Produção Científica

**Artigo em Revista**

Reverse time migration using phase cross-correlationAdditional information regarding the continuity and resolution of selected seismic reflectors in reverse time migration (RTM) images can be beneficial for seismic interpretation. We have developed and evaluated new imaging conditions for RTM based on the phase coherence between the forward- and backward-propagated wavefields. These imaging conditions make use of the instantaneous phase and envelope of the analytical signals of the source and receiver wavefields, in addition to their real parts. Once the analytical wavefields are available, these imaging conditions can be calculated simultaneously with conventional conditions at little or no extra cost. The availability of these fields at each image point enables several alternative ways to define imaging conditions. We explore, in addition to pure phase crosscorrelation (PC), two approaches of amplitude-weighted PC. Our numerical experiments, imaging synthetic and field data sets, indicate that these new imaging conditions provide additional images that can highlight some weak reflectors by locally improving the resolution of RTM images. In our examples, this happens particularly in the deep portions of the seismic images. In addition, reflection events produced at discontinuities are enhanced as sharp signals, suggesting that the proposed imaging conditions can help to delineate stratigraphic and structural features that are harder to see in conventional images. These properties of the PC imaging conditions make them an interesting tool to provide additional information that can aid seismic interpretation in complex structural settings. |

**Artigo em Revista**

Extending the useful angle range for elastic inversion through the amplitude-versus-angle full-waveform inversion methodWe have developed the amplitude versus angle full-waveform inversion (AVA-FWI) method. This method considers the complete seismic response of the layered medium, and so it is capable of correctly handling seismic amplitudes from prestack data with a wide angle range. This capability is very important because a reliable estimate of the elastic parameters and the density requires an incidence angle that goes beyond 30Â°. Our method inputs seismic traces from prestack time-migrated gathers ordered by angle of incidence and works under the local 1D assumption. AVA-FWI is a nonlinear inversion based on forward modeling by the reflectivity method, which substantially increases its computational cost with respect to conventional AVA inversion. To address this problem, we developed an efficient routine for angle gather modeling and a new method for differential seismogram generation that greatly reduces the amount of computation involved in this task. The AVA-FWI method was applied to synthetic data and to a geophysical reservoir characterization case study using the North Viking Graben open data set. |

**Artigo em Revista**

Error analysis of the spectral element method with Gauss-Lobatto-Legendre points for the acoustic wave equation in heterogeneous media.We present the error analysis of a high-order method for the two-dimensional acoustic wave equation in the particular case of constant compressibility and variable density. The domain discretization is based on the spectral element method with Gaussâ€“Lobattoâ€“Legendre (GLL) collocation points, whereas the time discretization is based on the explicit leapfrog scheme. As usual, GLL points are also employed in the numerical quadrature, so that the mass matrix is diagonal and the resulting algebraic scheme is explicit in time. The analysis provides an a priori estimate which depends on the time step, the element length, and the polynomial degree, generalizing several known results for the wave equation in homogeneous media. Numerical examples illustrate the validity of the estimate under certain regularity assumptions and provide expected error estimates when the medium is discontinuous. |

**Artigo em Revista**

Estimation of quality factor based on peak frequency-shift method and redatuming operator: Application in real data setQuality factor estimation and correction are necessary to compensate the seismic energy dissipated during acoustic-/elastic-wave propagation in the earth. In this process, known as QQ-filtering in the realm of seismic processing, the main goal is to improve the resolution of the seismic signal, as well as to recover part of the energy dissipated by the anelastic attenuation. We have found a way to improve QQ-factor estimation from seismic reflection data. Our methodology is based on the combination of the peak-frequency-shift (PFS) method and the redatuming operator. Our innovation is in the way we correct traveltimes when the medium consists of many layers. In other words, the correction of the traveltime table used in the PFS method is performed using the redatuming operator. This operation, performed iteratively, allows a more accurate estimation of the QQ factor layer by layer. Applications to synthetic and real data (Viking Graben) reveal the feasibility of our analysis. |

**Artigo em Revista**

Limitations of correlation-based redatuming methodsRedatuming aims to correct seismic data for the consequences of an acquisition far from the target. That includes the effects of an irregular acquisition surface and of complex geological structures in the overburden such as strong lateral heterogeneities or layers with low or very high velocity. Interferometric techniques can be used to relocate sources to positions where only receivers are available and have been used to move acquisition geometries to the ocean bottom or transform data between surfaceâ€“seismic and vertical seismic profiles. Even if no receivers are available at the new datum, the acquisition system can be relocated to any datum in the subsurface to which the propagation of waves can be modeled with sufficient accuracy. By correlating the modeled wavefield with seismic surface data, one can carry the seismic acquisition geometry from the surface closer to geologic horizons of interest. Specifically, we show the derivation and approximation of the one-sided seismic interferometry equation for surface-data redatuming, conveniently using Green's theorem for the Helmholtz equation with density variation. Our numerical examples demonstrate that correlation-based single-boundary redatuming works perfectly in a homogeneous overburden. If the overburden is inhomogeneous, primary reflections from deeper interfaces are still repositioned with satisfactory accuracy. However, in this case artifacts are generated as a consequence of incorrectly redatumed overburden multiples. These artifacts get even worse if the complete wavefield is used instead of the direct wavefield. Therefore, we conclude that correlation-based interferometric redatuming of surfaceâ€“seismic data should always be applied using direct waves only, which can be approximated with sufficient quality if a smooth velocity model for the overburden is available. |

