Nonhyperbolic reflection moveout for horizontal transverse isotropy

Al-Dajani, AbdulFattah; Tsvankin, Ilya

doi:10.1190/1.1826400

Cited by 21 publications

(39 citation statements)

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“…3a -7a) all remain hyperbolic even though the material has 25% velocity-anisotropy for the P-waves. However, Alkhalifah and Tsvankin (1995), Tsvankin (1998), Al-Dajani and and Grechka and Tsvankin (2000) have previously used the nonhyperbolic reflection NMO to derive the anisotropic parameters of a stratum. Intuitively, we used the isotropic NMO velocity to process the seismic data.…”

Section: Discussionmentioning

confidence: 99%

“…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%

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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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Section: Discussionmentioning

confidence: 99%

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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“…Although equation (5) was originally designed for VTI media, it is generic and can be used in arbitrary anisotropic media if the appropriate coefficients (A 2 , A 4 , and A) were found, honoring the azimuthal anisotropic dependency. In fact, earlier studies by Al-Dajani and Tsvankin (1998) and Al-Dajani and ToksDz (1999) demonstrate the accuracy of equation (5) for P-wave propagation in azimuthally anisotropic media. Our objective is to study the validity of equation (5) for shear-wave propagation.…”

Section: The Nonhyperbolic Moveout (Nhmo) Equationmentioning

confidence: 99%

“…It is obvious that the conventional NMO equation (I), which is parameterized by the azimuthally-dependent NMO velocity (equations (2) and (3)), accurately represents the reflection moveout for shear-wave propagation {especially for conventional spreadlengths (X/D :$ 1)). Interestingly, the anisotropy-induced deviations of the moveout curve from a hyperbola, a phenomenon which is well-known for Pwave propagation in azimuthally anisotropic media (Al-Dajani and Tsvankin, 1998;AlDajani and Toksiiz, 1999), is rather different in the case of shear-wave propagation in orthorhombic media. To understand this difference we need to look at the nonhyperbolic portion of the reflection moveout for shear-wave propagation.…”

Section: The Normal Moveout (Nmo) Velocitymentioning

confidence: 99%

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Shear‐wave reflection moveout for azimuthally anisotropic media

Toksöz¹,

Al-Dajani²

1999

SEG Technical Program Expanded Abstracts 1999

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The presence of azimuthal anisotropy causes shear wave propagation to split into fast and slow shear waves. The most common azimuthally anisotropic models used to describe fractured reservoirs are transverse isotropy with a horizontal axis of symmetry (HTI), and orthorhombic. In this paper, we study shear-wave reflection moveout in azimuthally anisotropic media with special attention paid to orthorhombic media with horizontal interfaces. In such cases the shear-wave reflection moveout is azimuthally variant and nonhyperbolic. We analyze the azimuthal dependence of normal moveout (NMO) velocity and we validate the accuracy of the conventional hyperbolic moveout equation. The azimuthal variation of NMO velocity is elliptical for both wave modes. In the presence of anisotropy-induced, nonhyperbolic moveout (NHMO), the hyperbolic moveout equation loses its accuracy with increasing offset (e.g., offset-to-depth ratio> 1). To study the azimuthal behavior of the NHMO for shear-wave reflections, we introduce an analytic representation for the quartic coefficient of the Taylor's series expansion of the two-way traveltime. In an orthorhombic medium the quartic coefficient for shearwave reflections has a relatively simple form, especially in comparison to P-wave. The reflection moveout for each shear-wave mode in a homogeneous orthorhombic medium is purely hyperbolic in the direction normal to the polarization. The nonhyperbolic portion of the moveout, on the other hand, reaches its maximum along the polarization direction, and it reduces rapidly away from the direction of pOlarization. As a result, the anisotropy-induced, nonhyperbolic reflection moveout is significant in the vicinity of the polarization directions (e.g., ±30°and for large offset-to-depth ratios). The implementation of the NHM0 equation and the utilization of the moveout coefficients allow for not only enhanced seismic imaging but also provide the link between seismic signatures and medium parameters. 9-1

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The Characteristic of Quartic Moveout Coefficient of P‐Wave in the TI Homogeneous Media with an Arbitrary Orientation Symmetric‐Axis

Chen¹,

Chen²

2008

Chinese J of Geophysics

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Deviations of any pure mode (non‐converted) wave reflection traveltimes from a hyperbola, called the nonhyperbolic or quartic moveout, need to be corrected properly in processing long‐spread anisotropic seismic data. Based on our exact analytic expression for the quartic moveout coefficient (A4) of pure mode (non‐converted) wave reflection on a horizontal interface in the TI media with an arbitrarily orientated symmetry axis (ATI) in space, we numerically study the characteristics of the P‐wave A4 with the CMP survey line azimuth variation. The forward modeling results show that the characteristics of the A4 are related not only to the anisotropy parameters of the TI, but also the spatial orientation of the TI. The variation characteristic of the A4 is determined by the anisotropy parameters and tilt angle of the TI symmetric‐axis, and the azimuth of the TI symmetric‐axis results in the azimuth symmetry of the A4 with the survey line variation. Our numerical results will benefit the explanation of the anisotropic seismic data and the parameter inversion.

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Nonhyperbolic reflection moveout for horizontal transverse isotropy

Cited by 21 publications

References 1 publication

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

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

Shear‐wave reflection moveout for azimuthally anisotropic media

The Characteristic of Quartic Moveout Coefficient of P‐Wave in the TI Homogeneous Media with an Arbitrary Orientation Symmetric‐Axis

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