas array. These numbers preserve certain properties of a random choice, but avoid the occurrence of patterns in the distribution. Our objective was to avoid nearby source being added to the same group of shots, which cannot be guaranteed with a random choice. Finally, we determined that the crosstalk noise can be reduced after migration by image processing. Keywords: migration, crosscorrelation, imaging, noise 

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Symplectic scheme and the Poynting vector in reversetime migration We developed a new numerical solution for the wave equation that combines symplectic integrators and the rapid expansion method (REM). This solution can be used for seismic modeling and reversetime migration (RTM). In seismic modeling and RTM, spatial derivatives are usually calculated by finite differences (FDs) or by the Fourier method, and the time evolution is normally obtained by a secondorder FD approach. If the spatial derivatives are computed by higher order FD schemes, then the time step needs to be small enough to avoid numerical dispersion, therefore increasing the computational time. However, by using REM with the Fourier method for the spatial derivatives, we can apply the proposed method to propagate the wavefield for larger time steps. Moreover, if the appropriate number of expansion terms is chosen, thismethod is unconditionally stable and propagates seismic waves free of numerical dispersion. The use of a symplectic numerical scheme provides the solution of the wave equation and its first time derivative at the current time step. Thus, the Poynting vector can also be computed during the time extrapolation process at very low computational cost. Based on the Poynting vector information, we also used a new methodology to separate the wavefield in its upgoing and downgoing components. Additionally, Poynting vector components can be used to compute common gathers in the reflection angle domain, and the stack of some angle gathers can be used to eliminate lowfrequency noise produced by the RTM imaging condition. We numerically evaluated the applicability of the proposed method to extrapolate a wavefield with a time step larger than the ones commonly used by symplectic methods as well as the efficiency of this new symplectic method combined with REM to successfully handle the Poynting vector calculation. 
Artigo em Revista
Fast Seismic Inversion Methods Using Ant Colony Optimization Algorithm This letter presents ACOBBR  V, a new computationally efficient antcolonyoptimizationbased algorithm, tailored for continuousdomain problems. The ACOBBR  V algorithm is well suited for application in seismic inversion problems, owing to its intrinsic features, such as heuristics in generating the initial solution population and its facility to deal with multiobjective optimization problems. Here, we show how the ACOBBR  V algorithm can be applied in two methodologies to obtain 3D impedance maps from poststack seismic amplitude data. The first methodology pertains to the traditional method of forward convolution of a reflectivity model with the estimated wavelet, where ACOBBR  V is used to guess the appropriate wavelet as the reflectivity model. In the second methodology, we propose an even faster inversion algorithm based on inverse filter optimization, where ACOBBR  V optimizes the inverse filter that is deconvolved with the seismic traces and results in a reflectivity model similar to that found in well logs. This modeled inverse filter is then deconvolved with the entire 3D seismic volume. In experiments, both the methodologies are applied to a synthetic 3D seismic volume. The results validate their feasibility and the suitability of ACOBBR  V as an optimization algorithm. The results also show that the second methodology has the advantages of a much higher convergence speed and effectiveness as a seismic inversion tool. 