On the reflection and transmission of viscoelastic waves—Some numerical results

Krebes, Edward S.

doi:10.1190/1.1441765

Cited by 57 publications

(22 citation statements)

References 6 publications

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“…However, for the phase there are large differences for supercritical angles. This large difference in phase between the elastic and the viscoelastic case, as computed by the "continuity criterion", has been noticed by several others (Krebes, 1984;Hearn and Krebes, 1990;Thybo, 1991;Carcione, 1999).…”

Section: Bo Ruudsupporting

confidence: 59%

“…The requirement of continuously varying R/T coefficients with angle (or offset) was called the "continuity criterion" by Brokešová and Červený (2002). Essentially, the same choice has been used by most researchers in this area (e.g., Richards, 1984;Krebes, 1984;Carcione, 1997). For elastic media the term "critical angle" (or distance) is used when the propagation direction of the transmitted wave becomes exactly parallel to the interface, i.e., when p = 1/v.…”

Section: Bo Ruudmentioning

confidence: 99%

“…(Alternatively, a complex slowness vector can be specified instead of a real slowness vector.) In the early seismological literature on plane waves in anelastic media (e.g., Buchen, 1971;Borcherdt, 1973Borcherdt, , 1977Krebes, 1983Krebes, , 1984, the R/T problem was discussed without considering how the attenuation vector should be determined. Then Hearn and Krebes (1990) connected the R/T problem with that of complex raytracing where the "stationary ray", i.e., the complex ray satisfying Fermat's principle, provides the complex slowness vector of the ray for a given (complexvalued and frequency-dependent) velocity model.…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, it is commonly concluded from Richards' paper that the R/T coefficients should vary continuously with offset (or incidence angle), not only for subcritical incidence angles, but also through the critical angle and into the supercritical angles. This idea, sometimes called the "continuity criterion", is currently the predominant principle used to decide between up-and downgoing waves (Krebes, 1984;Hearn and Krebes, 1990;Carcione, 1997;Brokešová and Červený, 2002). The main point of the present paper is to show that this criterion can lead to unreasonable results, and that it is better to accept a discontinuity in the R/T coefficients near the critical angle.…”

Section: Introductionmentioning

confidence: 99%

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Ambiguous reflection coefficients for anelastic media

Ruud

2006

Stud Geophys Geod

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The calculation of reflection and transmission coefficients of plane waves at a plane interface between two homogeneous anelastic media may become ambiguous because it is not always obvious how to determine the sign of the vertical component of the slowness vector of the scattered waves. For elastic media, the sign is determined by applying socalled radiation condition when the slowness vector is complex-valued, but it has long been known that this approach does not work satisfactorily for anelastic media. Other approaches have been suggested, e.g., by requiring that the reflection and transmission coefficients should vary continuously with increasing incident angles, or by relating the sign to the direction of the energy flux. In the present paper, it is shown that these approaches may give different results, and that the results can be inconsistent with the elastic case even for weak attenuation. Instead, it is demonstrated that the ambiguity in the reflection coefficient can be resolved by expressing the seismic response of a point source over an interface as a superposition of plane waves and their reflection coefficients, and solving the resulting integral by the saddle point approximation. Although the saddle point itself (point of stationary phase) does not provide new insight, the ambiguity is removed by considering the steepest descent path through the point. Ray synthetic seismograms computed by this method compare well with synthetics computed by the reflectivity method, which does not suffer from the above-mentioned ambiguity since the integration path is taken along the real axis. This paper concentrates on the isotropic case, but it is discussed how the result may be extended to layered transversely isotropic media. The suggested approach, derived for a point source and plane layers, does not directly apply to 2-D or 3-D laterally inhomogeneous media, or to media of general anisotropy. A generalization of the result found is that the sign of the vertical slowness components should be chosen according to the energy flux direction for subcritical incidence and according to the radiation condition for supercritical incidence, even if this creates a discontinuity in the coefficients at the critical incidence angle. Such a discontinuity is sometimes necessary to get results which are consistent with the elastic case. It is discussed how the generalized result can be obtained by applying certain continuity criteria for the sub-and supercritical angle intervals, but the validity of this approach for general models remains to be proved.

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Section: Bo Ruudsupporting

confidence: 59%

Section: Bo Ruudmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ambiguous reflection coefficients for anelastic media

Ruud

2006

Stud Geophys Geod

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“…Rose (1976) analyzed P-P and SH-SH wave reflection coefficients from the homogeneous interface. Krebes (1984) and…”

Section: Accepted Manuscriptmentioning

confidence: 99%

The application of quantitative gas saturation estimation based on the seismic wave dispersion inversion

Chen

Chapman

et al. 2015

Journal of Applied Geophysics

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Analysis of Reflection and Transmission Problems of Waves in Viscoelastic Anisotropic Media

Liu

Guo

Yang

et al. 2007

Chinese J of Geophysics

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The waves propagating in the viscoelastic anisotropic media are inhomogeneous. The patterns of reflection and transmission are not only related to the velocity contrast, but also to the Q contrast of the correlated media. By modeling reflection and transmission of waves on the interface between viscoelastic anisotropic media using pseudospectrum method, the results in the elastic anisotropic, viscoelastic isotropic, and elastic isotropic media are compared. Reflection and transmission coefficients are calculated and the effects of viscoelasticity and anisotropy of media on these coefficients are studied. By modeling the wave fields in a three‐layers media, the natures of reflection and transmission waves generated on two interfaces are investigated. In viscoelastic anisotropic media, qS waves have more inclination to attenuate than qP waves.

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On the reflection and transmission of viscoelastic waves—Some numerical results

Cited by 57 publications

References 6 publications

Ambiguous reflection coefficients for anelastic media

Ambiguous reflection coefficients for anelastic media

The application of quantitative gas saturation estimation based on the seismic wave dispersion inversion

Analysis of Reflection and Transmission Problems of Waves in Viscoelastic Anisotropic Media

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