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
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. 
Apresentação
Lanczos Bidiagonalization Method for Parallel 3D Gravity Inversion  Application to Basement Relief Definition It is present an efficient parallel algorithm for the inversion of 3D gravity data, which goal is to estimate the depth of a sedimentary basin in which the density contrast varies parabolically with depth. The efficiency of the gravity inversion methods applied to the interpretation of sedimentary basins depends on the number of data and model parameters to be estimated, making it very poor when the number of parameters is very large. We present the simulation results with a synthetic model of a sedimentary basin inspired in a real situation, taking advantage of a parallel LevenbergMarquardt algorithm implemented using both MPI and OpenMP. Lanczos bidiagonalization method has been used to obtain the solution for the linearized subproblem at each iteration. The idea of obtaining the solution of a large system of equations using the bidiagonalization procedure is quite useful in practical problems, and allows to implement selection methods for the optimal regularization parameter in an easy way, like the weighted generalized cross validation method, adopted in this work. The hybrid parallel implementation combined with Lanczos bidiagonalization allows us to achieve a significant reduction of the computational cost, which is otherwise very high due to the scale of the problem. 
Apresentação
Remigrationtrajectory Timemigration Velocity Analysis in Regions with Strong Velocity Variations. Remigration trajectories describe the position of an image point in the image domain for different sourcereceiver offsets as a function of the migration velocity. They can be used for prestack time migration velocity analysis by means of determining kinematic migration parameters, which in turn, allow to locally correct the velocity model. The main advantage of this technique is that it takes the reflectionpoint displacement in the midpoint direction into account, thus allowing for a moveout correction for a single reflection point at all offsets of a common image gather (CIG). We have tested the feasibility of the method on synthetic data from three simple models and the Marmousoft data. Our tests show that the proposed tool increases the velocitymodel resolution and provides a plausible timemigrated image, even in regions with strong velocity variations. The most effort was spent on the event picking, which is critical to the method. 
Apresentação
A Wavefrontpropagation Strategy for Timetodepth Conversion We present a strategy to timetodepth conversion and velocity estimation based only on the imagewavefront propagation. It has two main features: (1) it computes the velocity field and the traveltime directly, avoiding the raytracing step; and (2) it requires only the knowledge of the image wavefront at the previous time step. As a consequence, our method tends to be faster than usual techniques and does not carry the constraints and limitations inherent to common raytracing strategies. We have tested the feasibility of the method on the original Marmousi velocity model and two smoothed versions of it. Moreover, we migrated the Marmousi data set using the estimated depth velocity models. Our results indicate that the present strategy can be used to construct starting models for velocitymodel building in depth migration and/or tomographic methods. 
Apresentação
Timefrequency Decomposition and Qestimation Using Complex Filters Two ideas are presented in this paper. First, we develop an analytic extension of a timefrequency decomposition, the amplitude of which is a highresolution timefrequency decomposition that produces very tight energy peaks around the instantaneous frequency and the phase of which is a high precision and structured representation of the frequency content over signalâ€™s entire bandwidth. Second, we build upon this signal representation by developing a Qfactor estimation method that does so by balancing both the amplitude and phase information content of the complex time frequency decomposition. This estimator uses a propagator based on the KolsyFutterman formalism, which has a real part associated with attenuation and an imaginary part associated with dispersion, both of which are Qdependent. The two methods are matched to take advantage of both amplitude and phase information of the timefrequency distribution. We apply both methods to a synthetic seismic trace and to real marine data. In the synthetic example, instantaneous frequency and Qfactor are determined successfully. The phase of the TFD reveals the instantaneous frequency, with greater sharpness, in both the synthetic and, most markedly, in the marine data. 
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. 
Artigo em Revista
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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