Produção Científica

**Artigo em Revista**

On the elastic wave equation in weakly anisotropic VTI mediaThe knowledge of the wave equation is of fundamental importance for a good and satisfying understanding of the phenomena of wave propagation. However, it is unsatisfactory and inefficient to work with the full anisotropic wave equation in media that exhibit certain symmetries. We derive a specific elastic wave equation for weakly anisotropic VTI media by linearizing the expression of the stiffness tensor in terms of the Thomsen parameters. The resulting wave equation is a system of three coupled differential equations for the three components of the displacement vector. For Î´ = 0, the third equation becomes an independent equation for the third component of the particle displacement, identical to the isotropic situation, and the first two equations remain coupled. Using zero-order ray theory, we derive the associated eikonal and transport equations for q-P, q-SV and q-SH waves. These are finally reduced to the pseudo-acoustic case where the vertical S-wave velocity is zero. This allows for a better understanding of the pseudo-S-wave artefact in such media. |

**Artigo em Revista**

Using SVD filters for velocity analysis and ground-roll attenuationThis study investigates the adaptive filtering approach based on the Singular Value Decomposition (SVD) method to improve velocity analysis and ground-roll attenuation. The SVD filtering is an adaptive multichannel filtering method where each filtered seismic trace keeps a degree of coherence with the immediate neighboring traces. Before applying the adaptive filtering, in order to flatten the primary reflections the seismogram is corrected using the Normal Move Out (NMO) method. The SVD filtering helps to strengthen the spatial coherence of reflectors. It works as multichannel and can be applied by selecting a set of seismic traces taken from around the target trace. Thus traces from different shots can be represented by a five-point areal operator, which we call five-point cross operator. In this paper we run this operator along the coverage map of the seismic survey. At each operator position, the filtered trace (center of the operator) is obtained by taking the firstor adding the first eigenimages. Thereby we enhance the coherence corresponding to the primary reflections in detriment of the remaining events (ground-roll, multiples, and other non-correlated events) remained in the other eigenimages. The method was tested on a seismic line of the Tacutu, Brazil. The obtained results show the velocity spectra with better definition, as well as better post-stacked section exhibiting better continuity of seismic reflections and lower noise, compared with the raw processing results (without SVD filtering). |

**Artigo em Revista**

True-amplitude single-stack redatumingBased on the chaining of diffraction-stack migration and isochron-stack demigration, we derive a general true-amplitude Kirchhoff-type single-stack operator for 3D and 2.5D redatuming. It consists of performing a single weighted stack along adequately chosen stacking surfaces or lines. The corresponding traveltimes and weight functions can be calculated using quantities obtained from dynamic ray tracing. The operator simplifies when specified for zero-offset data. For simple types of media, we derive analytic expressions for the stacking lines and weight functions and demonstrate their functionality with numerical examples. |

**Artigo em Revista**

Symplectic scheme and the Poynting vector in reverse-time migrationWe 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 reverse-time 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 second-order 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, this method 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 low-frequency 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**

Signal and traveltime parameter estimation using singular value decompositionSignal detection and traveltime parameter estimation can be performed by computing a coherence function in a data window centered around a traveltime function defined by its parameters. We used singular value decomposition of the data matrix, not eigendecomposition of a covariance matrix, to review the most commonly used coherence measures. This resulted in a new reduced semblance coefficient defined from the first eigenimage, assuming that the signal amplitude was the same on all data channels (as in classical semblance). In a second signal model, the time signal was constant on each channel, but the amplitude changed. Then, the semblance coefficient is the square of the first singular value divided by the energy of the data. Two normalized crosscorrelation coefficients derived from the first eigenimage can also be used as a coherence measure: The normalized crosscorrelation of the spatial singular vector with a vector with all elements equal to one, and the normalized crosscorrelation of the temporal singular vector and the average time signal (the stacked trace). We defined a multiple signal classification (MUSIC) measure as the inverse of one minus any of the normalized coherence measures described above. To reduce the numerical range, we preferred to use log10 MUSIC. Numerical examples with different coherence measures applied to seismic velocity analysis of synthetic and real data revealed that the normalized crosscorrelation coefficients performed poorly and that log MUSIC gave no resolution enhancement on real data. The normalized eigenimage-energy coherence measure performed poorly on synthetic data but gave the best result for a simulated reflection with a polarity reversal. It also gave good time resolution on the real data. The classical semblance coefficient and the reduced semblance coefficient gave similar results with the reduced semblance coefficient having better resolution. |

