Partial Global Recovery in the Elastic Travel Time Tomography Problem for Transversely Isotropic Media
Annales de l'Institut Fourier, Online first, 63 p.

We consider the problem of recovering material parameters in a transversely isotropic medium from the qP and qSV waves’ travel times, given the axis of isotropy and the material parameters associated to the qSH wave speed. The operators obtained from the pseudolinearization argument are of parabolic type, and so we discuss inverting operators whose symbols are of parabolic type. We present stability estimates for recovering either one parameter from one wave speed or two parameters from two wave speeds with the remaining parameters either known or with a known functional relationship, and these estimates provide injectivity among parameters that differ on sets of small width.

Nous considérons le problème de la récupération des paramètres matériaux dans un milieu transversalement isotrope à partir des temps de parcours des ondes qP et qSV, étant donné l’axe d’isotropie et les paramètres matériaux associés à la vitesse d’onde qSH. Les opérateurs obtenus à partir de l’argument de pseudo-linéarisation sont de type parabolique, et nous discutons donc des opérateurs d’inversion dont les symboles sont de type parabolique. Nous présentons des estimations de stabilité pour récupérer soit un paramètre à partir d’une vitesse d’onde, soit deux paramètres à partir de deux vitesses d’onde avec les paramètres restants connus ou avec une relation fonctionnelle connue, et ces estimations montrent l’injectivité parmi les paramètres qui diffèrent sur des ensembles de petite largeur.

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DOI: 10.5802/aif.3617
Classification: 74J25, 86A22, 35R30
Keywords: Travel time tomography, elastic waves, microlocal analysis.
Mot clés : Tomographie à temps de parcours, ondes élastiques, analyse microlocale.
Zou, Yuzhou 1

1 Department of Mathematics Stanford University Stanford, CA 94305-2125 (U.S.A.)
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Zou, Yuzhou. Partial Global Recovery in the Elastic Travel Time Tomography Problem for Transversely Isotropic Media. Annales de l'Institut Fourier, Online first, 63 p.

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