Produção Científica

**Artigo em Revista**

Up/down acoustic wavefield decomposition using a single propagation and its application in reverse time migrationThe separation of up- and downgoing wavefields is an important technique in the processing of multicomponent recorded data, propagating wavefields, and reverse time migration (RTM). Most of the previous methods for separating up/down propagating wavefields can be grouped according to their implementation strategy: a requirement to save time steps to perform Fourier transform over time or construction of the analytical wavefield through a solution of the wave equation twice (one for the source and another for the Hilbert-transformed source), in which both strategies have a high computational cost. For computing the analytical wavefield, we are proposing an alternative method based on the first-order partial equation in time and by just solving the wave equation once. Our strategy improves the computation of wavefield separation, and it can bring the causal imaging condition into practice. For time extrapolation, we are using the rapid expansion method to compute the wavefield and its first-order time derivative and then we can compute the analytical wavefield. By computing the analytical wavefield, we can, therefore, separate the wavefield into up- and downgoing components for each time step in an explicit way. Applications to synthetic models indicate that our method allows performing the wavefield decomposition similarly to the conventional method, as well as a potential application for the 3D case. For RTM applications, we can now use the causal imaging condition for several synthetic examples. Acoustic RTM up/down decomposition demonstrates that it can successfully remove the low-frequency noise, which is common in the typical crosscorrelation imaging condition, and it is usually removed by applying a Laplacian filter. Moreover, our method is efficient in terms of computational time when compared to RTM using an analytical wavefield computed by two propagations, and it is a little more costly than conventional RTM using the crosscorrelation imaging condition. |

**Artigo em Revista**

Time-stepping wave-equation solution for seismic modeling using a multiple-angle formula and the Taylor expansionWe have developed an analytical solution for wave equations using a multiple-angle formula. The new solution based on the multiple-angle expansion allows us to generate a family of solutions for the acoustic-wave equation, which may be combined with Taylor-series, Chebyshev, Hermite, and Legendre polynomial expansions or any other expansion for the cosine function and used for seismic modeling, reverse time migration, and inverse problems. Extension of this method to the solution of elastic and anisotropic wave equations is also straightforward. We also derive a criterion using the stability and dispersion relations to determine the order of the solution for a given time step and, thus, obtaining stable wavefields free of numerical dispersion. Afterward, numerical tests are performed using complex 2D velocity models to evaluate the effectiveness and robustness of our method, combined with second- or fourth-order Taylor approximations. Our multiple-angle approach is stable and provides reliable seismic modeling results for larger times steps than those usually used by conventional finite-difference methods. Moreover, multiple-angle schemes using a second-order Taylor approximation for each cosine term have a lower computational cost than the mixed wavenumber-space rapid expansion method. |

**Artigo em Revista**

Basement fabric controls rift nucleation and postrift basin inversion in the continental margin of NE BrazilIn passive continental margins, the brittle reactivation of shear zones and their role in the deformation and deposition of sedimentary basins are still a matter of debate. In this research, we investigated the role of the brittle reactivation of Precambrian shear zones in the nucleation of rift and postrift faults in the onshore portion of the Sergipe-Alagoas and Pernambuco basins in northeastern Brazil. We combine and interpret a dataset of aeromagnetic and topographic data, associated with reflection seismic and borehole data, to analyze the evolution of a portion of the Atlantic continental margin of Brazil. Our results indicate that in the crystalline basement, the magnetic lineaments are correlated with ductile structures as shear zones, and the continuity of these lineaments in the Sergipe-Alagoas and Pernambuco basins is interpreted as the shear zones below the sedimentary cover of these basins. We document the following phases of the brittle reactivation of basement shear zones: (1) the opening of the South Atlantic Ocean in the Early Cretaceous under an extensional stress regime and (2) tectonic inversion induced by the Mid-Atlantic Ridge push and the Andean Cordillera rise in the Neogene-Quaternary under a predominantly strike-slip stress regime. During the rift phase, the brittle reactivation of the shear zones controlled the locations and architectures of the rifts. These structures acted as zones of weakness and were reactivated as normal faults. The brittle reactivation of shear zones was still active during the postrift phase and was responsible for the development of compressional structures. The reverse faulting and related folding pattern indicate tectonic inversion in the Late Cretaceous-Cenozoic. The structures formed during the postrift phase under a strike-slip regime are consistent with the present-day stress field, indicating that tectonic inversion is an active phase of the Brazilian margin. |