**Artigo em Revista**

Time-to-depth conversion and velocity estimation by image-wavefront propagationA new strategy for time-to-depth conversion and interval-velocity estimation is based entirely on image-wavefront propagation without the need to follow individual image rays. The procedure has three main features: (1) It computes the velocity field and the traveltime directly, allowing us to dispense with dynamic ray tracing; (2) it requires only the knowledge of the image wavefront at the previous time step; and (3) it inherently smooths the image wavefront, inhibiting the formation of caustics. As a consequence, the method tends to be faster than the usual techniques and does not carry the constraints and limitations inherent to common ray-tracing strategies. Synthetic tests using a Gaussian velocity anomaly as well as the Marmousi velocity model, and two smoothed versions of it show the feasibility of the method. A field-data example demonstrates the use of different numerical procedures. Our results indicate that the present strategy can be used to construct reasonable depth-velocity models that can be used as reliable starting models for velocity-model building in depth migration or for tomographic methods. |

**Artigo em Revista**

Optimization of the parameters in complex PadÃ© Fourier finite-difference migrationComplex PadÃ© Fourier finite-difference migration is a stable one-way wave-equation technique that allows for better treatment of evanescent modes than its real counterpart, in this way producing fewer artifacts. As for real Fourier finite-difference (FFD) migration, its parameters can be optimized to improve the imaging of steeply dipping reflectors. The dip limitation of the FFD operator depends on the variation of the velocity field. We have developed a wide-angle approximation for the one-way continuation operator by means of optimization of the PadÃ© coefficients and the most important velocity-dependent parameter. We have evaluated the achieved quality of the approximate dispersion relation in dependence on the chosen function of the ratio between the model and reference velocities under consideration of the number of terms in the PadÃ© approximation and the branch-cut rotation angle. The optimized parameters are chosen based on the migration results and the computational cost. We found that by using the optimized parameters, a one-term expansion achieves the highest dip angles. The implementations were validated on the Marmousi data set and SEG/EAGE salt model data. |

**Artigo em Revista**

Source wavelet and local wave propagation effects on the amplitude-variation-with-offset response of thin-layer models: A physical modeling study.In target layers with thicknesses below the vertical seismic resolution as thin layers, the tuning effect/interference between the wave propagation modes may increase the challenge of doing amplitude-variation-with-offset (AVO) analysis because it is difficult to recover the primary PP amplitudes embedded in the data by further seismic data processing. Thus, we have investigated the importance of the primary PP reflections, locally P-SV converted waves, and internal multiple reflections in the amplitude response of two thin-layer seismic physical models. One model consists of a thin water layer embedded between two nylon plates, and another model with a thin acrylic layer surrounded by water. Numerical modeling using the reflectivity method was applied to analyze each wave propagation mode and the source waveform role in the experimental data. Before the experimental reflection data acquisition, we characterized two source and receiver piezoelectric transducer (PET) pairs: one with a circular plane face and the other with a semispherical face. We measured the source wavelet, its dominant frequency, and the PETsâ€™ directivity pattern. Semispherical PETs were chosen to acquire common midpoint reflection data. Thereafter, a processing workflow was applied to remove linear events interfering with the target reflections and to correct amplitudes due to transmission losses, source/receiver directivity, and geometric spreading effects. Finally, we investigated the thin-layer targets near incidence angle amplitude and the AVO response. The results showed that the interference between the primary PP reflections and the locally converted shear waves may considerably affect the observed amplitude response. The source wavelet bandwidth appeared as a second-order effect, and the internal multiple reflections were practically negligible. These results suggested that in real data sets, it is important to investigate the wave propagation modes and source wavelet role in the amplitudes observed, before deciding the AVO analysis/inversion workflow that should be adopted. |

**Artigo em Revista**

The magnetometric resistivity method in a stratified medium having resistivities varying exponentially with depthUsing a known solution for the electric potential and AmpÃ¨reâ€™s law, the azimuthal component of the magnetic field is deduced in a horizontally layered medium with a current point source placed anywhere, considering that the resistivity in each layer varies exponentially with depth. This theoretical result contributes to model the magnetometric resistivity method, which had been applied onshore, e.g., for mineral exploration, offshore to investigate the permafrost layer at bottom sea, hydrothermal flux, and natural resources. We have numerically tested the obtained formulation against previous results found in the literature that use distinct electrode and sensor dispositions, with models having three and four layers. Introducing the exponential variation, it verified the sensitivity to physical and geometric parameters comparing the exponential and homogeneous models. |

**Artigo em Revista**

A high-resolution weighted AB semblance for dealing with amplitude-variation-with-offset phenomenonVelocity analysis is an essential step in seismic reflection data processing. The conventional and fastest method to estimate how velocity changes with increasing depth is to calculate semblance coefficients. Traditional semblance has two problems: low time and velocity resolution and an inability to handle amplitude variation-with-offset (AVO) phenomenon. Although a method known as the AB semblance can arrive at peak velocities in the areas with an AVO anomaly, it has a lower velocity resolution than conventional semblance. We have developed a weighted AB semblance method that can handle both problems simultaneously. We have developed two new weighting functions to weight the AB semblance to enhance the resolution of velocity spectra in the time and velocity directions. In this way, we increase the time and velocity resolution while eliminating the AVO problem. The first weighting function is defined based on the ratio between the first and the second singular values of the time window to improve the resolution of velocity spectra in velocity direction. The second weighting function is based on the position of the seismic wavelet in the time window, thus enhancing the resolution of velocity spectra in time direction.We use synthetic and field data examples to show the superior performance of our approach over the traditional one. |

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