Produção Científica

**Artigo em Revista**

Filtering and frequency interpretations of Singular Spectrum AnalysisNew filtering and spectral interpretations of Singular Spectrum Analysis(SSA)are provided. It is shown that the variables reconstructed fromd iagonal averaging of reduced-rank approximations to the trajec-tory matrix can be obtained from a noncausal convolution filte rwith zero-phase characteristics. There-constructed variables are readily constructed using a two-pass filtering algorithm that is well known in the signal processing literature. When the number of rows in the trajectory matrix is much larger than number of columns, many results reported in the signal processing literature can be used to derive the properties of the resulting filters and their spectra. New features of there constructed series are revealed using these results. Two examples are used to illustrate the results derived in this paper. |

**Artigo em Revista**

OtimizacÌ§aÌƒo global para resolver problemas inversos em eletrorresistividade com flexibilidade na escolha dos viÌnculosInversion in DC-resistivity is an ill-posed inverse problem because different realizations of the same model might satisfy approximately the same data fitting criterium. It is therefore necessary to use constraints to obtain unique and / or stable solutions to small perturbations in the measurements. However, in general, the introduction of constraints has been restricted to cases of differentiable constraints, which can be treated with local optimization algorithms. 1D and 2D modeling in DC-resistivity is computationally inexpensive, allowing the use of global optimization methods (GOMs) to solve 1.5D and 2D inverse problems with flexibility in constraint incorporation. Changes in the cost function, either in the constraints or data fitting criteria, can be easily performed, since each term of the cost function is properly normalized to allow the approximate invariance of the Lagrange multipliers. GOMs have the potential to support a computational environment suitable for quantitative interpretation in which the comparison of solutions incorporating different constraints is one way of inferring characteristics of the actual distribution of the underground resistivity. In this work, we developed: (i) comparison of the performances of the Simulated Annealing (SA), Genetic Algorithm (GA) and Particle Swarm optimization (PSO) methods to solve the 1.5D inverse problem in DC resistivity using synthetic and field data; (ii) an inversion approach based on particle swarm optimization (PSO) to solve the 2D DC-resistivity inverse problem; (iii) exploration of several constraints in the variation of log-resistivity, including spatial continuity in both L1 andL2 norms, total variation and sparsity constraints using discrete cosine and Daubechies bases. In addition, we explore the minimum inertia constraint, including the case of using the Earthâ€™s surface as the target axis, to impose the concentration of resistive or conductive materials along target axes. The main results of the comparison for the 1.5D case are: a) all methods reproduce quite well the resistivity distribution of synthetic models, b) PSO and GA are very robust to changes in the cost function and SA is comparatively much more sensitive, c) PSO first and GA second present the best computational performances, requiring smaller number of forwarding modeling than SA, and d) GA shows the best performance with respect to the final attained value of the cost function and its standard deviation, whilst SA has the worst performance in this aspect. Equally important for both 1.5 and 2D cases, from the stopping criteria of the PSO algorithm results not only the best solution but also a cluster of suboptimal quasi-solutions from which uncertainty analyses can be performed. As a result, the interpreter has freedom to perform a quantitative interpretation process based on a feedback trial-and-error inversion approach, in a similar manner he/she has when using a friendly forward |

**Artigo em Revista**

Evaluation of model performances in reproducing measures of thermal conductivity of crystalline rocksWe evaluate the performances of the Krischer-Esdorn (KE), Hashin-Shtrikman (HS), classic Maxwell (CM), Maxwell-Wiener (MW), and geometric mean (GM) models in reproducing 1,105 measurements of thermal conductivity of crystalline rocks collected in Borborema Province (NE-Brazil). Percent volumes of quartz, K-feldspar, plagioclase, andmafic minerals were also measured. Rock samples were divided into the IOG (igneous and ortho-derived) and MET (metasedimentary) groups. IOG-group (939 samples) covered most the lithologies of the Streckeisen diagram and MET-group (166 samples) covered low-to-medium metamorphic grade lithologies. Reproducing rock conductivities was treated as an inverse problem, where conductivity measurements and constituent mineral volumes are the known quantities while the constituent mineral effective conductivities and model parameters are the unknowns. To identify the model better reproducing the measurements, model performances were compared by using the percentage of number of samples whose estimated conductivities are close to the measured conductivities within the tolerance level of 15%. For all models, the performances are relatively inferior for the MET-group. In the IOG-group, the KE- and HS-model performances are relatively superior. In the MET-group, model performances are very contrasting but the KE-model is again superior. The KE-model thus presents the best performance in reproducing thermal conductivities of crystalline rocks. |

**Artigo em Revista**

Retrieval of Body-Wave Reflections Using Ambient Noise Interferometry Using a Small-Scale ExperimentWe report the retrieval of body-wave reflections from noise records using a small-scale experiment over a mature oil field. The reflections are obtained by cross-correlation and stacking of the data. We used the stacked correlograms to create virtual source-to-receiver common shot gathers and are able to obtain body-wave reflections. Surface waves that obliterate the body-waves in our noise correlations were attenuated following a standard procedure from active source seismics. Further different strategies were employed to cross-correlate and stack the data: classical geometrical normalized cross-correlation (CCGN), phase cross-correlation (PCC), linear stacking**** and phase weighted stacking (PWS). PCC and PWS are based on the instantaneous phase coherence of analytic signals. The four approaches are independent and reveal the reflections; nevertheless, the combination of PWS and CCGN provided the best results. Our analysis is based on 2145 cross-correlations of 600 s data segments. We also compare the resulted virtual shot gathers with an active 2D seismic line near the passive experiment. It is shown that our ambient noise analysis reproduces reflections which are present in the active seismic data. |

**Artigo em Revista**

Neogeneâ€“Quaternary fault reactivation influences coastal basin sedimentation and landform in the continental margin of NE BrazilWe investigate the role of reactivation of Precambrian basement fabric in the tectono-sedimentary and geomorphological evolution of the ParaÃba Basin, continental margin of northeastern Brazil, during the Cretaceous, Neogene, and Quaternary. This basin represents part of the last bridge between South America and Africa before the last breakup stage of the South Atlantic rifting in the early Cretaceous. The ParaÃba Basin infill is composed of siliciclastic and carbonate Cretaceous units, as well as aeolian, fluvial and marine Quaternary units. We used shuttle radar imagery, aeromagnetic, wellbore and field data. The reduced-to-the-pole magnetic map (RTP) indicates the continuity of the steeply dipping Precambrian basement shear zones beneath the ParaÃba Basin. The combined analysis of surface and subsurface data shows that NEâ€“SW and Eâ€“W-striking shear zones were subjected to brittle reactivation in the Aptianâ€“Middle Albian during the basin opening and again in the Neogeneâ€“Quaternary, forming a system of horsts and grabens along the basin; some of these structures such as the Eâ€“W-oriented Pernambuco shear zone present modern-day seismicity. Nâ€“S- and mainly NWâ€“SE-striking transfer faults cut across Aptianâ€“Middle Albian to Neogeneâ€“Quaternary strata. These four main fault directions control main river channels and alluvial valleys up to 2 km wide. Topographic breaks up to 50 m were created by late reactivation of rift faults, which mark the boundary between horsts and grabens along the basin. In addition, structural data evidence syn-tectonic faulting with vertical offsets up to 80 m in the Cretaceous and up to 70 m in the Neogeneâ€“Quaternary. We conclude that shear zones across the study area are long-lived structures that have behaved as weakness zones. Their neotectonic brittle reactivation has controlled sediment deposition and landform development, which continued through the Neogeneâ€“Quaternary. |

**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. |

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