Three‐parameter AVO crossplotting in anisotropic media

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1359-1363 ◽  
Author(s):  
He Chen ◽  
John P. Castagna ◽  
Raymon L. Brown ◽  
Antonio C. B. Ramos
Keyword(s):  
Real World ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Anisotropic Behavior ◽  
Amplitude Versus Offset ◽  
Transversely Isotropic Media ◽  
Interpretation Errors ◽  
Isotropic Media ◽  
Empirical Corrections ◽  
Amplitude Versus

Amplitude versus offset (AVO) interpretation can be facilitated by crossplotting AVO intercept (A), gradient (B), and curvature (C) terms. However, anisotropy, which exists in the real world, usually complicates AVO analysis. Recognizing anisotropic behavior on AVO crossplots can help avoid AVO interpretation errors. Using a modification to a three‐term (A, B, and C) approximation to the exact anisotropic reflection coefficients for transversely isotropic media, we find that anisotropy has a nonlinear effect on an A versus C crossplot yet causes slope changes and differing intercepts on A versus B or C crossplots. Empirical corrections that result in more accurate crossplot interpretation are introduced for specific circumstances.

PP-wave reflection coefficients in weakly anisotropic elastic media

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 2129-2141 ◽  
Author(s):  
Václav Vavryuk ◽  
Ivan Peník
Keyword(s):  
Reflection Coefficient ◽  
Approximate Formula ◽  
Wave Reflection ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Pp Wave ◽  
Axis Of Symmetry ◽  
Amplitude Versus

Approximate PP-wave reflection coefficients for weak contrast interfaces separating elastic, weakly transversely isotropic media have been derived recently by several authors. Application of these coefficients is limited because the axis of symmetry of transversely isotropic media must be either perpendicular or parallel to the reflector. In this paper, we remove this limitation by deriving a formula for the PP-wave reflection coefficient for weak contrast interfaces separating two weakly but arbitrarily anisotropic media. The formula is obtained by applying the first‐order perturbation theory. The approximate coefficient consists of a sum of the PP-wave reflection coefficient for a weak contrast interface separating two background isotropic half‐spaces and a perturbation attributable to the deviation of anisotropic half‐spaces from their isotropic backgrounds. The coefficient depends linearly on differences of weak anisotropy parameters across the interface. This simplifies studies of sensitivity of such coefficients to the parameters of the surrounding structure, which represent a basic part of the amplitude‐versus‐offset (AVO) or amplitude‐versus‐azimuth (AVA) analysis. The reflection coefficient is reciprocal. In the same way, the formula for the PP-wave transmission coefficient can be derived. The generalization of the procedure presented for the derivation of coefficients of converted waves is also possible although slightly more complicated. Dependence of the reflection coefficient on the angle of incidence is expressed in terms of three factors, as in isotropic media. The first factor alone describes normal incidence reflection. The second yields the low‐order angular variations. All three factors describe the coefficient in the whole region, in which the approximate formula is valid. In symmetry planes of weakly anisotropic media of higher symmetry, the approximate formula reduces to the formulas presented by other authors. The accuracy of the approximate formula for the PP reflection coefficient is illustrated on the model with an interface separating an isotropic half‐space from a half‐space filled by a transversely isotropic material with a horizontal axis of symmetry. The results show a very good fit with results of the exact formula, even in cases of strong anisotropy and strong velocity contrast.

The effects of transverse isotropy on reflection amplitude versus offset

Geophysics ◽  
1987 ◽  
Vol 52 (4) ◽  
pp. 564-567 ◽  
Author(s):  
J. Wright
Keyword(s):  
Wave Velocity ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
S Wave ◽  
Reflection Amplitude ◽  
Amplitude Versus Offset ◽  
Transversely Isotropic Media ◽  
P Wave Velocity ◽  
Isotropic Media

Studies have shown that elastic properties of materials such as shale and chalk are anisotropic. With the increasing emphasis on extraction of lithology and fluid content from changes in reflection amplitude with shot‐to‐group offset, one needs to know the effects of anisotropy on reflectivity. Since anisotropy means that velocity depends upon the direction of propagation, this angular dependence of velocity is expected to influence reflectivity changes with offset. These effects might be particularly evident in deltaic sand‐shale sequences since measurements have shown that the P-wave velocity of shales in the horizontal direction can be 20 percent higher than the vertical P-wave velocity. To investigate this behavior, a computer program was written to find the P- and S-wave reflectivities at an interface between two transversely isotropic media with the axis of symmetry perpendicular to the interface. Models for shale‐chalk and shale‐sand P-wave reflectivities were analyzed.