**Artigo em Revista**

A multiscale approach to full-waveform inversion using a sequence of time-domain misfit functionsMost of the approaches designed to avoid cycle skipping in full-waveform inversion (FWI) involve calculating a sequence of inversions in a multiscale fashion. We have adopted an alternative strategy, which is inverting a sequence of different misfit functions in the time domain. This is an implicit multiscale approach in the sense that the used misfit functions are sensitive to different wavelengths, but all of the inversion steps use the same modeling algorithm and the same model grid. In the first and third inversion steps, the transmitted (early arrivals) and reflected (late arrivals) components of the wavefield envelopes are respectively fitted. The second step promotes a smooth transition between the first and third steps, by using the envelope of the complete waveform. Because fitting just the envelope of the reflected waves has a minor effect on the misfit function of the whole data set, the phases of the reflected waves are mostly fitted in the fourth step, which is based on the waveform misfit function preserving only the late arrivals. The third and fourth steps are of crucial importance to fit the reflected events. We test the sequential inversion approach with the Marmousi model using data sets with different frequencies, obtaining better estimates of the velocity field than those obtained with the classic FWI. The solutions obtained with classic FWI and sequential inversion approach degrade with a progressively higher peak frequency data set, but the classic FWI solution degrades more rapidly. |

**Artigo em Revista**

3D Seismic survey design using mixed-radix based algorithm inversionThe determination of three-dimensional geometry and acquisition parameters, the seismic acquisition survey design, is constantly subject of studies in obtaining data with the highest seismic quality, operational efficiency and cost minimization. In this paper, we propose a methodology for inverting geometry parameters of threedimensional orthogonal land seismic surveys based on a direct search method using a mixed-radix based algorithm. In this algorithm, the search space is discretized on a mixed-radix base, which depends on the extreme values and the search resolution of each parameter. We will show how to reparametrize the orthogonal acquisition geometry elements in order to obtain the independents and integers parameters that are necessary to construct the mixed-radix base. For the optimization purpose, we define an objective function to contemplate target parameters associated with the elements of the acquisition geometry directly related to the geophysical and operationa constraints. Taking in account that the mathematical functions and the objective function we define for the problem have no significant computational cost, all model space parameters are fast and efficiently tested. We applied the algorithm, using as input data, provided by a one-line roll orthogonal reference geometry, assuming a pair of geological objectives as shallow and deep targets. All selected models that meet both the proposed objectives and the constraints are organized by decreasing order of fitness so that with the mixed-radix inversion algorithm we found not only the best model, but also a set of suitable models. Likewise, with the best set of geometries, it is possible to establish a direct comparison between them, analysing their adherence to the technical and operational requirements according to the availability and degree of detail of each one. We show the top 10 best results as a table, allowing a direct comparison between all aspects of these geometries, and we summarize the results showing graphically the fitness of all selected geometries and the inverted geometry elements for the 1000 best geometries. These graphical displays provide a direct way to understand how each model behaves as the fitness decreases. The algorithm is very flexible and its application can be extended to any environment and type of acquisition geometry, and in any phase study of an area be it regional, exploratory or development. Key words: 3D seismic survey design, Geophysical inversion, Mixed-radix representation, Optimization. |

