3-D description of normal moveout in anisotropic inhomogeneous media

Grechka, Vladimir; Tsvankin, Ilya

doi:10.1190/1.1444386

Cited by 258 publications

(211 citation statements)

References 20 publications

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“…The components of the coefficients are presented in terms of the medium parameters while the azimuthal dependence is governed by the trigonometric functions. Equation (A-6) and/or equation (A-11) are used in Grechka and Tsvankin (1998) to derive an expression for the normal-moveout (NMO) velocity in an azimuthally anisotropic medium. Here, our attention is focused on the quartic coefficient A 4 given by equation (A-7) and equation (A-10).…”

Section: Discussionmentioning

confidence: 99%

“…The quadratic moveout coefficient A 2 (or the NMO velocity) in a single arbitrary anisotropic layer was introduced by Grechka and Tsvankin (1998) for pure mode propagation and arbitrary strength of anisotropy as an ellipse (see, Appendix A). After recasting, it is given as:…”

Section: Normal-moveout (Nmo) Velocitymentioning

confidence: 99%

“…Tsvankin (1997a) introduced an analytic expression for the NMO velocity for pure modes of wave propagation in an HTI layer. Recentently, Grechka and Tsvankin (1998) introduced an analytic representations for the NMO velocity in orthorhomic media. In other publication, Grechka et al (1997) introduced a generalized Dix equation for the NMO velocity in arbitrary anisotropic media.…”

Section: Introductionmentioning

confidence: 99%

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Nonhyperbolic Reflection Moveout for Orthorhombic Media

Al-Dajani¹,

Toksöz²

1998

60th EAGE Conference and Exhibition

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Reflection moveout in azimuthally anisotropic media is not only azimuthally dependent but it is also nonhyperbolic. As a result, the conventional hyperbolic normal moveout (NMO) equation parameterized by the exact NMO (stacking) velocity loses accuracy with increasing offset (i.e., spreadlength). This is true even for a single-homogeneous azimuthally anisotropic layer. The most common azimuthally anisotropic models used to describe fractured media are the horizontal transverse isotropy (HTI) and the orthorhombic (ORT).Here, we introduce an analytic representation for the quartic coefficient of the Taylor's series expansion of the two-way traveltime for pure mode reflection (i.e., no conversion) in arbitrary anisotropic media with arbitrary strength of anisotropy. In addition, we present an analytic expression for the long-spread (large-offset) nonhyperbolic reflection moveout (NHMO). In this study, special attention is given to Pwave propagation in orthorhombic media with horizontal interfaces. The quartic coefficient, in general, has a relatively simple form, especially for shear wave propagation. The reflection moveout for each shear-wave mode in a homogeneous orthorhombic medium is purely hyperbolic in the direction normal to the polarization. In addition, the nonhyperbolic portion of the moveout for shear-wave propagation reaches its maximum along the polarization direction, and it decreases rapidly away from the direction of polarization. Hence, the anisotropy-induced nonhyperbolic reflection moveout for shear-wave propagation is significant in the vicinity of the polarization directions.In multilayered azimuthally anisotropic media, the NMO (stacking) velocity and the quartic moveout coefficient can be calculated with good accuracy using Dix-type averaging (e.g., the known averaging equations for VTI media). The interval NMO velocities and the interval quartic coefficients, however, are azimuthally dependent. This allows us to extend the nonhyperbolic moveout (NHMO) equation, originally designed for VTI media, to more general horizontally stratified azimuthally anisotropic media. Numerical examples from reflection moveout in orthorhombic media, the focus of this paper, show that this NHMO equation accurately describes the azimuthally-dependent P -wave reflection traveltimes, even on spreadlengths twice as large as the reflector depth. This work provides analytic insight into the behavior of nonhyperbolic moveout, and it has important applications in modeling and inversion of reflection moveout in azimuthally anisotropic media.