**Artigo em Revista**

Entropic Regularization to Assist a Geologist in Producing a Geologic MapThe gravity and magnetic data measured on the Earthâ€™s surface or above it (collected from an aircraft flying at low altitude) can be used to assist in geologic mapping by estimating the spatial density and magnetization distributions, respectively, presumably confined to the interior of a horizontal slab with known depths to the top and bottom. To estimate density or magnetization distributions we assume a piecewise constant function defined on a user-specified grid of cells and invert the gravity or magnetic data by using the entropic regularization as a stabilizing function that allows estimating abrupt changes in the physical-property distribution. The entropic regularization combines the minimization of the first-order entropy measure with the maximization of the zeroth-order entropy measure of the solution vector. The aim of this approach is to detect sharp-bounded geologic units through the discontinuities in the estimated density or magnetization distributions. Tests conducted with synthetic data show that the entropic regularization can delineate discontinuous geologic units, allowing a better mapping of sharp-bounded (but buried) geologic bodies. We demonstrate the potential of the entropic regularization to assist a geologist in obtaining a geologic map by analyzing the estimated magnetization distributions from field magnetic data over a magnetic skarn in Butte Valley, Nevada, U.S.A. We show that it is an exoskarn where the ion exchange between the intrusive and the host rock occurs along a limited portion of the southern intrusive border. |

**Artigo em Revista**

Reconstruction of geologic bodies in depth associated with a sedimentary basin using gravity and magnetic dataWe present a comprehensive review of the most common gravity and magnetic interpretation methods to in depth retrieval of the geometry of geologic bodies associated with a sedimentary basin. We identify three types of bodies: 1) the sedimentary basement relief, 2) salt bodies and 3) mafic intrusions in a sedimentary section. In reconstructing basement topography through gravity and/or magnetic data we identify three groups of methods: the automatic, the spectral and the nonspectral methods. The reconstruction of salt bodies from gravity data usually uses interactive forward modelling but recently gravity inversion methods have been developed to interpret this kind of geologic environment. Finally, the problem of reconstructing intrusive bodies using magnetic and/or gravity data employs three strategies to interpret mafic or ultramafic intrusions in a sedimentary section: the automatic methods, interactive forward modelling and the inversion methods. |

**Artigo em Revista**

DECONVOLUTION OF SEISMIC DATA USING PHASE CHANGE OPERATORSApresentamos uma nova abordagem para deconvoluÃ§Ã£o do pulso sÃsmico. Investigamos o uso de operadores de mudanÃ§a de fase para obtenÃ§Ã£o de filtros de fase mista a partir de filtros de fase mÃnima. Os operadores de mudanÃ§a de fase sÃ£o construÃdos a partir das raÃzes associadas aos filtros de Wiener-Levinson. Escolhendo subconjuntos daquelas raÃzes Ã© possÃvel gerar um conjunto de filtros inversos de fase mista. A escolha do filtro Ã³timo Ã© realizada atravÃ©s do mÃ©todo de otimizaÃ§Ã£o conhecido com algoritmo genÃ©tico. Para tanto utilizamos a norma varimax para medida da simplicidade do traÃ§o deconvolvido. O mÃ©todo foi testado utilizando dados sÃsmicos sintÃ©ticos e reais. |

**Artigo em Revista**

Using NARX model with wavelet network to inferring the polished rod position.Although several studies have been conducted on the sucker-rod pumping system, even today, the acquisition of the polished rod position is carried out by using position transducers. In this paper, we present experimental results showing that the dynamic position of the polished rod can be inferred from the torque current of a three-phase induction motor (which is given by sensorless vector AC-drive) using nonlinear autoregressive model with exogenous input (NARX) with wavelet network (wavenet). The results obtained in the validation stage show that, on the basis of the experimental set used in this work, the best estimated model is suitable to represent the dynamic behavior of the polished-rod of the pumping unit. |

**Artigo em Revista**

High-resolution gathers by inverse filtering in the wavelet domain. We have developed and applied an inverse Q filter formulation using the continuous wavelet transform (CWT), which provides a natural domain for time-variant operations, such as compensation for propagation in attenuating and dispersive media. The well-known linear attenuation model, given as a function of time and frequency, was applied very efficiently over wavelet coefficients in the time-frequency domain to correct for amplitude and phase distortions, as necessary. The inverse CWT yields the recovered trace with a broader bandwidth. The process works on a trace-by-trace basis, making no distinction if the data is pre- or poststack. Our motivation was to develop gather conditioning tools to enhance prestack interpretation techniques such as amplitude variation with offset (AVO) analysis and inversion â€” a technique that is often compromised by tuning and other propagation related issues that degrade seismic resolution. Thus, we investigated the AVO fidelity of our filter and the sensitivity of the results to incorrect values of Q, using real and synthetic data. Our synthetic data experiments clearly showed that AVO anomalies are recovered and preserved in a stable manner, even with values of Q off by 50% of its correct value. The application in time-migrated gathers shows a very natural increase in the vertical definition of the events, especially due to the partial elimination of the tuning effect. The benefits for imaging are also evidenced by comparing stacked sections before and after inverse Q filtering. The higher resolution of seismic sections leads to a better definition of smaller scale stratigraphic and structural features. |