On uniqueness in the inverse problem for transversely isotropic elastic media with a disjoint wave mode

Anna L. Mazzucato; Lizabeth V. Rachele

doi:10.1016/j.wavemoti.2007.03.004

On uniqueness in the inverse problem for transversely isotropic elastic media with a disjoint wave mode

Anna L. Mazzucato, Lizabeth V. Rachele

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Abstract

We study general anisotropic elastic media that have a disjoint wave mode, that is, elastic media with the property that one sheet of the slowness surface never intersects the others. We extend results from microlocal analysis to describe the propagation of singularities for the disjoint mode. Applying these results to the study of the dynamic inverse problem, we show that displacement-traction surface measurements uniquely determine the travel time between boundary points for the disjoint mode. We conclude that two of the five elastic parameters describing transversely isotropic elastodynamics with ellipsoidal slowness surfaces and a disjoint mode are partially determined by surface measurements. Our approach is well suited to inhomogeneous materials and applying microlocal analysis to the inverse problem.

Original language	English (US)
Pages (from-to)	605-625
Number of pages	21
Journal	Wave Motion
Volume	44
Issue number	7-8
DOIs	https://doi.org/10.1016/j.wavemoti.2007.03.004
State	Published - Aug 2007

All Science Journal Classification (ASJC) codes

Modeling and Simulation
General Physics and Astronomy
Computational Mathematics
Applied Mathematics

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10.1016/j.wavemoti.2007.03.004

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title = "On uniqueness in the inverse problem for transversely isotropic elastic media with a disjoint wave mode",

abstract = "We study general anisotropic elastic media that have a disjoint wave mode, that is, elastic media with the property that one sheet of the slowness surface never intersects the others. We extend results from microlocal analysis to describe the propagation of singularities for the disjoint mode. Applying these results to the study of the dynamic inverse problem, we show that displacement-traction surface measurements uniquely determine the travel time between boundary points for the disjoint mode. We conclude that two of the five elastic parameters describing transversely isotropic elastodynamics with ellipsoidal slowness surfaces and a disjoint mode are partially determined by surface measurements. Our approach is well suited to inhomogeneous materials and applying microlocal analysis to the inverse problem.",

author = "Mazzucato, {Anna L.} and Rachele, {Lizabeth V.}",

note = "Funding Information: The authors thank M. de Hoop, P. Stefanov, and C. Stolk for useful discussions. They would also like to acknowledge the continuous support of their Ph.D. advisers, M.E. Taylor and G. Uhlmann. The first author was partially supported by NSF grant DMS-0405803. The second author was supported by NSF grant DMS-0340530. ",

year = "2007",

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doi = "10.1016/j.wavemoti.2007.03.004",

language = "English (US)",

volume = "44",

pages = "605--625",

journal = "Wave Motion",

issn = "0165-2125",

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T1 - On uniqueness in the inverse problem for transversely isotropic elastic media with a disjoint wave mode

AU - Mazzucato, Anna L.

AU - Rachele, Lizabeth V.

N1 - Funding Information: The authors thank M. de Hoop, P. Stefanov, and C. Stolk for useful discussions. They would also like to acknowledge the continuous support of their Ph.D. advisers, M.E. Taylor and G. Uhlmann. The first author was partially supported by NSF grant DMS-0405803. The second author was supported by NSF grant DMS-0340530.

PY - 2007/8

Y1 - 2007/8

N2 - We study general anisotropic elastic media that have a disjoint wave mode, that is, elastic media with the property that one sheet of the slowness surface never intersects the others. We extend results from microlocal analysis to describe the propagation of singularities for the disjoint mode. Applying these results to the study of the dynamic inverse problem, we show that displacement-traction surface measurements uniquely determine the travel time between boundary points for the disjoint mode. We conclude that two of the five elastic parameters describing transversely isotropic elastodynamics with ellipsoidal slowness surfaces and a disjoint mode are partially determined by surface measurements. Our approach is well suited to inhomogeneous materials and applying microlocal analysis to the inverse problem.

AB - We study general anisotropic elastic media that have a disjoint wave mode, that is, elastic media with the property that one sheet of the slowness surface never intersects the others. We extend results from microlocal analysis to describe the propagation of singularities for the disjoint mode. Applying these results to the study of the dynamic inverse problem, we show that displacement-traction surface measurements uniquely determine the travel time between boundary points for the disjoint mode. We conclude that two of the five elastic parameters describing transversely isotropic elastodynamics with ellipsoidal slowness surfaces and a disjoint mode are partially determined by surface measurements. Our approach is well suited to inhomogeneous materials and applying microlocal analysis to the inverse problem.

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JO - Wave Motion

JF - Wave Motion

IS - 7-8

ER -

On uniqueness in the inverse problem for transversely isotropic elastic media with a disjoint wave mode

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