Produção Científica

**Artigo em Revista**

Wave equation depth migration using complex PadÃ© approximation.Propomos um novo mÃ©todo de migraÃ§Ã£o em profundidade baseado na soluÃ§Ã£o da equaÃ§Ã£o da onda com densidade constante no domÃnio da freqÃ¼Ãªncia. Uma aproximaÃ§Ã£o de PadÃ© complexa Ã© usada para aproximar o operador de evoluÃ§Ã£o aplicado na extrapolaÃ§Ã£o do campo de ondas. Esse mÃ©todo reduz as imprecisÃµes e instabilidades devido Ã s ondas evanescentes e produz imagens com menos ruÃdos numÃ©ricos que aquelas obtidas usando-se a aproximaÃ§Ã£o de PadÃ© real para o operador exponencial, principalmente em meios com fortes variaÃ§Ãµes de velocidades. Testes em dados de afastamento nulo do modelo de sal SEG/EAGE e nos dados de tiro comum 2-D Marmousi foram realizados. Os resultados obtidos mostram que o mÃ©todo de migraÃ§Ã£o proposto consegue lidar com fortes variaÃ§Ãµes laterais e tambÃ©m tem uma boa resposta para refletores com mergulhos Ãngremes. Os resultados foram comparados Ã queles resultados obtidos com os mÃ©todos split-step Fourier (SSF), phase shift plus interpolarion (PSPI) e Fourier diferenÃ§as-finitas (FFD). |

**Artigo em Revista**

Filtragem SVD aplicada Ã melhoria do rastreamento de horizontes sÃsmicos.No presente artigo apresentamos uma aplicaÃ§Ã£o da filtragem SVD (Singular Value Decomposition ) para o mapeamento automÃ¡tico de horizontes sÃsmico. A filtragem SVD pode ser vista como um mÃ©todo de filtragem multicanal onde cada traÃ§o filtrado guarda certo grau de coerÃªncia com os traÃ§os imediatamente vizinhos. Esta filtragem preserva as relaÃ§Ãµes de amplitude, fase e correlaÃ§Ã£o espacial dos eventos sismicos, ao tempo em que permite eliminar o ruÃdo incoerente, normalmente associado aos Ãºltimos autovalores. A decomposiÃ§Ã£o SVD Ã© realizada sobre o subconjunto de traÃ§os vizinhos a cada traÃ§o da linha sÃsmica 2D ou de um volume 3D. O traÃ§o filtrado Ã© obtido utilizando apenas alguns dos autovetores e autovalores associados. Ilustramos a aplicaÃ§Ã£o do mÃ©todo sobre dados sÃsmicos terrestres. A melhoria da coerÃªncia dos eventos sÃsmicos permitiu maior robustez ao autotracking no mapeamento e interpretaÃ§Ã£o automÃ¡tica dos horizontes sÃsmicos. A filtragem SVD e Ì computacionalmente eficiente e tem o mÃ©rito de melhorar significativamente a coerÃªncia, a consistÃªncia e a continuidade dos eventos de reflexÃ£o facilitando muito o â€œtrabalhoâ€, do tracker na busca de padrÃµes no processo de autotracking. |

**Artigo em Revista**

Traveltime approximations for q-P waves in vertical transversely isotropy media. As exploration targets have become deeper, cable lengths have increased accordingly, making the conventional two term hyperbolic traveltime approximation produce increasingly erroneous traveltimes. To overcome this problem, many traveltime formulas were proposed in the literature that provide approximations of different quality. In this paper, we concentrate on simple traveltime approximations that depend on a single anisotropy parameter. We give an overview of a collection of such traveltime approximations found in the literature and compare their quality. Moreover, we propose some new single-parameter traveltime approximations based on the approximations found in the literature. The main advantage of our approximations is that some of them are rather simple analytic expressions that make them easy to use, while achieving the same quality as the better of the established formulas. |

**Artigo em Revista**

Anisotropic complex Pade hybrid finite-difference depth migration.Standard real-valued finite-difference (FD) and Fourier finite-difference (FFD) migrations cannot handle evanescent waves correctly, which can lead to numerical instabilities in the presence of strong velocity variations. A possible solution to these problems is the complex PadÃ© approximation, which avoids problems with evanescent waves by rotating the branch cut of the complex square root. We have applied this approximation to the acoustic wave equation for vertical transversely isotropic media to derive more stable FD and hybrid FD/FFD migrations for such media. Our analysis of the dispersion relation of the new method indicates that it should provide more stable migration results with fewer artifacts and higher accuracy at steep dips. Our studies lead to the conclusion that the rotation angle of the branch cut that should yield the most stable image is 60Â° for FD migration, as confirmed by numerical impulse responses and work with synthetic data. |