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Section: Discussionmentioning

confidence: 99%

Section: Normal-moveout (Nmo) Velocitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonhyperbolic Reflection Moveout for Orthorhombic Media

Al-Dajani¹,

Toksöz²

1998

60th EAGE Conference and Exhibition

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“…However, the two-term fitting of amplitude on both incidence angle and azimuth is not straightforward, since φ is measured from the major axis of the anisotropic ellipse, which is unknown in general. Following a similar derivation due to Grechka & Tsvankin (1998) on elliptical NMO velocity fitting, Jenner (2002) used elementary trigonometric identities to recast the two-term AVOAz equation in a general form…”

Section: Avoaz Surface Fittingmentioning

confidence: 99%

Fracture detection from seismic P-wave azimuthal AVO analysis – application to Valhall LOFS data

Xia¹,

Thomsen²,

Barkved³

2006

In-Situ Rock Stress

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The P-wave reflection amplitude variation as a function of offset and azimuth reveals much about the anisotropic nature of the subsurface rocks. Stress in the fractured reservoir may be closely linked to the seismic anisotropy. We propose and implement a method that systematically examines the amplitude vs. offset and azimuth (AVOAz) behavior of CMP gathers to invert for the implied fracture orientations and density, without arbitrary procedures such as azimuthal sectoring. Standard statistical methods, applied in this context, give us confidence interval and acceptance criteria for our results. We applied the technique to the Valhall Life Of Field Seismic (LOFS) dataset and produced relevant attribute maps at the reservoir level. The results indicate a strong correlation with changes in stress state associated with production-induced compaction in a fractured reservoir.

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“…Thomsen (1986) was the first to derive the normal moveout (NMO) velocity at a shortoffset for waves reflected from transversely isotropic (TI) strata. Among the most notable researchers to attempt to use the nonhyperbolic reflection NMO technique to inverse the anisotropic parameters of a stratum are Alkhalifah and Tsvankin (1995); Grechka and Tsvankin (1998); Al-Dajani and Tsvankin (1998) and Grechka and Tsvankin (2000). In the case of seismic migration which repositions reflected energy from its apparent position to its true subsurface location, care must be taken when treating the reflection points for waves reflected from anisotropic strata (Larner and Cohen 1993;Alkhalifah and Larner 1994;Uzcategui 1995;Alkhalifah 1995;Ball 1995).…”

Section: Introductionmentioning

confidence: 99%

Travel times and reflection points for reflected P-waves in transversely isotropic media

Chang¹,

Kuo²

2005

Terr. Atmos. Ocean. Sci.

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ABSTRACT1 Institute of Seismology, National Chung Cheng University, Chia-Yi, Taiwan, ROC * Corresponding author address: Prof. Young-Fo Chang, Institute of Seismology, National Chung Cheng University, Chia-Yi, Taiwan, ROC; E-mail: seichyo@eq.ccu.edu.twThe travel time curve of reflection waves may not be hyperbolic, and the reflection point may not be located at the midpoint between the source and receiver for P-waves reflected from the bottom of a horizontal anisotropic layer. In this study, we used a physical model and numerical calculations to study travel times and reflection points for P-waves reflected from transversely isotropic media. We show that the reflection normal moveout (NMO) of the P-waves reflected from the bottom of a horizontal transversely isotropic (TI) layer is hyperbolic within the intermediate offset. The reflection points in the common midpoint (CMP) gather are located at the CMP of the P-waves reflected from TI strata with vertical (VTI) and horizontal (HTI) symmetry axes. However, the reflection points deviate from the CMP for media where the dip angles of the symmetry axes are not vertical and horizontal. The amount of deviation of the reflection points from the CMP depends not only on the offset but also on the dip angle, and the deviations are visualized by physical modeling. Thus, we must be extremely cautious about using the common depth point (CDP) shooting technique and NMO velocity to process seismic data reflected from anisotropic media.

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3-D description of normal moveout in anisotropic inhomogeneous media

Cited by 258 publications

References 20 publications

Nonhyperbolic Reflection Moveout for Orthorhombic Media

Nonhyperbolic Reflection Moveout for Orthorhombic Media

Fracture detection from seismic P-wave azimuthal AVO analysis – application to Valhall LOFS data

Travel times and reflection points for reflected P-waves in transversely isotropic media

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