Effective reflection coefficients for curved interfaces in transversely isotropic media

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. WB33-WB53 ◽  
Author(s):  
Milana Ayzenberg ◽  
Ilya Tsvankin ◽  
Arkady Aizenberg ◽  
Bjørn Ursin
Keyword(s):  
Plane Wave ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Superposition Method ◽  
Low Frequencies ◽  
Amplitude Variation With Offset ◽  
Reflection Data ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
The Difference

Plane-wave reflection coefficients (PWRCs) are routinely used in amplitude-variation-with-offset analysis and for generating boundary data in Kirchhoff modeling. However, the geometrical-seismics approximation based on PWRCs becomes inadequate in describing reflected wavefields at near- and postcritical incidence angles. Also, PWRCs are derived for plane interfaces and break down in the presence of significant reflector curvature. Here, we discuss effective reflection coefficients (ERCs) designed to overcome the limitations of PWRCs for multicomponent data from heterogeneous anisotropic media. We represent the reflected wavefield in the immediate vicinity of a curved interface by a generalized plane-wave decomposition, which approximately reduces to the conventional Weyl-type integral computed for an apparent source location. The ERC then is obtainedas the ratio of the reflected and incident wavefields at each point of the interface. To conduct diffraction modeling, we combine ERCs with the tip-wave superposition method (TWSM), extended to elastic media. This methodology is implemented for curved interfaces that separate an isotropic incidence half-space and a transversely isotropic (TI) medium with the symmetry axis orthogonal to the reflector. If the interface is plane, ERCs generally are close to the exact solution, sensitive to the anisotropy parameters and source-receiver geometry. Numerical tests demonstrate that the difference between ERCs and PWRCs for typical TI models can be significant, especially at low frequencies and in the postcritical domain. For curved interfaces, ERCs provide a practical approximate tool to compute the reflected wavefield. We analyze the dependence of ERCs on reflector shape and demonstrate their advantages over PWRCs in 3D diffraction modeling of PP and PS reflection data.

scholarly journals Body‐wave radiation patterns and AVO in transversely isotropic media

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1409-1425 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Reflection Coefficient ◽  
Radiation Pattern ◽  
Transversely Isotropic ◽  
P Wave ◽  
Wave Radiation ◽  
Reflection Coefficients ◽  
Radiation Patterns ◽  
Avo Analysis ◽  
Transversely Isotropic Media ◽  
Isotropic Media

The angular dependence of reflection coefficients may be significantly distorted in the presence of elastic anisotropy. However, the influence of anisotropy on amplitude variation with offset (AVO) analysis is not limited to reflection coefficients. AVO signatures (e.g., AVO gradient) in anisotropic media are also distorted by the redistribution of energy along the wavefront of the wave traveling down to the reflector and back up to the surface. Significant anisotropy above the target horizon may be rather typical of sand‐shale sequences commonly encountered in AVO analysis. Here, I examine the influence of P‐ and S‐wave radiation patterns on AVO in the most common anisotropic model—transversely isotropic media. A concise analytic solution, obtained in the weak‐anisotropy approximation, provides a convenient way to estimate the impact of the distortions of the radiation patterns on AVO results. It is shown that the shape of the P‐wave radiation pattern in the range of angles most important to AVO analysis (0–40°) is primarily dependent on the difference between Thomsen parameters ε and δ. For media with ε − δ > 0 (the most common case), the P‐wave amplitude may drop substantially over the first 25–40° from vertical. There is no simple correlation between the strength of velocity anisotropy and angular amplitude variations. For instance, for models with a fixed positive ε − δ the amplitude distortions are less pronounced for larger values of ε and δ. The distortions of the SV‐wave radiation pattern are usually much more significant than those for the P‐wave. The anisotropic directivity factor for the incident wave may be of equal or greater importance for AVO than the influence of anisotropy on the reflection coefficient. Therefore, interpretation of AVO anomalies in the presence of anisotropy requires an integrated approach that takes into account not only the reflection coefficient but also the wave propagation above the reflector.

