Produção Científica

**Artigo em Revista**

Offset continuation (OCO) ray tracing using OCO trajectories.Offset continuation (OCO) is a seismic configuration transform designed to simulate a seismic section as if obtained with a certain source-receiver offset using the data measured with another offset. Since OCO is dependent on the velocity model used in the process, comparison of the simulated section to an acquired section allows for the extraction of velocity information. An algorithm for such a horizon-oriented velocity analysis is based on so-called OCO rays. These OCO rays describe the output point of an OCO as a function of the Root Mean Square (RMS) velocity. The intersection point of an OCO ray with the picked traveltime curve in the acquired data corresponding to the output half-offset defines the RMS velocity at that position. We theoretically relate the OCO rays to the kinematic properties of OCO image waves that describe the continuous transformation of the common-offset reflection event from one offset to another. By applying the method of characteristics to the OCO image-wave equation, we obtain a raytracing-like procedure that allows to construct OCO trajectories describing the position of the OCO output point under varying offset. The endpoints of these OCO trajectories for a single input point and different values of the RMS velocity form then the OCO rays. A numerical example demonstrates that the developed ray-tracing procedure leads to reliable OCO rays, which in turn provide high-quality RMS velocities. The proposed procedure can be carried out fully automatically, while conventional velocity analysis needs human intervention. Moreover, since velocities are extracted using offset sections, more redundancy is available or, alternatively, OCO velocities can be studied as a function of offset. |

**Artigo em Revista**

Exploring self-affine properties in seismogramsSelf-affine properties have been observed in a large variety of rough profiles and time series from natural data sets. In this work, seismograms used for oil prospecting, which contain information of distinct subsurface features collected by seismic waves reflected or scattered at their interfaces, are taken into consideration. It is expected that any self-affine property, measured by the Hurst exponent H, depends on the depth. For each seismic trace, H is evaluated locally within a moving window, which is chosen narrow enough to reveal space dependency but also wide enough to display scale invariance. With the use of color code diagrams, it is possible to draw two-dimensional diagrams that show the local dependence of H for the analyzed seismogram. The reliability of the method is tested by the investigation of seismograms that contain ground roll components, as well as multiple reflections. The effect of different kinds of filter in the scaling properties is also investigated. In this case, comparisons are drawn among the diagrams obtained from original seismograms and those subjected to appropriate filter to eliminate spurious components. |

**Artigo em Revista**

Amplitudes e padrÃµes de polarizaÃ§Ã£o de pulsos em meios anisotrÃ³picosExtrair informaÃ§Ãµes litolÃ³gicas da subsuperfÃcie atravÃ©s de dados sÃsmicos constitui-se num grande desafio Ã prospecÃ§Ã£o sÃsmica, pois a hipÃ³tese de estratificaÃ§Ãµes formadas por camadas isotrÃ³picas se mostra insuficiente para representar o comportamento do campo elÃ¡stico em levantamentos com grandes afastamentos entre fonte e receptor, geofones multicomponentes, medidas de VSP tridimensional, entre outros. Sob este panorama, a prospecÃ§Ã£o sÃsmica passa a considerar modelos anisotrÃ³picos de subsuperfÃcie para, por exemplo, caracterizar reservatÃ³rios. O objetivo deste texto Ã© apresentar um formalismo para modelar o espalhamento de pulsos a partir de ondas planas incidentes em interfaces planas horizontais que separam meios anisotrÃ³picos. Este espalhamento Ã© obtido primeiramente, atravÃ©s da formulaÃ§Ã£o explÃcita dos campos de deformaÃ§Ã£o e traÃ§Ã£o como funÃ§Ã£o das matrizes propagadoras, de polarizaÃ§Ã£o e de impedÃ¢ncia do meio. Em seguida, este formalismo Ã© usado para a obtenÃ§Ã£o das matrizes dos coeficientes de reflexÃ£o e transmissÃ£o atravÃ©s de uma interface plana horizontal para posteriormente, ser generalizado para o espalhamento atravÃ©s de mÃºltiplas camadas. Finalmente, inserem-se ao campo da onda incidente as amplitudes de um pulso analÃtico para calcular o espalhamento do pulso atravÃ©s de estratificaÃ§Ãµes. |

