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 DataProny 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 short-time 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 short-time 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 frequency-dependent 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 systemIn 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 3D-magnetoelasticityWe 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 so-called magnetoelastic effect. Uniqueness is proved under additional assumptions on the smoothness of the solution. |

**Apresentação**

Lanczos Bidiagonalization Method for Parallel 3-D Gravity Inversion - Application to Basement Relief DefinitionIt is present an efficient parallel algorithm for the inversion of 3-D 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 Levenberg-Marquardt 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**

Remigration-trajectory Time-migration Velocity Analysis in Regions with Strong Velocity Variations.Remigration trajectories describe the position of an image point in the image domain for different source-receiver 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 reflection-point 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 velocity-model resolution and provides a plausible time-migrated 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 Wavefront-propagation Strategy for Time-to-depth ConversionWe present a strategy to time-to-depth conversion and velocity estimation based only on the image-wavefront propagation. It has two main features: (1) it computes the velocity field and the traveltime directly, avoiding the ray-tracing 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 ray-tracing 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 velocity-model building in depth migration and/or tomographic methods. |

**Apresentação**

Time-frequency Decomposition and Q-estimation Using Complex FiltersTwo ideas are presented in this paper. First, we develop an analytic extension of a time-frequency decomposition, the amplitude of which is a high-resolution time-frequency 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 Q-factor 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 Kolsy-Futterman formalism, which has a real part associated with attenuation and an imaginary part associated with dispersion, both of which are Q-dependent. The two methods are matched to take advantage of both amplitude and phase information of the time-frequency distribution. We apply both methods to a synthetic seismic trace and to real marine data. In the synthetic example, instantaneous frequency and Q-factor 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 DERIVATIVESWe 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**

3-D SEISMIC MODELING AND DEPTH MIGRATION COMBINING THE EXTRAPOLATION OF UPGOING AND DOWNGOING WAVEFIELDSThe 3-D 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 Split-Step-Plus-Interpolation (SS-PSPI). This method has been proven to be quite adequate for migration problems in 3-D media, providing satisfactory results at low computational cost. In this work, 3-D 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 pre-stack migration of 3-D 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 3-D 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. |