We have developed a procedure to derive low-rank evolution operators in the mixed space-wavenumber domain for modeling the qP Born-scattered wavefield at perturbations of an anisotropic medium under the pseudoacoustic approximation. To approximate the full wavefield, this scattered field is then added to the reference wavefield obtained with the corresponding low-rank evolution operator in the background medium. Being built upon a Hamiltonian formulation using the dispersion relation for qP-waves, this procedure avoids pseudo-S-wave artifacts and provides a unified approach for linearizing anisotropic pseudoacoustic evolution operators. Therefore, it is immediately applicable to any arbitrary class of anisotropy. As an additional asset, the scattering operators explicitly contain the sensitivity kernels of the Born-scattered wavefield with respect to the anisotropic medium parameters. This enables direct access to important information such as its offset dependence or directional characteristics as a function of the individual parameter perturbations. For our numerical tests, we specify the operators for a mildly anisotropic tilted transversely isotropic (TTI) medium. We validate our implementation in a simple model with weak contrasts and simulate reflection data in the BP TTI model to indicate that the procedure works in a more realistic scenario. The Born-scattering results indicate that our procedure is applicable to strongly heterogeneous anisotropic media. Moreover, we use the analytical capabilities of the kernels by means of sensitivity tests to demonstrate that using two different medium parameterizations leads to different results. The mathematical formulation of the method is such that it allows for an immediate application to least-squares migration in pseudoacoustic anisotropic media.

ABSTRACTWavelet estimation and well‐tie procedures are important tasks in seismic processing and interpretation. Deconvolutional statistical methods to estimate the proper wavelet, in general, are based on the assumptions of the classical convolutional model, which implies a random process reflectivity and a minimum‐phase wavelet. The homomorphic deconvolution, however, does not take these premises into account. In this work, we propose an approach to estimate the seismic wavelet using the advantages of the homomorphic deconvolution and the deterministic estimation of the wavelet, which uses both seismic and well log data. The feasibility of this approach is verified on well‐to‐seismic tie from a real data set from Viking Graben Field, North Sea, Norway. The results show that the wavelet estimated through this methodology produced a higher quality well tie when compared to methods of estimation of the wavelet that consider the classical assumptions of the convolutional model.

Many effective medium theories are designed to describe the macroscopic properties of a medium (the rock, or reservoir in this case) in terms of the properties of its constituents (the background matrix of the rock and the inclusions, for our scenario). A very well known effective medium theory is the Eshelby-Cheng model, which was studied by us in previous work, being tested for the case where the background medium was weakly-anisotropic and porous. The analysis was done testing elastic velocities and Thomsen parameters - as a function of crack density for fixed values of aspect ratio - predicted by the model with data acquired from synthetic rock samples. In this work, we aim to complete the analysis of the Eshelby-Cheng model capabilities when applied to rocks with porous and vertical transversely isotropic (VTI) backgrounds, testing the model for the elastic velocities as functions of aspect ratio - for fixed values of crack density - against experimental data. The data used to test the model were obtained from 17 synthetic rock samples, one uncracked and 16 cracked, the latter divided into four groups of four samples each, each group with cracks having the same aspect ratio, but with the samples having different crack densities. In these samples, ultrasonic pulse transmission measurements were performed to obtain the experimental velocities used to test the model. As was not possible to acquire data for velocity as a function of aspect ratio for fixed values of crack density, we performed interpolations of the experimental data to estimate these velocities. Eshelby-Cheng model effective velocities and Thomsen parameters were calculated using three formulations proposed for the crack porosity: one proposed by Thomsen, the second one proposed in our previous work (which depends only on the crack density) and the third one proposed in this work (which depends on the crack porosity and the aspect ratio, just like Thomsen's proposal). The comparisons between elastic velocities and Thomsen parameters - as function of crack aspect ratio, for fixed values of crack density - predicted by the model and estimated from the data via interpolation showed that the third formulation produced better fittings (lower root-mean-square errors) between model and experimental data for all ranges of aspect ratio and crack density.

