Plane-wave attenuation anisotropy in orthorhombic media

Zhu, Yongmei; Tsvankin, Ilya

doi:10.1190/1.2387137

Cited by 54 publications

(17 citation statements)

References 32 publications

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“…The definition of Q as , where is given by removes the mentioned problems. This definition may also represent an alternative to other definitions of the Q factor for viscoelastic anisotropic media, which appear in the literature, see, for example, Zhu & Tsvankin (2006, 2007), Zhu et al (2007). A detailed study of the behaviour of the Q factor defined in the above manner will be published elsewhere.…”

Section: Discussionmentioning

confidence: 99%

Weakly inhomogeneous plane waves in anisotropic, weakly dissipative media

Červený¹,

Pšenčı́k

2008

Geophysical Journal International

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S U M M A R YWeakly inhomogeneous time-harmonic plane waves propagating in homogeneous anisotropic, weakly dissipative media are studied using the perturbation method. Only dissipation mechanisms, which can be described within the framework of linear viscoelasticity, are considered. As a reference (non-perturbed) case, plane waves with a real-valued slowness vector propagating in perfectly elastic anisotropic media are used. Simple approximate expressions for the complex-valued slowness and polarization vectors of weakly inhomogeneous plane waves propagating in anisotropic, weakly dissipative media are derived. Special attention is devoted to the imaginary part of the slowness vector, known as the attenuation vector, which is responsible for the amplitude attenuation of a plane wave. The derived approximate expression for the attenuation vector depends on the material (intrinsic) dissipation parameters as well as on the inhomogeneity of the plane wave. Its scalar product with the energy-velocity vector yields, however, the intrinsic attenuation factor, which does not depend on the inhomogeneity of the wave, and which thus represents a very suitable measure of the material dissipation. The derived expression for the intrinsic attenuation factor is valid for media of unrestricted anisotropy and weak dissipation and for homogeneous as well as weakly inhomogeneous plane waves. The intrinsic attenuation factor is inversely proportional to the scalar quantity, which, in isotropic viscoelastic media, corresponds to the well-known quality factor Q. Its generalization to anisotropic weakly viscoelastic media is directionally dependent. Numerical examples are presented, in which the accuracy of the approximate formulae based on the perturbation method is studied. The results indicate that the presented perturbation results are sufficiently accurate to be used in practical applications. Strong directivity of the intrinsic attenuation factor shows its great potential in solving inverse problems.

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Section: Discussionmentioning

confidence: 99%

Weakly inhomogeneous plane waves in anisotropic, weakly dissipative media

Červený¹,

Pšenčı́k

2008

Geophysical Journal International

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“…The acoustic eikonal equation may also be extended to the case of attenuating orthorhombic media. In this case, we will need the Thomsen-type notations (Tsvankin, 1997;Zhu and Tsvankin, 2007) and the acoustic approximation (Alkhalifah, 2003).…”

Section: Discussionmentioning

confidence: 99%

An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis

Hao

Alkhalifah

2017

GEOPHYSICS

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Seismic-wave attenuation is an important component of describing wave propagation. Certain regions, such as gas clouds inside the earth, exert highly localized attenuation. In fact, the anisotropic nature of the earth induces anisotropic attenuation because the quasi P-wave dispersion effect should be profound along the symmetry direction. We have developed a 2D acoustic eikonal equation governing the complex-valued traveltime of quasi P-waves in attenuating, transversely isotropic media with a vertical-symmetry axis (VTI). This equation is derived under the assumption that the complex-valued traveltime of quasi P-waves in attenuating VTI media are independent of the S-wave velocity parameter υ S0 in Thomsen's notation and the S-wave attenuation coefficient A S0 in Zhu and Tsvankin's notation. We combine perturbation theory and Shanks transform to develop practical approximations to the acoustic attenuating eikonal equation, capable of admitting an analytical description of the attenuation in homogeneous media. For a horizontal-attenuating VTI layer, we also derive the nonhyperbolic approximations for the real and imaginary parts of the complex-valued reflection traveltime. These equations reveal that (1) the quasi SV-wave velocity and the corresponding quasi SV-wave attenuation coefficient given as part of Thomsen-type notation barely affect the ray velocity and ray attenuation of quasi P-waves in attenuating VTI media; (2) combining the perturbation method and Shanks transform provides an accurate analytic eikonal solution for homogeneous attenuating VTI media; (3) for a horizontal attenuating VTI layer with weak attenuation, the real part of the complex-valued reflection traveltime may still be described by the existing nonhyperbolic approximations developed for nonattenuating VTI media, and the imaginary part of the complex-valued reflection traveltime still has the shape of nonhyperbolic curves. In addition, we have evaluated the possible extension of the proposed eikonal equation to realistic attenuating media, an alternative perturbation solution to the proposed eikonal equation, and the feasibility of applying the proposed nonhyperbolic equation for the imaginary part of the complex-valued traveltime to invert for interval attenuation parameters.

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“…A brief description of all these phenomenological models can be found in Carcione (2007). Zhu and Tsvankin (2007) analyze in detail the attenuation in orthorhombic media, assuming homogeneous viscoelastic waves. They simplify the interpretation for processing purposes by introducing a set of attenuation anisotropy parameters.…”

Section: Introductionmentioning

confidence: 99%

Fracture-Induced Anisotropic Attenuation

2012

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The triaxial nature of the tectonic stress in the earth's crust favors the appearance of vertical fractures. The resulting rheology is usually effective anisotropy with orthorhombic and monoclinic symmetries. In addition, the presence of fluids leads to azimuthally varying attenuation of seismic waves. A dense set of fractures embedded in a background medium enhances anisotropy and rock compliance. Fractures are modeled as boundary discontinuities in the displacement u and particle velocity v as ½j Á u þ g Á v; where the brackets denote discontinuities across the fracture surface, j is a fracture stiffness, and g is a viscosity related to the energy loss. We consider a transversely isotropic background medium (e.g., thin horizontal plane layers), with sets of long vertical fractures. Schoenberg and Muir's theory combines the background medium and sets of vertical fractures to provide the 13 complex stiffnesses of the long-wavelength equivalent monoclinic and viscoelastic medium. Long-wavelength equivalent means that the dominant wavelength of the signal is much longer than the fracture spacing. The symmetry plane is the horizontal plane. The equations for orthorhombic and transversely isotropic media follow as particular cases. We compute the complex velocities of the medium as a function of frequency and propagation direction, which provide the phase velocities, energy velocities (wavefronts), and quality factors. The effective medium ranges from monoclinic symmetry to hexagonal (transversely isotropic) symmetry from the low-to the high-frequency limits in the case of a particle-velocity discontinuity (lossy case) and the attenuation shows typical Zener relaxation peaks as a function of frequency. The attenuation of the coupled waves may show important differences when computed versus the ray or phase angles, with triplication appearing in the Q factor of the qS wave. We have performed a full-wave simulation to compute the field corresponding to the coupled qP-qS waves in the symmetry plane of an effective monoclinic medium. The simulations agree with the predictions of the plane-wave analysis.

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Plane-wave attenuation anisotropy in orthorhombic media

Cited by 54 publications

References 32 publications

Weakly inhomogeneous plane waves in anisotropic, weakly dissipative media

Weakly inhomogeneous plane waves in anisotropic, weakly dissipative media

An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis

Fracture-Induced Anisotropic Attenuation

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