**Artigo em Revista**

SoluÃ§Ãµes de Problemas envolvendo EquaÃ§Ãµes Diferenciais Sujeitas a IncertezasEste trabalho objetiva analisar, atravÃ©s de alguns exemplos, a influÃªncia de se considerar aleatoriedades na soluÃ§Ã£o de equaÃ§Ãµes diferenciais com dados e/ou parÃ¢metros aleatÃ³rios. Um comparativo das mÃ©dias das soluÃ§Ãµes das equaÃ§Ãµes estocÃ¡sticas com as soluÃ§Ãµes das equaÃ§Ãµes determinÃsticas simplificadas, nas quais substituÃmos os parÃ¢metros aleatÃ³rios por suas mÃ©dias, Ã© apresentado. Estes exemplos mostram que a mÃ©dia da soluÃ§Ã£o, que normalmente Ã© uma informaÃ§Ã£o relevante em aplicaÃ§Ãµes, pode ser qualitativamente diferente da aproximaÃ§Ã£o obtida pela soluÃ§Ã£o de uma equaÃ§Ã£o diferencial determinÃstica na qual substituÃmos os parÃ¢metros aleatÃ³rios por suas mÃ©dias. |

**Artigo em Revista**

A spaceâ€“time multiscale method for computing statistical moments in strongly heterogeneous poroelastic media of evolving scalesA new multiscale procedure is proposed to compute flow in compressible heterogeneous porous media with geology characterized by power-law covariance structure. At the fine scale, the deformable medium is modeled by the partially coupled formulation of poroelasticity with Youngâ€™s modulus and permeability treated as stationary random fields represented by their Karhunenâ€“LoÃ¨ve decompositions. The framework underlying the multiscale procedure is based on mapping these random parameters to an auxiliary domain and constructing a family of equivalent stochastic processes at different length scales characterized by the same ensemble mean and covariance function. The poromechanical variables inherit a spaceâ€“time version of the scaling relations of the random input parameters which allows for constructing a set of multiscale solutions of the same governing equations posed at different space and time scales. A notable feature of the multiscale method proposed herein is the feasibility of solving both the poroelastic model and the Fredholm integral equation for the eigenpairs of the Karhunenâ€“LoÃ¨ve expansion in an auxiliary domain with much lower computational effort and then derive the long term behavior at a coarser scale from a straightforward rescaling of the auxiliary solution. Within the framework of the finite element approximation, in conjunction with the Monte Carlo algorithm, numerical simulations of fluid withdrawal and injection problems in a heterogeneous poroelastic reservoir are performed to illustrate the potential of the method in drastically reducing the computational burden in the computation of the statistical moments of the poromechanical unknowns in large-scale simulations. |

**Artigo em Revista**

A Numerical Comparison Between Quasi-MonteCarlo and Sparse Grid Stochastic Collocation MethodsQuasi-Monte Carlo methods and stochastic collocation methods based on sparse grids have become popular with solving stochastic partial differential equations.These methods use deterministic points for multi-dimensional integration or interpolation without suffering from the curse of dimensionality. It is not evident which method is best, specially on random models of physical phenomena. We numerically study the error of quasi-Monte Carlo and sparse gridmethods in the context of groundwater flow in heterogeneous media. In particular, we consider the dependence of the variance error on the stochastic dimension and the number of samples/collocation points for steady flow problems in which the hydraulic conductivity is a lognormal process. The suitability of each technique is identified in terms of computational cost and error tolerance. |

**Artigo em Revista**

Effect of Element Distortion on the Numerical Dispersion of Spectral Element MethodsSpectral element methods are well established in the field of wave propagation,in particular because they inherit the flexibility of finite element methods and have low numerical dispersion error. The latter is experimentally acknowledged, but has been theoretically shown only in limited cases, such as Cartesian meshes. It is well known that a finite element mesh can contain distorted elements that generate numerical errors for very large distortions. In the present work, we study the effect of element distortion on the numerical dispersion error and determine the distortion range in which an accurate solution is obtained for a given error tolerance. We also discuss a double-grid calculation of the spectral element matrices that preserves accuracy in deformed geometries. |