The study of fractures in subsurface is very important since they are, in some cases, the main conduits for hydrocarbon flow in a reservoir. There are many ways to study the behavior of seismic waves in different fracturing conditions, including the use of physical modeling. This method allows, among other approaches, the analysis of the behavior of seismic wave properties in complex fractured media, such as media with orthorhombic symmetry. In this work we performed ultrasonic measurements on fractured physical models with orthorhombic symmetry from which we analyzed the behavior of elastic velocities and anisotropy parameters for different number of fractures. The presented results show the efficiency of the construction methodology used in the study by presenting P- and S- wave velocity values consistent with the theory for an orthorhombic medium. It was observed that for the direction perpendicular to the fracture system the values of P and S-wave velocities were the smallest for each model, and that the velocities decreased as the number of fractures increased in all models. Furthermore, most of the ∊ and γ values show a decreasing behavior as a function of the decreasing number of cracks, being the trend curves of ∊ linear and most of the trend curves of γ quadratic. Additionally, all the ∊ parameters presented a high correlation with the γ parameters for a small number of fractures, lower than 5.

ABSTRACT. The study of seismic wave velocities and their related anisotropy parameters provides important tools to the study of Earth"™s subsurface. The analysis of temperature"™s influence in the elastic properties of synthetic rocks, e.g., may be a good alternative for modelling the response of elastic properties of rocks surrounding deep wells and/or that are submitted to the process of steam injection. In order to understand the effects of temperature on the elastic parameters, in this work we constructed four porous synthetic sandstones, one representing an uncracked medium and three cracked samples. They were submitted to variable temperatures, while their elastic properties were calculated during heating and cooling processes. It was noted that P- and S-wave velocities decreased with increasing temperature. This behavior may be caused by changes in the background stiffness and by the generation of secondary cracks inside the samples. However, P- and S- anisotropy parameters were not affected by the changes in temperature. This can be an indicative that randomly distributed secondary cracks were created. Other indicative of secondary cracking formation can be associated to the difference between seismic velocities during the heating and cooling processes.Keywords: Cracked media, Anisotropy, Temperature dependence, Elastic parameters.RESUMO. O estudo das ondas sísmicas e de seus parâmetros anisotrópicos associados fornece ferramentas importantes para o estudo da subsuperfície da Terra. A análise da influência da temperatura nos parâmetros elásticos de rochas sintéticas, por exemplo, pode ser uma boa alternativa para modelar a resposta das propriedades elásticas de rochas circundando poços profundos e/ou que são submetidas a processos de injeção de vapor. Para entender os efeitos da temperatura nos parâmetros elásticos, neste trabalho construímos quatro arenitos sintéticos porosos, um representando um meio não-fissurado e três amostras fissuradas. As amostras foram submetidas a temperaturas variadas, enquanto suas propriedades elásticas foram calculadas ao longo dos processos de aquecimento e resfriamento. Notou-se que as velocidades das ondas P e S diminuíram com o aumento da temperatura. Esse comportamento talvez seja causado por variações na rigidez do background e pela formação de fissuras secundárias nas amostras. Entretanto, os parâmetros anisotrópicos P e S não foram afetados pelas mudanças de temperatura. Isso pode ser considerado um indicativo de que fissuras secundárias distribuídas aleatoriamente foram formadas. Outro indicador da formação de fissuras secundárias pode ser associado à diferença entre as velocidades sísmicas durante os processos de aquecimento e resfriamento.Palavras-chave: Meios fissurados, aniostropia, dependência de temperatura, parâmetros elásticos.

ABSTRACT. The manufacture of synthetic rock samples has a great importance in the study of the elastic properties of the rocks based on the variation of heterogeneities. For this work we constructed synthetic sandstones with different number of heterogeneities in the samples. We analyzed all samples from ultrasonic point of view (in dry and saturated condition). In total, twelve heterogeneous samples and an isotropic sample for reference were constructed. The heterogeneous samples were divided in three groups (A, B and C): group A with heterogeneities of 3.75-4.25 mm in diameter, group B with heterogeneities of 5-6 mm in diameter and group C with heterogeneities of 6.5-7.5 mm in diameter. From the first arrival picking on P- and S-waveforms, we calculated VP and VS velocities. We also compared the experimental velocities with ones predicted by the theoretical models of modified Maxwell-Garnett and the Kuster-Toksöz models. The theoretical predictions were made for the P and S velocities for the dry and saturated cases. In general, we noted that the best fit between the theoretical and experimental values occurred for the prediction of the modified Maxwell-Garnett model.Keywords: ultrasonic waves, effective model theories, synthetic samples, heterogeneous media.RESUMO. A fabricação de amostras de rochas sintéticas tem uma grande importância no estudo das propriedades elásticas das rochas com base na variação de heterogeneidades. Para este trabalho construímos arenitos sintéticos com diferentes números de heterogeneidades nas amostras. Analisamos todas as amostras do ponto de vista ultrassônico (em condição seca e saturada). No total, foram construídas doze amostras heterogêneas e uma amostra isotrópica para referência. As amostras heterogêneas foram divididas em três grupos (A, B e C): grupo A com heterogeneidades de 3,75 a 4,25 mm de diâmetro, grupo B com heterogeneidades de 5 a 6 mm de diâmetro e grupo C com heterogeneidades de 6,5 a 7,5 mm de diâmetro. A partir das escolhas de primeira chegada, tomando as formas de onda P e S, calculamos as velocidades VP e VS. Também comparamos as velocidades experimentais com as previstas pelos modelos teóricos dos modelos de Maxwell-Garnett e Kuster-Toksöz modificados. As previsões teóricas foram feitas para as velocidades P e S para os casos seco e saturado. Em geral, notamos que o melhor ajuste entre os valores teóricos e experimentais ocorreu para a predição do modelo de Maxwell-Garnett modificado.Palavras-chave: ondas ultrassônicas, teorias de modelos efetivos, amostras sintéticas, meios heterogêneos.

