Produção Científica

**Artigo em Revista**

Time evolution of the wave equation using rapid expansion method.Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. |

**Artigo em Revista**

Trigonal meshes in diffraction tomography with optimum regularization: an application for carbon sequestration monitoring. |

**Artigo em Revista**

Migration velocity analysis by double path-integral migration.The idea of path-integral imaging is to sum over the migrated images obtained for a set of migration velocity models. Those velocities where common-image gathers align horizontally are stationary, thus favoring these images in the overall stack. In this way, the overall image forms with no knowledge of the true velocity model. However, the velocity information associated with the final image can be determined in the process. By executing the path-integral imaging twice, weighting one of the stacks with the velocity value, the stationary velocities that produce the final image can then be extracted by a division of the two images. A numerical example demonstrates that quantitative information about the migration velocity model can be determined by double path-integral migration. |

**Artigo em Revista**

On the estimation of local slopes.Current time-processing algorithms often are based on one-parameter or multiparameter coherency analysis (semblance) schemes applied to the data. Such procedures, besides being computationally expensive, lead to significant uncertainties in the searched parameters. Conventional semblance methods can be avoided for a number of imaging tasks if local slopes can be extracted directly from prestack data—for example, by filtering schemes. Although the idea is not new, it has revived for various purposes, such as velocity analysis, τ-p imaging, migration to zero offset, and time migration. We propose a simple, straightforward correction to linear plane-wave destructors based on the observation that in addition to the local slope, its inverse can be extracted from the data in a fully analogous way. Combining the information of both extractions yields a simple yet effective correction to the local slopes. The naive application of linear plane-wave destructors with our correction produces high-quality results, even with a high noise level and interfering events. |

**Artigo em Revista**

Source parameters and rupture velocity of small? 2.1 reservoir induced earthquakes.We calculate stress drop and rupture speed for ML ≤ 2.1 shallow reservoir induced earthquakes and ﬁnd them to be similar to those of large, natural earthquakes. Previous studies have suggested that hydrofractures, mining and reservoir-induced earthquakes have lower average stress drop than natural tectonic earthquakes. This difference might result from the different tectonic setting or the shallower hypocentral depths of induced earthquakes. Alternatively, difﬁculties in correcting for attenuation and site effects in earlier studies may lead to underestimation of stress drop. In addition, most studies assume the rupture velocity of small reservoir induced earthquakes to be the same as for the large earthquakes. We analyse a set of 101 ML ≤ 2.1 earthquakes induced by changing water level in the Ac¸u Reservoir, NE Brazil. The earthquakes are shallow, (depth <5 km) and the region has negligible natural seismicity. We use three different approaches to calculate the source parameters of the six largest (1.9 ≤ ML ≤ 2.1) earthquakes. We model the individual spectra to ﬁnd corner frequency, frequency-independent Q, and long period amplitude. We use collocated small earthquakes as empirical Green’s functions to calculate the spectral ratios, and determine the relative source time functions. Estimates of the source duration and corner frequency imply stress drops in the range of 26–179 MPa. These are similar to, or higher than tectonic earthquakes suggesting that the shallow hypocentral depth and the presence of water do not affect stress drop. We observe clear directivity for one of the earthquakes, and use the azimuthal variation in pulse width to estimate a rupture velocity of ≥0.6β. |

**Artigo em Revista**

SS-traveltime parameters from PP and PS reflections.The SS-wave traveltimes can be derived from PP- and PS-wave data with the previously derived method. We have extended this method as follows. (1) The previous requirement that sources and receivers be located on a common acquisition surface is removed, which makes the method directly applicable to PS-waves recorded on the ocean bottom and PP-waves recorded at the ocean surface. (2) By using the concept and properties of surface-to-surface propagator matrices, the second-order traveltime derivatives of the SS-waves are obtained. In the same way as for the original method, the proposed extension is valid for arbitrary anisotropic media. The propagator matrix and geometric spreading of an SS-wave reflected at a given point on a target reflector are obtained explicitly from the propagators of the PP- and PS-waves reflected at the same point. These additional parameters provided by the extended method can be used for a partial reconstruction of the SS-wave amplitude as well as for tomographic estimation of the elastic velocity model. A full simulation of the SS-wave, which includes reflection and transmission coefficients, cannot be obtained directly from recorded PP- and PS-wave amplitudes. |

**Artigo em Revista**

A new stabilized least-squares imaging condition.The classical deconvolution imaging condition consists of dividing the upgoing wave field by the downgoing wave field and summing over all frequencies and sources. The least-squares imaging condition consists of summing the cross-correlation of the upgoing and downgoing wave fields over all frequencies and sources, and dividing the result by the total energy of the downgoing wave field. This procedure is more stable than using the classical imaging condition, but it still requires stabilization in zones where the energy of the downgoing wave field is small. To stabilize the least-squares imaging condition, the energy of the downgoing wave field is replaced by its average value computed in a horizontal plane in poorly illuminated regions. Applications to the Marmousi and Sigsbee2A data sets show that the stabilized least-squares imaging condition produces better images than the least-squares and cross-correlation imaging conditions. |

**Material Didático**

Carlos Alberto Dias - A saga da Geofísica Aplicada e da Engenharia de E&P do Petróleo no Brasil.Fernando S. de Moraes (Org.); Lima, O. A. L. de (Org.); Jessé C. Costa (Org.); Francisco Nepomuceno Filho (Org.). 1. ed. Salvador: Editora da Universidade Federal da Bahia, 2009. v. 1. 265 p. |

**Material Didático**

Cálculo Numérico.Marcelo Gomes Pereira ; Roberto Hugo Bielschowsky. 1. ed. Natal: SEDIS - EDUFRN, 2009. v. 01. 300 p. |

**Material Didático**

Conceitos de Geofísica.A.F. do Nascimento, F.H.R. Bezerra, W.E. Medeiros, 2010. Natal: Editora EDUFRN. (Livro texto para a disciplina Conceitos de Geofísica do Curso de Física à distancia da UFRN.) |