Seismic Signatures and Analysis of Reflection Data in Anisotropic Media, Third edition

Tsvankin, Ilya

doi:10.1190/1.9781560803003

Cited by 303 publications

(349 citation statements)

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“…The phase velocities v ph (ψ, ϑ s ) are obtained from the polycrystal elasticity tensor C p by applying the analytical solution to find the eigenvalues v ph of the Christoffel matrix for an arbitrarily anisotropic medium, following Tsvankin (2001). The algorithm is presented in Appendix B and variables associated with the cx framework are marked with a superscript cx.…”

Section: Deriving Seismic Interval Phase Velocities For An Arbitrarilmentioning

confidence: 99%

Deriving micro- to macro-scale seismic velocities from ice-core <i>c</i> axis orientations

et al. 2018

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Abstract. One of the great challenges in glaciology is the ability to estimate the bulk ice anisotropy in ice sheets and glaciers, which is needed to improve our understanding of ice-sheet dynamics. We investigate the effect of crystal anisotropy on seismic velocities in glacier ice and revisit the framework which is based on fabric eigenvalues to derive approximate seismic velocities by exploiting the assumed symmetry. In contrast to previous studies, we calculate the seismic velocities using the exact c axis angles describing the orientations of the crystal ensemble in an icecore sample. We apply this approach to fabric data sets from an alpine and a polar ice core. Our results provide a quantitative evaluation of the earlier approximative eigenvalue framework. For near-vertical incidence our results differ by up to 135 m s −1 for P-wave and 200 m s −1 for S-wave velocity compared to the earlier framework (estimated 1 % difference in average P-wave velocity at the bedrock for the short alpine ice core). We quantify the influence of shearwave splitting at the bedrock as 45 m s −1 for the alpine ice core and 59 m s −1 for the polar ice core. At non-vertical incidence we obtain differences of up to 185 m s −1 for P-wave and 280 m s −1 for S-wave velocities. Additionally, our findings highlight the variation in seismic velocity at non-vertical incidence as a function of the horizontal azimuth of the seismic plane, which can be significant for non-symmetric orientation distributions and results in a strong azimuth-dependent shear-wave splitting of max. 281 m s −1 at some depths. For a given incidence angle and depth we estimated changes in phase velocity of almost 200 m s −1 for P wave and more than 200 m s −1 for S wave and shear-wave splitting under a rotating seismic plane. We assess for the first time the change in seismic anisotropy that can be expected on a short spatial (vertical) scale in a glacier due to strong variability in crystalorientation fabric (±50 m s −1 per 10 cm). Our investigation of seismic anisotropy based on ice-core data contributes to advancing the interpretation of seismic data, with respect to extracting bulk information about crystal anisotropy, without having to drill an ice core and with special regard to future applications employing ultrasonic sounding.

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Section: Deriving Seismic Interval Phase Velocities For An Arbitrarilmentioning

confidence: 99%

Deriving micro- to macro-scale seismic velocities from ice-core <i>c</i> axis orientations

et al. 2018

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“…Therefore, sedimentary rocks such as shale are commonly treated as being transversely isotropic [2,20]. For an elastic wave in isotropic media, the wave-front is spherical; the phase velocity is perpendicular to its wavefront, the energy velocity and the density vector are in the same direction, and the direction and magnitude of the phase velocity are the same as those of the energy velocity, as shown in Figure 1.…”

Section: Theoretical Backgroundmentioning

confidence: 93%

“…Elastic anisotropy is arguably one of the most important phenomena in the Earth's interior [2]. It has been reported that rock anisotropy can significantly influence the phase velocity and energy velocity, as well as the reflection and transmission coefficients of elastic waves [3,4].…”

