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Thomsen parameters

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Book Chapter

Thomsen parameters Available to Purchase

Author(s)
Vladimir Grechka
Book: Applications of Seismic Anisotropy in the Oil and Gas Industry
Series: EAGE Education Tour Series CIS
Publisher: EAGE
Published: 01 January 2009
EISBN: 9789462820197
... for anisotropy parameter, it does not relate to the P-wave NMO velocity in the way Thomsen δ does and, for this reason, is not as useful for seismic data processing. Since the definition of δ is not as transparent as those of ϵ and γ , other alternatives exist. Nevsky (1974) proposes two...
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Journal Article

Thomsen-type parameters and attenuation coefficients for constant- Q transverse isotropy Available to Purchase

Qi Hao, Ilya Tsvankin
Journal: Geophysics
Published: 22 June 2023
Geophysics (2023) 88 (5): C123–C134.
DOI: https://doi.org/10.1190/geo2022-0575.1
... be conveniently defined in terms of the Thomsen-type attenuation-anisotropy parameters. Recent research indicates that not all those parameters for such constant- Q media are frequency-independent. Here, we present concise analytic formulas for the Thomsen-type attenuation parameters for Kjartansson’s constant- Q...
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View PDF for article title, <span class="search-highlight">Thomsen</span>-type <span class="search-highlight">parameters</span> and attenuation coefficients for constant- Q transverse isotropy
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Journal Article

C 13 and Thomsen anisotropic parameter distributions for hydraulic fracture monitoring Available to Purchase

Hugues A. Djikpesse
Journal: Interpretation
Published: 03 April 2015
Interpretation (2015) 3 (3): SW1–SW10.
DOI: https://doi.org/10.1190/INT-2014-0244.1
...Hugues A. Djikpesse Abstract Most shale reservoirs are described assuming transverse isotropy. A full characterization of such reservoirs requires the knowledge of six elastic parameters comprising, for instance, the density; P- and S-wave vertical velocities; and the three anisotropic Thomsen...
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View PDF for article title, C 13 and <span class="search-highlight">Thomsen</span> anisotropic <span class="search-highlight">parameter</span> distributions for hydraulic fracture monitoring
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Journal Article

A robust experimental determination of Thomsen’s δ parameter Open Access

Joel Sarout, Claudio Delle Piane, Dariush Nadri, Lionel Esteban, David N. Dewhurst
Journal: Geophysics
Published: 30 December 2014
Geophysics (2015) 80 (1): A19–A24.
DOI: https://doi.org/10.1190/geo2014-0391.1
...Joel Sarout; Claudio Delle Piane; Dariush Nadri; Lionel Esteban; David N. Dewhurst ABSTRACT A novel inversion method for the laboratory determination of Thomsen’s δ anisotropy parameter on cylindrical rock specimens from ultrasonic data has been recently reported in the literature. We further...
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Example of Thomsen parameters' estimation using the rock physics model.

Example of Thomsen parameters' estimation using the rock physics model. Available to Purchase

Published: 01 June 2025
Figure 9. Example of Thomsen parameters' estimation using the rock physics model.
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Crossplots of the Thomsen parameters with (a) VP0, (b) bulk density, and (c) clay content.

Crossplots of the Thomsen parameters with (a)  V P 0 , (b) bu... Available to Purchase

Published: 18 December 2024
Figure 6. Crossplots of the Thomsen parameters with (a)  V P 0 , (b) bulk density, and (c) clay content.
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The relative phase velocity error for different Thomsen parameters. The medium parameter VP=3000  m/s: (a) first-order Taylor approximation and (b) second-order Taylor approximation.

The relative phase velocity error for different Thomsen parameters. The med... Available to Purchase

Published: 23 February 2024
Figure 3. The relative phase velocity error for different Thomsen parameters. The medium parameter V P = 3000    m / s : (a) first-order Taylor approximation and (b) second-order Taylor approximation.
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Inversion results of the five Thomsen parameters with the CDD method. (a-e) are the inverted α, β, ε, δ, and γ, respectively. The black and blue dashed lines are the initial and inverted parameter values using the CDD method, respectively.

Inversion results of the five Thomsen parameters with the CDD method. (a-e)... Available to Purchase

Published: 06 March 2020
Figure 11. Inversion results of the five Thomsen parameters with the CDD method. (a-e) are the inverted α , β , ε , δ , and γ , respectively. The black and blue dashed lines are the initial and inverted parameter values using the CDD method, respectively.
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Inversion results of the five Thomsen parameters with 0.6 ms random picking errors. The symbols are the same as in Figure 4.

Inversion results of the five Thomsen parameters with 0.6 ms random picking... Available to Purchase

Published: 06 March 2020
Figure 6. Inversion results of the five Thomsen parameters with 0.6 ms random picking errors. The symbols are the same as in Figure  4 .
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Inversion results of the five Thomsen parameters with 0.3 ms random picking errors. The black and red lines indicate the initial and true values of the five Thomsen parameters, respectively. The green and blue dashed lines indicate the inverted Thomsen parameters by the CDD (a, c, e, g, and i) and DD (b, d, f, h, and j) methods, respectively.