Effects of attenuation and anisotropy on reflection amplitude versus offset

Geophysics ◽  
1998 ◽  
Vol 63 (5) ◽  
pp. 1652-1658 ◽  
Author(s):  
José M. Carcione ◽  
Hans B. Helle ◽  
Tong Zhao
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Critical Distance ◽  
Reflection Coefficients ◽  
Amplitude Variation With Offset ◽  
Reflection Amplitude ◽  
Amplitude Versus Offset ◽  
Viscoelastic Wave ◽  
Lossy Media ◽  
Amplitude Versus

To investigate the effects that attenuation and anisotropy have on reflection coefficients, we consider a homogeneous and viscoelastic wave incident on an interface between two transversely isotropic and lossy media with the symmetry axis perpendicular to the interface. Analysis of P P and P S reflection coefficients shows that anisotropy should be taken into account in amplitude variation with offset (AVO) studies involving shales. Different anisotropic characteristics may reverse the reflection trend and substantially influence the position of the critical angle versus offset. The analysis of a shale‐chalk interface indicates that when the critical distance is close to the near offsets, the AVO response is substantially affected by the presence of dissipation. In a second example, we compute reflection coefficients and synthetic seismograms for a limestone/black shale interface with different rheological properties of the underlying shale. This case shows reversal of the reflection trend with increasing offset and compensation between the anisotropic and anelastic effects.

Reverse time migration in tilted transversely isotropic media

2020 ◽  
Vol 38 (2) ◽  
Author(s):  
Razec Cezar Sampaio Pinto da Silva Torres ◽  
Leandro Di Bartolo
Keyword(s):  
Seismic Anisotropy ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Computer Clusters ◽  
Time Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Tti Media

ABSTRACT. Reverse time migration (RTM) is one of the most powerful methods used to generate images of the subsurface. The RTM was proposed in the early 1980s, but only recently it has been routinely used in exploratory projects involving complex geology – Brazilian pre-salt, for example. Because the method uses the two-way wave equation, RTM is able to correctly image any kind of geological environment (simple or complex), including those with anisotropy. On the other hand, RTM is computationally expensive and requires the use of computer clusters. This paper proposes to investigate the influence of anisotropy on seismic imaging through the application of RTM for tilted transversely isotropic (TTI) media in pre-stack synthetic data. This work presents in detail how to implement RTM for TTI media, addressing the main issues and specific details, e.g., the computational resources required. A couple of simple models results are presented, including the application to a BP TTI 2007 benchmark model.Keywords: finite differences, wave numerical modeling, seismic anisotropy. Migração reversa no tempo em meios transversalmente isotrópicos inclinadosRESUMO. A migração reversa no tempo (RTM) é um dos mais poderosos métodos utilizados para gerar imagens da subsuperfície. A RTM foi proposta no início da década de 80, mas apenas recentemente tem sido rotineiramente utilizada em projetos exploratórios envolvendo geologia complexa, em especial no pré-sal brasileiro. Por ser um método que utiliza a equação completa da onda, qualquer configuração do meio geológico pode ser corretamente tratada, em especial na presença de anisotropia. Por outro lado, a RTM é dispendiosa computacionalmente e requer o uso de clusters de computadores por parte da indústria. Este artigo apresenta em detalhes uma implementação da RTM para meios transversalmente isotrópicos inclinados (TTI), abordando as principais dificuldades na sua implementação, além dos recursos computacionais exigidos. O algoritmo desenvolvido é aplicado a casos simples e a um benchmark padrão, conhecido como BP TTI 2007.Palavras-chave: diferenças finitas, modelagem numérica de ondas, anisotropia sísmica.

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