**Artigo em Revista**

Colored and linear inversions to relative acoustic impedanceAcoustic impedance (AI) is a widely used seismic attribute in stratigraphic interpretation. Because of the frequency-band-limited nature of seismic data, seismic amplitude inversion cannot determine AI itself, but it can only provide an estimate of its variations, the relative AI (RAI). We have revisited and compared two alternative methods to transform stacked seismic data into RAI. One is colored inversion (CI), which requires well-log information, and the other is linear inversion (LI), which requires knowledge of the seismic source wavelet. We start by formulating the two approaches in a theoretically comparable manner. This allows us to conclude that both procedures are theoretically equivalent. We proceed to check whether the use of the CI results as the initial solution for LI can improve the RAI estimation. In our experiments, combining CI and LI cannot provide superior RAI results to those produced by each approach applied individually. Then, we analyze the LI performance with two distinct solvers for the associated linear system. Moreover, we investigate the sensitivity of both methods regarding the frequency content present in synthetic data. The numerical tests using the Marmousi2 model demonstrate that the CI and LI techniques can provide an RAI estimate of similar accuracy. A field-data example confirms the analysis using synthetic-data experiments. Our investigations confirm the theoretical and practical similarities of CI and LI regardless of the numerical strategy used in LI. An important result of our tests is that an increase in the low-frequency gap in the data leads to slightly deteriorated CI quality. In this case, LI required more iterations for the conjugate-gradient least-squares solver, but the final results were not much affected. Both methodologies provided interesting RAI profiles compared with well-log data, at low computational cost and with a simple parameterization. |

**Artigo em Revista**

Automatic seismic velocity analysis based on nonlinear optimization of the semblance functionWe developed and analyzed a method for automatic velocity picking in the semblance domain as a nonlinear optimization problem that is computationally fast, robust, and a simple model for testing. The obtained results can be considered as an initial model for other data-driven methods. Seismic velocity analysis can be considered the major aim for application in data imaging and post-imaging processes. It falls into several classes ofmathematical and computational problems, such as manual or automatic, stack ormigration, and nonlinear local or global optimization. In all cases the process needs assistance in terms of a priori information and input-output constraints, that can be geological (fromwell logs), geometrical, and physical parameters. In addition, all geophysics problems are to be considered three dimensional spatially, as twodimensional imaging suffers from structural side effects. In the conventionalmethod, the steps of velocity analysis for each common-mid-point are as follows: (1) normalmoveout stack velocities are estimated by means of semblance summation along hyperbolic time trajectories producing a map of S(vrms, t0); (2) manual picking is performed in the semblance map for several stack times t0; and (3) interval velocities, vint, are calculated based on the picked smooth stack velocities, vrms, to construct an earth velocity time model that does not require a reference subsurface model. In conclusion, the present automatic velocity analysis hasmultiple tasks: (1) diminishing the picking step by considering that the stack velocities are based on an interval velocity model; (2) searching for an interval velocity model that best explains the estimated stack velocities; and (3) automatically searching, subject to geological, physical and mathematical constraints, and editing. |

**Artigo em Revista**

Constraint nip-tomographic inversion of strong sparse seismic dataThis work is a result of specific numerical experimentsmotivated by real cases of processing strong sparse seismic data, as an application of techniques based on the common-reflection-surface (CRS) stack technology aiming at estimating a smooth velocity depth distribution. The paper is primarily limited to numerical tests with a depth velocity model that attends closely the paraxial theory validated by the seismic ray hypotheses. A complete modeling of a seismic surveywas performed, and the common-shot sections were submitted to random muting of traces, to noise addition, and afterwards followed by reconstruction of the section by trace interpolation. The interpolation was controlled by the 2D spectral non-aliasing condition, where the t − x spectral amplitude content was limited to the two main Fourier quadrants f − k. It was admitted that most information was based on primary compressional (P) wave content; therefore, multiples and the P − S conversion were considered as noise. The trace interpolation used the stack attributes of the original gather (conventional stack) with sparse data to construct supergather sections (for the supergather stack). The velocity distribution in depth uses the principle of interpreting the inversion data as normal incidence point (NPI) information. The applied inversion algorithm is NIP-tomographic, classified as curve fitting, non-linear, multi-parametric, that uses the wave front kinematic and dynamic CRS attributes as data-driven constraints to estimate a consistent depth velocity distribution. As a general conclusion, we emphasized also interpolation, inclusive of sparse data, as a step for spectral analysis, consequently in filtering, stacking, and tomography to obtain a velocity distribution for further use in the estimation for velocity distribution, imaging, geological interpretation and sedimentary basin modeling. |