Inversion results of the five Thomsen parameters with 0.3 ms random picking... Available to Purchase

Published: 06 March 2020
Figure 4. Inversion results of the five Thomsen parameters with 0.3 ms random picking errors. The black and red lines indicate the initial and true values of the five Thomsen parameters, respectively. The green and blue dashed lines indicate the inverted Thomsen parameters by the CDD (a, c, e, g
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Maximum relative phase velocity error for different Thomsen parameters. (a) our new method, (b) method of Chu et al. (2011), and (c) method of Li and Zhu (2018).

Maximum relative phase velocity error for different Thomsen parameters. (a)... Available to Purchase

Published: 26 February 2020
Figure 5. Maximum relative phase velocity error for different Thomsen parameters. (a) our new method, (b) method of Chu et al. (2011) , and (c) method of Li and Zhu (2018) .
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Comparison of Thomsen parameters estimated by Backus averaging and ray theory for different classifications of rocks. In total, 1000 simulations are run for each type of rocks. The subscript B denotes Backus averaging and R denotes ray theory in this study.

Comparison of Thomsen parameters estimated by Backus averaging and ray theo... Available to Purchase

Published: 22 November 2019
Figure 2. Comparison of Thomsen parameters estimated by Backus averaging and ray theory for different classifications of rocks. In total, 1000 simulations are run for each type of rocks. The subscript B denotes Backus averaging and R denotes ray theory in this study.
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Probability densities of (a) , (b) , and (c) Thomsen parameters of the laboratory data used in this study. In (c), only the Thomsen parameters of shales are shown because they are all zero for isotropic rocks (after Yan et al., 2016a).

Probability densities of (a) , (b) , and (c) Thomsen parameters of the labo... Available to Purchase

Published: 22 November 2019
Figure 1. Probability densities of (a) , (b) , and (c) Thomsen parameters of the laboratory data used in this study. In (c), only the Thomsen parameters of shales are shown because they are all zero for isotropic rocks (after Yan et al., 2016a ).
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Comparison of Thomsen parameters estimated by Backus averaging and ray theory. Each cloud of points is from 1000 simulations of 15-layer cake model. Different colors represent interbedding of shale layers and different classifications of isotropic rock layers with a mixture ratio of 1:1.

Comparison of Thomsen parameters estimated by Backus averaging and ray theo... Available to Purchase

Published: 22 November 2019
Figure 7. Comparison of Thomsen parameters estimated by Backus averaging and ray theory. Each cloud of points is from 1000 simulations of 15-layer cake model. Different colors represent interbedding of shale layers and different classifications of isotropic rock layers with a mixture ratio of 1:1.
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Correlation between δ and the other Thomsen parameters. The same data sources as in Figure 3 are used.

Correlation between δ and the other Thomsen parameters. The same da... Available to Purchase

Published: 16 October 2019
Figure 4. Correlation between δ and the other Thomsen parameters. The same data sources as in Figure  3 are used.
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Correlation between δ and the other Thomsen parameters using data points with c13 lying within the physical constraints. The same data sources as Figure 3 are used.

Correlation between δ and the other Thomsen parameters using data p... Available to Purchase

Published: 16 October 2019
Figure 7. Correlation between δ and the other Thomsen parameters using data points with c 13 lying within the physical constraints. The same data sources as Figure  3 are used.
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Correlation between δ and the other Thomsen parameters using data sets 2 and 5 shown in Figure 5.

Correlation between δ and the other Thomsen parameters using data s... Available to Purchase

Published: 16 October 2019
Figure 9. Correlation between δ and the other Thomsen parameters using data sets 2 and 5 shown in Figure  5 .
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Effect of positive Thomsen parameters on the radiation pattern considering propagation anisotropy. First column: effect of ε, second column: effect of δ, and third column: effect of γ.

Effect of positive Thomsen parameters on the radiation pattern considering ... Available to Purchase

Published: 09 April 2018
Figure 8. Effect of positive Thomsen parameters on the radiation pattern considering propagation anisotropy. First column: effect of ε , second column: effect of δ , and third column: effect of γ .
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Radiation pattern for a normal faulting source and the Thomsen parameters shown in Table 2 for the data from Barnett Shale.

Radiation pattern for a normal faulting source and the Thomsen parameters s... Available to Purchase

Published: 09 April 2018
Figure 11. Radiation pattern for a normal faulting source and the Thomsen parameters shown in Table  2 for the data from Barnett Shale.
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Effect of positive Thomsen parameters on the radiation pattern of a normal faulting source considering source anisotropy. First column: effect of ε, second column: effect of δ, and third column: effect of γ. Note that reverse faulting will have the same beach balls, but with reverse colors (see equation 26). The matrices show moment tensors normalized to max{|M1|,|M2|,|M3|} of a corresponding isotropic moment tensor (see equation 4).

Effect of positive Thomsen parameters on the radiation pattern of a normal ... Available to Purchase

Published: 09 April 2018
Figure 3. Effect of positive Thomsen parameters on the radiation pattern of a normal faulting source considering source anisotropy. First column: effect of ε , second column: effect of δ , and third column: effect of γ . Note that reverse faulting will have the same beach