Produção Científica
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 signal’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 Huygens’ 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 time–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 time–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 time–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 

Apresentação
Detection of diffractions in seismic sections using Support Vector Classifiers Detection of diffractions is an essential step on diffraction imaging techniques. Due to their smaller amplitudes regarding reflection events, diffraction events are usually treated as noise in standard seismic processing. Diffraction imaging is often used to identify subsurface scattering features with enhanced resolution in comparison to conventional seismic reflection imaging. Several techniques have been presented in literature for separation of diffracted from reflected events. One way is to analyze amplitudes along diffraction time curves in commonoffset sections, where it is easier to perceive differences between diffraction and reflection events. Known pattern recognition methods can be used to separate the events. We analyze automatic detection of diffraction points using a twoclass k NearestNeighbours (kNN) and we present a routine for detection of diffractions using Support Vector Machines (SVM). We evaluate the ability of each method to detect scattering features, using synthetic seismic models. Results indicate that kNN method is more robust to noise and velocity model variation. On the other hand, SVM sensitiveness to velocity model can be useful on velocity analysis of scattering events. 
Artigo em Revista
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. 
Apresentação
RTM imaging condition using impedance sensitivity kernel combined with Poynting vector Reverse time migration (RTM) using crosscorrelation imaging condition is always contaminated by lowspatialfrequency artifacts due the presence of sharp wavespeed contrasts in the velocity model. Different techniques have been used and Laplacian filtering can lead to good results but it might damage the signal of interest. Recently it has been observed through numerical examples that RTM images obtained using the impedance sensitivity kernel are much less contaminated by lowfrequency artifacts. In this work, we are proposing to use the impedance sensitivity kernel instead of the conventional crosscorrelation RTM imaging condition to attenuate the low frequency artifacts. Using the impedance sensitivity kernel for the source downgoing wavefield separeted by the Poynting vector, we demostrate through syntethic examples that RTM image results preserve well the reflections and attenuate significantly the ackscattered low frequency noise. 
Apresentação
Chebyshev expansion applied to the onestep wave extrapolation matrix A new method of solving the acoustic onestep wave extrapolation matrix is proposed. In our method the analytical wavefield is separated in its real and imaginary parts and the firstorder coupled set of equations is solved by the TalEzer’s technique, and Chebyshev expansion is used to approximate the extrapolate operator eADt , where A is an antisymmetrical matrix and the pseudodifferential operator F is computed using the Fourier method. Thus, the proposed numerical algorithm can handle any velocity variation. Its implementation is straightforward and if an appropriate number of terms of the series expansion is chosen, the method is unconditionally stable and propagates seismic waves free of numerical dispersion. In our method the number of FFTs is explicitly determined and it is function of the maximum eigenvalue of the matrix A. Numerical modeling examples are shown to demonstrate that the proposed method has the capability to extrapolate waves in time using a time step up to Nyquist limit. 
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