Section: Introductionmentioning

confidence: 99%

Seismic Signal and Data Analysis of Rock Media with Vertical Anisotropy

Zhao¹,

Zhao²,

Fa³

et al. 2013

JMP

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This paper is concerned with anisotropic effects on seismic data and signal analysis for transversely isotropic rock media with vertical anisotropy. It is understood that these effects are significant in many practical applications, e.g. earthquake forecasting, materials exploration inside the Earth's crust, as well as various practical works in oil industry. Under the framework of the most accepted anisotropic media model (i.e. VTI media, transverse isotropy with a vertical axis symmetry), with applications of a set of available anisotropic rock parameters for sandstone and shale, we have performed numerical calculations of the anisotropic effects. We show that for rocks with strong anisotropy, the induced relative depth error can be significantly large. Nevertheless, with an improved understanding of the seismic-signal propagation and proper data processing, the error can be reduced, which in turn may enhance the probability of forecasting accurately the various wave propagations inside the Earth's crust, e.g. correctly forecasting the incoming earthquakes from the center of the Earth.

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“…The sensitivity analysis shows that shear-wave velocity b, as expected (e.g., Tsvankin, 2005), has very little effect on the objective function, and thus the estimate of b is not reliable in the presence of noise. Figure 6 shows the model space for a given b ¼ 1:5 Km/s.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Estimation of stress-dependent anisotropy from P-wave measurements on a spherical sample

et al. 2011

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Our aim is to understand the stress-dependent seismic anisotropy of the overburden shale in an oil field in the North West Shelf of Western Australia. We analyze data from measurements of ultrasonic P-wave velocities in 132 directions for confining pressures of 0.1-400 MPa on a spherical shale sample. First, we find the orientation of the symmetry axis, assuming that the sample is transversely isotropic, and then transform the ray velocities to the symmetry axis coordinates. We use two parameterizations of the phase velocity; one, in terms of the Thomsen anisotropy parameters a, b, e, d as the main approach, and the other in terms of a, b, g, d. We invert the ray velocities to estimate the anisotropy parameters a, e, d, and g using a very fast simulated reannealing algorithm. Both approaches result in the same estimation for the anisotropy parameters but with different uncertainties. The main approach is robust but produces higher uncertainties, in particular for g, whereas the alternative approach is unstable but gives lower uncertainties. These approaches are used to find the anisotropy parameters for the different confining pressures. The dependency of P-wave velocity, a, on pressure has exponential and linear components, which can be contributed to the compliant and stiff porosities. The exponential dependence at lower pressures up to 100 MPa corresponds to the closure of compliant pores and microcracks, whereas the linear dependence at higher pressures corresponds to contraction of the stiff pores. The anisotropy parameters e and d are quite large at lower pressures but decrease exponentially with pressure. For lower pressures up to 10 MPa, d always is larger than e; this trend is reversed for higher pressures. Despite the hydrostatic pressure, the symmetry axis orientation changes noticeably, in particular at lower pressures.

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Seismic Signatures and Analysis of Reflection Data in Anisotropic Media, Third edition

Cited by 303 publications

References 0 publications

Deriving micro- to macro-scale seismic velocities from ice-core <i>c</i> axis orientations

Deriving micro- to macro-scale seismic velocities from ice-core <i>c</i> axis orientations

Seismic Signal and Data Analysis of Rock Media with Vertical Anisotropy

Estimation of stress-dependent anisotropy from P-wave measurements on a spherical sample

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Seismic Signatures and Analysis of Reflection Data in Anisotropic Media, Third edition

Cited by 303 publications

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Deriving micro- to macro-scale seismic velocities from ice-core &lt;i&gt;c&lt;/i&gt; axis orientations

Deriving micro- to macro-scale seismic velocities from ice-core &lt;i&gt;c&lt;/i&gt; axis orientations

Seismic Signal and Data Analysis of Rock Media with Vertical Anisotropy

Estimation of stress-dependent anisotropy from P-wave measurements on a spherical sample

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Product

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Deriving micro- to macro-scale seismic velocities from ice-core <i>c</i> axis orientations

Deriving micro- to macro-scale seismic velocities from ice-core <i>c</i> axis orientations