**Artigo em Revista**

Including Lateral Velocity Variations into True-amplitude Common-Shot Wave-equation Migration.In heterogeneous media, standard one-way wave equations describe only the kinematic part of one-way wave propagation correctly. For a correct description of amplitudes, the one-way wave equations must be modified. In media with vertical velocity variations only, the resulting true-amplitude one-way wave equations can be solved analytically. In media with lateral velocity variations, these equations are much harder to solve and require sophisticated numerical techniques. We present an approach to circumvent these problems by implementing approximate solutions based on the one-dimensional analytic amplitude modifications. We use these approximations to show how to modify conventional migration methods such as split-step and Fourier finite-difference migrations in such a way that they more accurately handle migration amplitudes. Simple synthetic data examples in media with a constant vertical gradient demonstrate that the correction achieves the recovery of true migration amplitudes. Applications to the SEG/EAGE salt model and the Marmousi data show that the technique improves amplitude recovery in the migrated images in more realistic situations. |

**Artigo em Revista**

Obliquity-correction imaging condition for reverse time migration.The quality of seismic images obtained by reverse time migration (RTM) strongly depends on the imaging condition. We propose a new imaging condition that is motivated by stationary phase analysis of the classical crosscorrelation imaging condition. Its implementation requires the Poynting vector of the source and receiver wavefields at the imaging point. An obliquity correction is added to compensate for the reflector dip effect on amplitudes of RTM. Numerical experiments show that using an imaging condition with obliquity compensation improves reverse time migration by reducing backscattering artifacts and improving illumination compensation. |

**Artigo em Revista**

The role of fluids in triggering earthquakes: observations from reservoir induced seismicity in Brazil.We relocate precisely micro-earthquakes induced by the AÃ§u reservoir in Brazil and observe seismicity migration consistent with pore-pressure diffusion on a single fault zone. Fluids are believed to play a major role in triggering tectonic earthquakes; reservoir induced seismicity provides a natural laboratory in which to investigate the spatio-temporal evolution and triggering of earthquakes caused by fluid and pore-pressure diffusion. Between 1994 and 1997, 267 earthquakes (MLâ‰¤ 2.1) were recorded and located beneath the AÃ§u reservoir. The seismicity increased several months following annual water level peaks, implying that pore-pressure diffusion is the principal triggering mechanism. The small station spacing and very low-attenuation, Precambrian basement, rock enabled starting earthquake locations with uncertainties of only a few hundred metres. We relocate 155 earthquakes from the largest cluster at AÃ§u using waveform cross-correlation to obtain groups of similar events. We use these groups to improve the pick accuracy (to subsample accuracy in 200 sample per second data), and then invert for more accurate hypocentral locations. Our uncertainties are on the order of 10 m, and our locations are more tightly clustered. We observe temporal migration of the earthquakes, both along strike, and to increasing depth. We observe a seismicity migration rate between 15 and 58 m dâ€“1. The rate is highest during the time of peak seismicity rate, and there is some suggestion that the rate decreases with increasing depth. Peak depth in seismicity is reached 175 d after the water peak, that is 192 d after the water low, and the maximum depth then decreases at a similar rate to the rate of increase. Our observations are consistent with triggering by pore-pressure diffusion within a heterogeneous fault zone with an average hydraulic diffusivity of âˆ¼0.06 m2 sâ€“1 and fracture permeability of âˆ¼6 Ã— 10âˆ’16 m2. |