**Artigo em Revista**

Hypocentral relocation using clustering-along-planes constraints: implications for fault geometryHypocentre location is an ill-posed inverse problem even assuming that the velocity model is known, because different sets of hypocentre locations may satisfy the fitting criterion. We present a regularized hypocentre inversion in which the constraints of spatial proximity of the hypocentres to target planes are used. This constraint introduces the geological bias that earthquakes might occur along fault planes. Here, the target planes may be either (1) planes specified by the interpreter or (2) planes fitting groups of events. We assume also that initial estimates of hypocentres and origin times are available. Then, the initial hypocentre estimates, origin times and target planes are used as input to an inversion problem to relocate the hypocentres so that the maximum-possible clustering of events along the given planes is attained, matching the observed traveltimes. We use L1 norm for data fitting, L2 norm for the plane proximity criterion and a polytope algorithm to minimize the functional. Results from synthetic and real data indicate that the plane proximity constraint allows for hypocentre relocation presenting a high degree of clustering along planes. The real-data example is an intraplate earthquake sequence in NE Brazil. Our methodology defined the geometry and strike of fault segments close to known geology and focal mechanism data. In addition, the new method indicates that the fault is characterized by a splay geometry in its southern end and that more than three fault segments are necessary to explain the hypocentre distribution. |

**Artigo em Revista**

Evidences of buried loads in the base of the crust of Borborema Plateau (NE Brazil) from Bouguer admittance estimatesIn the Borborema Province (BP) e northeastern Brazil e two important Cenozoic events occurred at the surface: the Macau magmatism and the Borborema Plateau epeirogenesis. To obtain appropriated-scale geophysical data to explain the deep origins of these two events, different gravimetric/elevation databases were integrated with new surveys. Bouguer admittance estimates reveal that isostatic condition of the BP, especially in the Borborema Plateau, can be explained using elastic models to the lithosphere only if surface and buried loadings are combined. If the buried load is applied in the base of the crust, the ratio between buried and surface weights is circa 15 for a lithosphere with effective elastic thickness around 15 km and crust thickness around 33 km. From an nterpretative viewpoint of the buried load, it is assumed that the lower crust under the Borborema Plateau might have an anomalous high value of density. Magmatic underplating might explain this fact as well as the observed surface magmatism and epeirogenesis. Crustal thickening of about 4 km under the Borborema Plateau and intracrustal seismic velocity discontinuity with high Vp/Vs ratio are geophysical facts consistent with magmatic underplating. However, the surface magmatism presents low volume and mainly alkaline composition e facts that are not entirely consistent with the hypothesis of magmatic underplating. Regardless the validity of this hypothesis, Cenozoic-to-present events in BP might be somewhat associated with imbalances in lithosphere-asthenospheric mantle and/or crust-lithospheric mantle systems. The existence of free-air anomalies showing no null integral over area and of an expressive positive geoid anomaly are geophysical evidences of these imbalances. Possibly, the Borborema Plateau is still suffering epeirogenesis. Post-depositional deformation found in Barreiras Formation strata, Late Quaternay fault reactivations, and AFT thermochronology analysis suggesting the existence of a cooling stage between 20 and 0 Ma might be geologic evidences of the continued action of peirogenesis until the present. In addition, the relatively high level of the present intraplate seismicity recorded in several regions of the BP is another unequivocal geophysical evidence that the crust of the province is still submitted to accommodation processes. |

**Artigo em Revista**

A fast modified parabolic radon transform.We propose a fast and efficient frequency-domain implementation of a modified parabolic Radon transform (modified PRT) based on a singular value decomposition (SVD) with applications to multiple removal. The problem is transformed into a complex linear system involving a single operator after merging the curvature-frequency parameters into a new variable. A complex SVD is applied to this operator and the forward transform is computed by means of a complex back-substitution that is frequency independent. The new transform offers a wider curvature range at signal frequencies than the other PRT implementations, allowing the mapping in the transform domain of low-frequency events with important residual moveouts (long period multiples). The method is capable of resolving multiple energy from primaries when they interfere in a small time interval, a situation where most frequency-domain methods fail to discriminate the different wave types. Additionally, the method resists better to amplitude variations with offset (AVO) effects in the data than does the iteratively reweighted least-squares (IRLS) method.The proposed method was successfully applied to a deep-water seismic line in the Gulf of Mexico to attenuate water-bottom multiples and subsequent peg-legs originating from multiple paths in the water column. Combining the suggested method with the surface-related multiple elimination (SRME) has led to the best attenuation results in removing residual multiple energy in the stack. Â©2011 Society of Exploration Geophysicists |