Understanding the effect of cracks in elastic media is important for hydrocarbon recovery, especially in nonconventional reservoirs. Consequently, due to the presence of oriented cracks on these types of reservoirs, an anisotropic behavior can be induced. In terms of seismic or ultrasonic velocities, this means that elastic waves propagating on regions with oriented cracks have their velocities varying with the propagation and polarization directions. Thus, the analysis of the seismic wave velocities in a cracked medium can be used as a tool for reservoir characterization. For this reason, there is a variety of mathematical models to describe transversely isotropic cracked medium as well as the design of several experiments to test these models. We have experimentally analyzed the theoretical predictions of Eshelby-Cheng’s first-order model. For this proposal, we measured P- and S-wave ultrasonic velocities in 17 anisotropic samples. All samples indicate weak background anisotropy due to layering deposition; i.e., they are vertical transversely isotropic (VTI) media. Sixteen synthetic anisotropic samples with different crack densities and aspect ratios were simulated by penny-shaped void inclusions in a homogeneous porous matrix made with cement and sand. An uncracked sample, with weak VTI anisotropy, was constructed for reference. The crack densities and aspect ratios ranged from 0 to 0.102 and from 0 to 0.52, respectively. All measurements were performed in a dry condition. From the experimental and theoretical velocities, we calculated the Thomsen’s parameters and correlated them with the crack density. An efficient flowchart was developed to make feasible and clear the inversion of the output Eshelby-Cheng’s effective elastic coefficients in effective velocities. Our results suggest that the anisotropy increases with crack density. In general, we noted that the best fit between the Eshelby-Cheng’s model and the experimental results occurs when the crack density and aspect ratio were lower than 0.1 and 0.32, respectively, and it is largely dependent on the type of crack porosity’s equation used in the inversion of effective stiffness coefficients in the elastic effective velocities.

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We present 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 pseudo-acoustic 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 pseudo-acoustic 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 like 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 transversly isotropic (TTI) medium. We validate our implementation in a simple model with weak contrasts and simulate reflection data in the BP TTI model to show 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 pseudo-acoustic anisotropic media.

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.

A B S T R A C TWavelet 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.