Impedance‐type approximations of the P–P elastic reflection coefficient: Modeling and AVO inversion

Santos, Lúcio Tunes; Tygel, Martin

doi:10.1190/1.1707079

Cited by 32 publications

(13 citation statements)

References 11 publications

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“…All of the results herein are based on the two-term Shuey approximation in eqs (2) and (3). Since we do observe some changes in the optimal designs between the work of Guest & Curtis (2009) and those found here due to the difference in the forward function employed, it is possible that different information gains would be observed when using other AVO analysis methods [Connolly (1999); Sheriff (1991); Whitcombe et al (2002); Santos & Tygel (2004); Morozov (2010)]. This remains to be tested.…”

Section: Discussionmentioning

confidence: 73%

On standard and optimal designs of industrial-scale 2-D seismic surveys

Guest¹,

Curtis²

2011

Geophysical Journal International

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S U M M A R YThe principal aim of performing a survey or experiment is to maximize the desired information within a data set by minimizing the post-survey uncertainty on the ranges of the model parameter values. Using Bayesian, non-linear, statistical experimental design (SED) methods we show how industrial scale amplitude variations with offset (AVO) surveys can be constructed to maximize the information content contained in AVO crossplots, the principal source of petrophysical information from seismic surveys. The design method allows offset dependent errors, previously not allowed in non-linear geoscientific SED methods. The method is applied to a single common-midpoint gather. The results show that the optimal design is highly dependent on the ranges of the model parameter values when a low number of receivers is being used, but that a single optimal design exists for the complete range of parameters once the number of receivers is increased above a threshold value. However, when acquisition and processing costs are considered we find that a design with constant spatial receiver separation survey becomes close to optimal. This explains why regularly-spaced, 2-D seismic surveys have performed so well historically, not only from the point of view of noise attenuation and imaging in which homogeneous data coverage confers distinct advantages, but also to provide data to constrain subsurface petrophysical information.

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Section: Discussionmentioning

confidence: 73%

On standard and optimal designs of industrial-scale 2-D seismic surveys

Guest¹,

Curtis²

2011

Geophysical Journal International

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“…Because the ray impedance is defined along a seismic wave propagation raypath honoring Snell's law, it represents the physical properties of continuous subsurface media. Similar approximations of elastic impedances are proposed by Ma (2003), Santos and Tygel (2004), and VerWest (2004) based on Bortfeld's (1961) approximation. Theoretical analyses and real seismic data applications show that RI has high Manuscript received by the Editor 9 March 2015; revised manuscript received 14 July 2015; published online 26 February 2016.…”

Section: Introductionmentioning

confidence: 94%

Exact elastic impedance matrices for transversely isotropic medium

Zhang

2016

GEOPHYSICS

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Conventional elastic impedances are derived as scalars by means of the integration of reflectivity. In this sense, they are attributes of the seismic reflection but not the intrinsic physical property of the subsurface media. The derivation of these expressions shares the same assumptions as the reflectivity approximations, such as weak impedance contrast, small angle of incidence, or weak anisotropic media, and thus it limits the accuracy and interpretation capability. The exact P/SV impedance matrices relating the stress and strain represent the mechanical property of the subsurface media and yield reflection coefficients at an arbitrary angle of incidence. We have extended the impedance matrices to a transversely isotropic medium. The resulting elastic impedances (stress/velocity ratios) can be used to characterize those unconventional reservoir formations with strong seismic anisotropy, such as shale-gas and coal-bed methane. Our numerical analyses determined their variations with the phase angle and anisotropy parameters. The exact expressions of the P-and S-wave elastic impedances are used to model the seismic reflection coefficients, and thus they can be inverted simultaneously if all of the types of reflection waves are available. We then derive approximations of quasi-Pwave elastic impedances for seismic inversion of anisotropy parameters and further interpretation. Our applications on real logs and seismic data for a turbidite fan reservoir and a shale-gas reservoir determined the robust interpretation capability of derived elastic impedances in lithology characterizations.

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“…Based purely on expression , several extensions of the normal‐incidence acoustic impedance to oblique incidence were proposed and called elastic impedances (e.g., Connolly 1999; Whitcombe et al 2002; Ma 2003; Santos and Tygel 2004; VerWest 2004; Martins 2006). However, all of these definitions were based on the scaling ambiguity of impedance and heuristic integrations of the reflectivity time series and did not rigorously represent properties of the medium (for more on this, see Morozov 2010).…”

Section: Acoustic Impedancementioning

confidence: 99%

Anelastic acoustic impedance and the correspondence principle

Morozov

2010

Geophysical Prospecting

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A B S T R A C TA general definition of seismic wave impedance is proposed as a matrix differential operator transforming the displacement boundary conditions into traction ones. This impedance is proportional to the standard acoustic impedance at all incidence angles and allows extensions to attenuative media and to the full elastic case. In all cases, reflection amplitudes at the contact of two media are uniquely described by the ratios of their impedances. Here, the anelastic acoustic impedance is studied in detail and attenuation contrasts are shown to produce phase-shifted reflections. Notably, the correspondence principle (i.e., the approach based on complex-valued elastic modules in the frequency domain) leads to incorrect phase shifts of the impedance due to attenuation and consequently to wrong waveforms reflected from attenuation contrasts. Boundary conditions and the Lagrange formulation of elastodynamics suggest that elastic constants should remain real in the presence of attenuation and the various types of energy dissipation should be described by their specific mechanisms. The correspondence principle and complex-valued elastic moduli appear to be applicable only to homogeneous media and therefore they should be used with caution when applied to heterogeneous cases.

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Impedance‐type approximations of the P–P elastic reflection coefficient: Modeling and AVO inversion

Cited by 32 publications

References 11 publications

On standard and optimal designs of industrial-scale 2-D seismic surveys

On standard and optimal designs of industrial-scale 2-D seismic surveys

Exact elastic impedance matrices for transversely isotropic medium

Anelastic acoustic impedance and the correspondence principle

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