on Thomesn's strange anisotropy parameter
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In this presentation I tried to talk about Thomesn parameters based on published papers and related documents.
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on Thomesn's strange anisotropy parameter
- 1. Thomsen Parameters and their constraints for TI media Kamal Aghazade
- 2. Part1: Thomsen parameters Part 2: physical constraints on Thomsen parameter ( )𝛿
- 3. Part 1: Introducing Thomsen parameters to seismic anisotropy 3
- 4. Seismic isotropy vs anisotropy Isotropy comes from the Greek words isos (equal) and tropos (way) and means uniform in all directions. Isotropic materials like glass exhibit the same material properties in all directions. Physical properties are not direction dependent. Anisotropy: physical properties are direction dependent. Thomsen, 2014 Seismic anisotropy: The dependent of seismic velocity upon angle. 4
- 5. Beyond the simple definition of seismic anisotropy a) isotropic, b) anisotropic media Shear wave splitting in anisotropic media https://en.wikipedia.org/wiki/Shear_wave_splitting 5
- 6. Beyond the simple definition of seismic anisotropy isotropic wave equation simulation 6 anisotropic wave equation simulation
- 7. Lets go further: mathematical description Elastic media Linear Elastic material and Hook’s law 7
- 8. seismic anisotropy media (Transverse Isotropy) Common coring configuration for anisotropy measurements. Meléndez-Martínez (2014). Rüger, 1997 http://www.glossary.oilfield.slb.com 8
- 9. Stiffness matrix in Transverse Isotropy 9
- 10. Christoffel equation (eigenvalue problem) Directional dependence of three phase velocities (Daley and Horn, 1977) Algebraically complex 10Transverse Isotropy
- 11. A simpler and meaningful structure for anisotropic analysis (Tsvankin, 2012). Continue on next page 11
- 12. The problems mentioned above are already solved by Thomsen (1986) 12
- 13. Weak elastic anisotropy and “anisotropies” We can recast the equation for P-SV and SH waves velocity by using notation involving: 1 – two elastic moduli (Vertical P- and S-waves velocity ) + 2- Three measures of anisotropy (We call them anisotropies). 131 – Simplifying Velocity equations for types of waves 2 – anisotropies are non-dimensional. So, one may speak of X percent anisotropy. 3 – reduce to zero in the degenerate case of isotropy. So, material with small value of anisotropy may be denoted: “Weakly anisotropic”
- 14. 14 the algebraic complexity of new equations impedes a clear understanding of their physical content. Progress may be made. however, by observing that most rocks are only weakly anisotropic. even though many of their constituent minerals are highly anisotropic (Thomsen, 1986). Thomsen’s revolution 14
- 15. Weak anisotropy Based on laboratory data Thomsen (1986) showed that most of evaluated rocks have anisotropy in the weak to moderate (i.e. less than 0.2 ). We use Taylor series to expand equations for anisotropies and just retain only linear terms. Now, we can talk about anisotropies based on angles. 15
- 16. Some notes about Thomesn parameters 16
- 17. By measurements at 0, 45 and 90 degrees we have: Lets consider error propagation in 𝛿 17
- 18. For more information about previous topics see: Thomsen, L., [2014], Understanding Seismic Anisotropy in Exploration and Exploitation, Second edition, SEG. Tsvankin, I.,[2012] Seismic Signatures and Analysis of Reflection Data in Anisotropic Media ,Third Edition, Society of exploration Geophysicists. And related references. Leon Thomsen Ilya Tsvankin
- 19. Part 2: physical constraints on 𝐶13 & 𝛿 for transversely isotropic hydrocarbon source rocks Yan et.al (2015)
- 20. 20
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- 23. Coordinate system for following relations Young’s modulus and Poisson’s ration for TI media (see King,1964) 23
- 24. Schema of deformation of vertical plug (left) and horizontal plug (right) of organic shale under axial compressional testing. Dark grey represents plugs before deformation, and light grey represents plugs after deformation 24
- 25. 1- measurements uncertainty 2 – material should not be classified as a TI medium If a TI medium is infinitely stronger in the horizontal direction compared with vertical direction. 𝜐 𝐻𝑉 → 1 25
- 26. 26 Setting constraint on 𝐶13
- 27. 27On behavior of 𝛿
- 28. We have a constraint on 𝐶13 Substituting in 𝛿 Rewriting the relation based on other Thomsen’s parameters 28
- 29. Where 29
- 30. Constraints on anellipticity parameter “anellipticity” parameter (η) that describes the degree of deviation from elliptic anisotropy. The anellipticity parameter η is important for anisotropic seismic data processing because it determines the relation between the normal moveout velocity and the horizontal velocity (Tsvankin 2012). 30 Lower and upper bounds for 𝜂
- 31. Laboratory data and the constraints 31 several data points have negative values. The corresponding 𝛿 values are above the high bound, and they tend to have higher values of δ. 𝜐 𝐻𝐻 here are quite a few points with 𝜐 𝐻𝐻 > 𝜐 𝐻𝑉 . The corresponding values are lower than the low bound, and they tend to have lower values of δ . 𝐶13 About two-thirds of the data points lie in the center area, where believed that all the hydrocarbon source rocks with TI anisotropy should lie within. There is some uncertainty in the middle part of the figure. there are more data points lying below the low bound than above the high bound.
- 32. Uncertainty in labratory velocity anisotropy measurements Laboratory velocity anisotropy measurement on TI media requires at least five velocity component measurements, among which one velocity measurement must be made in oblique direction. 32
- 33. Case I: Negative angle error make about 20% of the data points lie below the low bound 2 𝑜 Case II: Negative 5 𝑜 angle error make about 62% of the data points lie below the low bound Case III: Positive 5 𝑜 angle error make about less than 8% of the data points lie above the high bound 1) If the phase velocity in 45 𝑜 is underestimated by 1%, 22% of the data points move below the low bound. 2) If the phase velocity in 45 𝑜 is overestimated by 1%, only one data point moves above the high bound 33
- 34. difference between group and phase velocities ray tracing of ultrasonic velocity measurement on the 45ºplug (left), transmission time versus angle (right) 34 I. if the transducer is not wide enough (or the sample is too long), the first arriving energy might be missed by the receiving transducer and the phase velocity tends to be underestimated
- 35. Phase to group correction effect 35
- 36. Applications The effect of the other Thomsen parameters on δ . 36
- 37. 37 Histogram of from laboratory velocity anisotropy measurement. 𝐶11−2𝐶66 here are only 2 data points with One data point is due to data entry error and the other data point is due to signals of substandard quality. 𝐶11−2𝐶66 < 0 37
- 38. The trends of the approximated bounds comply well with the laboratory measured data if data points lying outside of the δ bounds are not displayed. 𝛿+ 𝛿− Ignore data points outside the bounds 38
- 39. 39
- 40. Conclusions The physical constraints on the Thomsen parameter δ can help us understand the relation between δ and the other Thomsen parameters. Generally, δ increases with ε and decreases with increasing γ . Variation of β0/α0 of the hydrocarbon source rocks in a certain area is usually small so that δ is less sensitive to β0/α0. δ can be approximately predicted by the other Thomsen parameters . Using these constraints, there exist significant uncertainties in laboratory velocity anisotropy measurement.