PreviousNext No Access15th International Congress of the Brazilian Geophysical Society & EXPOGEF, Rio de Janeiro, Brazil, 31 July-3 August 2017Verificação experimental do modelo de efetivo de Hudson-Crampin para meios anisotrópicos fissurados cujo o background apresenta anisotropia VTIAuthors: José J. S. de FigueiredoBruce F. F. ChibaMurillo J. S. NascimentoCarolina B. da SilvaJosé J. S. de FigueiredoUniversidade Federal do Pará e INCT-GPSearch for more papers by this author, Bruce F. F. ChibaUniversidade Federal do ParáSearch for more papers by this author, Murillo J. S. NascimentoUniversidade Federal do ParáSearch for more papers by this author, and Carolina B. da SilvaUniversidade Federal do ParáSearch for more papers by this authorhttps://doi.org/10.1190/sbgf2017-308 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Abstract This paper is in Portuguese. A modelagem física de meios fissurados/ fraturados utilizando experimentos laboratoriais em escala reduzida reduzida tem funcionado como uma excelente alternativa para a compreensão do efeito da anisotropia na caracterização do reservatório de hidrocarbonetos fissurado/fraturado. O objetivo principal deste trabalho foi verificar experimentalmente asprevisão do modelo de meio efetivo para meios fissurados Hudson e Crampim. Para isso, foram realizadas medições ultrassônicas em amostras anisotrópicas sintéticas com diferentes densidade de fissuras distribuídas em quatro razões de aspectos. Dezesseis amostras (quatro amostra para cada razão de aspecto) fissuradas e uma amostra de referência com ansiostropia VTI e sem fissuras. As razões de aspectos variam entre Isso resulta em amostras com valores de razão de aspecto variando de 0.08 a 0.52. Todas as amostras fissuradas foram simuladas por espaços vazios na forma de discos numa matriz poro elástica com baixa anisotropia VTI homogênea feita com areia e cimento. Em relação às previsões de velocidade realizadas pelo modelos teórico, Crampin apresenta um melhor ajuste para VP e VS se propagando perpendicular ao plano de fissuras para as condições secas e saturadas. Estas previsões se tornam mais evidentes no caso em que a densidade de fissuras e razões de aspectos são baixas. A partir dos valores de velocidade, nossa comparação também foi realizada em termos dos parâmetros ε, γ e δ. Keywords: hydrocarbon, VTI, anisotropyPermalink: https://doi.org/10.1190/sbgf2017-308FiguresReferencesRelatedDetails 15th International Congress of the Brazilian Geophysical Society & EXPOGEF, Rio de Janeiro, Brazil, 31 July-3 August 2017ISSN (online):2159-6832Copyright: 2017 Pages: 1876 publication data© 2017 Published in electronic format with permission by the Brazilian Geophysical SocietyPublisher:Society of Exploration Geophysicists HistoryPublished Online: 03 Aug 2017 CITATION INFORMATION José J. S. de Figueiredo, Bruce F. F. Chiba, Murillo J. S. Nascimento, and Carolina B. da Silva, (2017), "Verificação experimental do modelo de efetivo de Hudson-Crampin para meios anisotrópicos fissurados cujo o background apresenta anisotropia VTI," SEG Global Meeting Abstracts : 1583-1588. https://doi.org/10.1190/sbgf2017-308 Plain-Language Summary KeywordshydrocarbonVTIanisotropyPDF DownloadLoading ...