**Artigo em Revista**

DetecÃ§Ã£o de camadas delgadas usando sÃsmica de reflexÃ£o.A melhoria da resoluÃ§Ã£o vertical no dado sÃsmico tem se constituÃdo em um dos maiores desafios para o mÃ©todo de reflexÃ£o sÃsmica. O grande problema estÃ¡ relacionado Ã maior perda das amplitudes das altas freqÃ¼Ãªncias, quando comparada Ã s baixas, durante a propagaÃ§Ã£o da onda. Isto faz com que na composiÃ§Ã£o final do pulso sÃsmico a contribuiÃ§Ã£o das baixas freqÃ¼Ãªncias seja maior do que a das altas. Em princÃpio, isto nÃ£o deveria se constituir em obstÃ¡culo para a recuperaÃ§Ã£o plena do espectro, na medida em que o processamento sÃsmico dispÃµe de vÃ¡rias ferramentas para a equalizaÃ§Ã£o de todas as freqÃ¼Ãªncias presentes no volume sÃsmico. O que impede que essas aÃ§Ãµes logrem Ãªxito Ã© a presenÃ§a de um ruÃdo com comportamento randÃ´mico, o que faz com que exista uma freqÃ¼Ãªncia limite, freqÃ¼Ãªncia crÃtica, a partir da qual nÃ£o Ã© possÃvel recuperar o sinal de forma a efetivamente contribuir para o encurtamento do pulso no tempo. Tentativas de contornar este problema, a partir da atenuaÃ§Ã£o do ruÃdo aleatÃ³rio, tÃªm se mostrado insuficientes. A alternativa a estas tentativas Ã© o aumento da multiplicidade de empilhamento. Como a perda de amplitude com a freqÃ¼Ãªncia Ã© uma relaÃ§Ã£o exponencial, Ã© necessÃ¡ria multiplicidade extremamente elevada para que o ganho seja efetivo. A capacidade de utilizaÃ§Ã£o de altÃssimas multiplicidades Ã© exatamente a grande virtude da tÃ©cnica CRS (Common Reflection Surface). Neste trabalho propomos a combinaÃ§Ã£o do mÃ©todo CRS com o chamado balanceamento espectral (spectral whitening), para a recuperaÃ§Ã£o de altas freqÃ¼Ãªncias, com o objetivo de aumentar ganhos na resoluÃ§Ã£o vertical e, como conseqÃ¼Ãªncia, propiciar melhor discriminaÃ§Ã£o de reservatÃ³rios delgados. Os primeiros testes em dados sintÃ©ticos e reais apresentados neste trabalho sÃ£o bastante encorajadores e permitem concluir que a estratÃ©gia proposta tem bom potencial de aplicaÃ§Ã£o prÃ¡tica. |

**Artigo em Revista**

Intraplate earthquake swarm in Belo Jardim, NE Brazil: reactivation of a major Neoproterozoic shear zone (Pernambuco Lineament).Intraplate earthquakes in stable continental areas have been explained basically by reactivation of pre-existing zones of weakness, stress concentration, or both. Zones of weakness are usually identified as sites of the last major orogeny, provinces of recent alkaline intrusions, or stretched crust in ancient rifts. However, it is difficult to identify specific zones of weakness and intraplate fault zones are not always easily correlated with known geological features. Although Northeastern Brazil is one of the most seismically active areas in the country (magnitudes 5 roughly every 5 yr), with hypocentral depths shallower than âˆ¼10 km and seismic zones as long as 30â€“40 km, no clear relationship with the known surface geology can be usually established with confidence, and a clear identification of zones of weakness has not yet been possible. Here we present the first clear case of seismic activity occurring as reactivation of an old structure in Brazil: the Pernambuco Lineament, a major Neoproterozoic shear zone. The 2004 earthquake swarm of Belo Jardim (magnitudes up to 3.1) and the recurrent activities in the nearby towns of SÃ£o Caetano and Caruaru (magnitudes up to 4.0 and 3.8), show that the Pernambuco Lineament is a weak zone. A local seismic network showed that the Belo Jardim swarm of 2004 November occurred by normal faulting on a North dipping, Eâ€“W oriented fault plane in close agreement with the Eâ€“W trending structures within the Pernambuco Lineament. The Belo Jardim activity was concentrated in a 1.5 km (Eâ€“W) by 2 km (downdip) fault area, and average depth of 4.5 km. The nearby Caruaru activity occurs as both strike-slip and normal faulting, also consistent with local structures of the Pernambuco Lineament. The focal mechanisms of Belo Jardim, Caruaru and S. Caetano, indicate Eâ€“W compressional and Nâ€“S extensional principal stresses. The NS extension of this stress field is larger than that predicted by numerical models such as those of Coblentz & Richardson and we propose that additional factors such as flexural stresses from the nearby Sergipe-Alagoas marginal basin could also affect the current stress field in the Pernambuco Lineament. |

**Artigo em Revista**

Applications of Information Theory, Genetic Algorithms, and Neural Models to Predict Oil Flow.This work introduces a new information-theoretic methodology for choosing variables and their time lags in a prediction setting, particularly when neural networks are used in non-linear modeling. The first contribution of this work is the Cross Entropy Function (XEF) proposed to select input variables and their lags in order to compose the input vector of black-box prediction models. The proposed XEF method is more appropriate than the usually applied Cross Correlation Function (XCF) when the relationship among the input and output signals comes from a non-linear dynamic system. The second contribution is a method that minimizes the Joint Conditional Entropy (JCE) between the input and output variables by means of a Genetic Algorithm (GA). The aim is to take into account the dependence among the input variables when selecting the most appropriate set of inputs for a prediction problem. In short, theses methods can be used to assist the selection of input training data that have the necessary information to predict the target data. The proposed methods are applied to a petroleum engineering problem; predicting oil production. Experimental results obtained with a real-world dataset are presented demonstrating the feasibility and effectiveness of the method. |