Produção Científica

**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 Earth’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 deconvolução do pulso sísmico. Investigamos o uso de operadores de mudança de fase para obtenção de filtros de fase mista a partir de filtros de fase mínima. Os operadores de mudança de fase são construídos a partir das raízes associadas aos filtros de Wiener-Levinson. Escolhendo subconjuntos daquelas raízes é possível gerar um conjunto de filtros inversos de fase mista. A escolha do filtro ótimo é realizada através do método de otimização conhecido com algoritmo genético. Para tanto utilizamos a norma varimax para medida da simplicidade do traço deconvolvido. O método foi testado utilizando dados sísmicos sintéticos 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 — 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. |

**Artigo em Revista**

Review of active faults in the Borborema Province, Intraplate South America Integration of seismological and paleoseismological data.In this paper, we provide a review of the properties and behavior of active faults in the Borborema Province, northeastern Brazil, using instrumental, historical and paleoseismological records. The Borborema Province is one of the most seismically active parts of the South American stable continental region (the South American Platform). The Province encompasses an area ~ 900 km long and ~ 600 km wide. It is composed of a branching system of Neoproterozoic orogens, encompassing Archean and Proterozoic inliers deformed during the Brasiliano orogeny at ~ 750–500 Ma. Active faults reactivate shear zones or regional foliation and quartz veins or cut across the preexisting fabric. Active faults are usually strike–slip and generate events ≤ 5.2 mb, which we interpret as the lower limit for maximum possible earthquakes. Seismicity is concentrated in the upper crust down to a depth of 12 km. Earthquake sequences illuminated naturally occurring faults up to 40 km long and segments in the order of 0.5–2.6 km in faults related to induced seismicity. Earthquakes have a recurrence interval of ~ 15 years for Ms = 4. Paleoseismological data indicate that although earthquakes associated with surface ruptures have not occurred in the last 200 years, they struck the region in the last ~ 100 ka. Paleoearthquakes have a recurrence interval of ~ 15.8 ka for magnitudes of ~ 5.5 Mw in individual faults. Moreover, earthquake-induced soft-sediment deformation caused by events of at least 5.5–6.0 Ms have occurred at least six times in the last 400–10 ka in one alluvial valley. Seismically defined faults are concentrated along the continental margin at the border of sedimentary basins as far as 250–300 km inland in areas of extended crust; faults in the paleoseismic record are also found in rift basins along this margin. Both records also reveal that active faults tend to be hydraulically conductive. |

**Artigo em Revista**

Entropic Regularization to Assist a Geologist in Producing a Geologic Map. EntropyThe gravity and magnetic data measured on the Earth’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. |