Elastic wave propagation in anisotropic polycrystals: inferring physical properties of glacier ice

Nicholas M. M. Rathmann; Aslak Grinsted; Klaus Mosegaard; David A. A. Lilien; Julien Westhoff; Christine S. S. Hvidberg; David J. J. Prior; Franz Lutz; Rilee E. E. Thomas; Dorthe Dahl-Jensen

doi:10.1098/rspa.2022.0574

Elastic wave propagation in anisotropic polycrystals: inferring physical properties of glacier ice

Nicholas M. M. Rathmann^*, Aslak Grinsted, Klaus Mosegaard, David A. A. Lilien, Julien Westhoff, Christine S. S. Hvidberg, David J. J. Prior, Franz Lutz, Rilee E. E. Thomas, Dorthe Dahl-Jensen

^*Corresponding author for this work

Physics of Ice, Climate and Earth

Research output: Contribution to journal › Journal article › Research › peer-review

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Abstract

An optimization problem is proposed for inferring physical properties of polycrystals given ultrasonic (elastic) wave velocity measurements, made across multiple sample orientations. The feasibility of the method is demonstrated by inferring both the effective grain elastic parameters and the grain c-axis orientation distribution function (ODF) of ice-core samples from Priestley glacier, Antarctica. The method relies on expanding the ODF in terms of a spherical harmonic series, which allows for a non-parametric estimation of the sample ODF. Moreover, any linear combination of the Voigt (strain) and Reuss (stress) homogenization scheme is allowed, although for glacier ice, the exact choice is found to matter little for bulk elastic behaviour, and thus for inferred physical properties, too. Finally, the accuracy of the inferred grain elastic parameters is discussed, including the well-posedness and shortcomings of the inverse problem, relevant for future adoptions in glaciology, geology and elsewhere.

Original language	English
Article number	20220574
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	478
Issue number	2268
Number of pages	25
ISSN	1364-5021
DOIs	https://doi.org/10.1098/rspa.2022.0574
Publication status	Published - 21 Dec 2022

Keywords

elastic wave propagation
polycrystals
composites
effective properties
ice
CRYSTALLOGRAPHIC PREFERRED ORIENTATIONS
GRAIN-BOUNDARY COMPLIANCE
SEISMIC ANISOTROPY
CRYSTAL-ORIENTATION
WEST ANTARCTICA
UPPER-MANTLE
SINGLE-CRYSTALS
SHEAR MARGIN
VELOCITY
TEXTURE

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Rathmann, N. M. M., Grinsted, A., Mosegaard, K., Lilien, D. A. A., Westhoff, J., Hvidberg, C. S. S., Prior, D. J. J., Lutz, F., Thomas, R. E. E., & Dahl-Jensen, D. (2022). Elastic wave propagation in anisotropic polycrystals: inferring physical properties of glacier ice. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478(2268), [20220574]. https://doi.org/10.1098/rspa.2022.0574

Elastic wave propagation in anisotropic polycrystals : inferring physical properties of glacier ice. / Rathmann, Nicholas M. M.; Grinsted, Aslak ; Mosegaard, Klaus; Lilien, David A. A.; Westhoff, Julien ; Hvidberg, Christine S. S.; Prior, David J. J.; Lutz, Franz; Thomas, Rilee E. E.; Dahl-Jensen, Dorthe.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 478, No. 2268, 20220574, 21.12.2022.

Research output: Contribution to journal › Journal article › Research › peer-review

Rathmann, NMM , Grinsted, A , Mosegaard, K, Lilien, DAA, Westhoff, J , Hvidberg, CSS, Prior, DJJ, Lutz, F, Thomas, REE & Dahl-Jensen, D 2022, 'Elastic wave propagation in anisotropic polycrystals: inferring physical properties of glacier ice', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 478, no. 2268, 20220574. https://doi.org/10.1098/rspa.2022.0574

Rathmann, Nicholas M. M. ; Grinsted, Aslak ; Mosegaard, Klaus ; Lilien, David A. A. ; Westhoff, Julien ; Hvidberg, Christine S. S. ; Prior, David J. J. ; Lutz, Franz ; Thomas, Rilee E. E. ; Dahl-Jensen, Dorthe. / Elastic wave propagation in anisotropic polycrystals : inferring physical properties of glacier ice. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2022 ; Vol. 478, No. 2268.

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abstract = "An optimization problem is proposed for inferring physical properties of polycrystals given ultrasonic (elastic) wave velocity measurements, made across multiple sample orientations. The feasibility of the method is demonstrated by inferring both the effective grain elastic parameters and the grain c-axis orientation distribution function (ODF) of ice-core samples from Priestley glacier, Antarctica. The method relies on expanding the ODF in terms of a spherical harmonic series, which allows for a non-parametric estimation of the sample ODF. Moreover, any linear combination of the Voigt (strain) and Reuss (stress) homogenization scheme is allowed, although for glacier ice, the exact choice is found to matter little for bulk elastic behaviour, and thus for inferred physical properties, too. Finally, the accuracy of the inferred grain elastic parameters is discussed, including the well-posedness and shortcomings of the inverse problem, relevant for future adoptions in glaciology, geology and elsewhere.",

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AU - Lilien, David A. A.

AU - Westhoff, Julien

AU - Hvidberg, Christine S. S.

AU - Prior, David J. J.

AU - Lutz, Franz

AU - Thomas, Rilee E. E.

AU - Dahl-Jensen, Dorthe

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N2 - An optimization problem is proposed for inferring physical properties of polycrystals given ultrasonic (elastic) wave velocity measurements, made across multiple sample orientations. The feasibility of the method is demonstrated by inferring both the effective grain elastic parameters and the grain c-axis orientation distribution function (ODF) of ice-core samples from Priestley glacier, Antarctica. The method relies on expanding the ODF in terms of a spherical harmonic series, which allows for a non-parametric estimation of the sample ODF. Moreover, any linear combination of the Voigt (strain) and Reuss (stress) homogenization scheme is allowed, although for glacier ice, the exact choice is found to matter little for bulk elastic behaviour, and thus for inferred physical properties, too. Finally, the accuracy of the inferred grain elastic parameters is discussed, including the well-posedness and shortcomings of the inverse problem, relevant for future adoptions in glaciology, geology and elsewhere.

AB - An optimization problem is proposed for inferring physical properties of polycrystals given ultrasonic (elastic) wave velocity measurements, made across multiple sample orientations. The feasibility of the method is demonstrated by inferring both the effective grain elastic parameters and the grain c-axis orientation distribution function (ODF) of ice-core samples from Priestley glacier, Antarctica. The method relies on expanding the ODF in terms of a spherical harmonic series, which allows for a non-parametric estimation of the sample ODF. Moreover, any linear combination of the Voigt (strain) and Reuss (stress) homogenization scheme is allowed, although for glacier ice, the exact choice is found to matter little for bulk elastic behaviour, and thus for inferred physical properties, too. Finally, the accuracy of the inferred grain elastic parameters is discussed, including the well-posedness and shortcomings of the inverse problem, relevant for future adoptions in glaciology, geology and elsewhere.

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