**Artigo em Revista**

Target-level waveform inversion: a prospective application of the convolution-type representation for the acoustic wavefieldNowadays, full-waveform inversion, based on fitting the measured surface data with modelled data, has become the preferred approach to recover detailed physical parameters from the subsurface. However, its application is computationally expensive for large inversion domains. Furthermore, when the subsurface has a complex geological setting, the inversion process requires an appropriate pre-conditioning scheme to retrieve the medium parameters for the desired target area in a reliable manner. One way of dealing with both aspects is by waveform inversion schemes in a target-oriented fashion. Therefore, we propose a prospective application of the convolution-type representation for the acoustic wavefield in the frequency–space domain formulated as a target-oriented waveform inversion method. Our approach aims at matching the observed and modelled upgoing wavefields at a target depth level in the subsurface, where the seismic wavefields, generated by sources distributed above this level, are available. The forward modelling is performed by combining the convolution-type representation for the acoustic wavefield with solving the two-way acoustic wave-equation in the frequency–space domain for the target area. We evaluate the effectiveness of our inversion method by comparing it with the full-domain full-waveform inversion process through some numerical examples using synthetic data from a horizontal well acquisition geometry, where the sources are located at the surface and the receivers are located along a horizontal well at the target level. Our proposed inversion method requires less computational effort and, for this particular acquisition, it has proven to provide more accurate estimates of the target zone below a complex overburden compared to both full-domain full-waveform inversion process and local full-waveform inversion after applying interferometry by multidimensional deconvolution to get local-impulse responses. |

**Artigo em Revista**

Multi-frequency electromagnetic method for inductive measurement of ground induced polarization and resistivityA geophysical electromagnetic method to inductively measure the ground electrical resistivity and induced polarization has recently been tested. Its basic characteristics involve three major differences from other methods: the two electrical ground parameters are obtained through measuring magnetic field. For this purpose, a transmitter–receiver (T, R) electromagnetic system is used that operates in the frequency domain and consists of a horizontal loop as the transmitter for the perpendicular loops configuration on the ground surface; the measured function is the (T, R) inductive coupling main variation produced due to the presence of the earth, that is the magnetic field radial component; the measurements are conducted at a large number of frequencies (139 in the more advanced prototype), and the measured function is explored in the frequency interval 0.2 Hz to 1 kHz, a much broader frequency range of the induced polarization effect spectrum, than the one conventionally used in field exploration. Three major aspects are emphasized: (1) the existence of a small ‘main zone’ interior to a half-space, which is responsible for most of the magnetic energy that the receiver measures on the half-space surface. This permits to substitute the entire half-space by the ‘main zone’ and, in a second step, to substitute the ‘main zone’ by an equiv- alent homogeneous half-space with the electrical characteristics of such ‘main zone';(2) the existence of a closed solution for the fields that the (T, R) system generates on the surface of a homogeneous isotropic half-space, which provides exact functions with the two electrical parameters of interest as the variables (the apparent resistivity and relative polarization parameter); (3) the values of the electrical parameters so determined can be attributed to the central point of the ‘main zone’. Three-horizontal layers half-space and a conductive sphere in the free-space are discussed as models. Four field surveys are analysed as examples and show a satisfactory performance of the method for detection of on-shore hydrocarbon reservoirs, description of induced reservoir variations and structural features mapping at depths up to 2.5 km. |