We consider the problem of recovering material parameters in a transversely isotropic medium from the and waves’ travel times, given the axis of isotropy and the material parameters associated to the 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 et , étant donné l’axe d’isotropie et les paramètres matériaux associés à la vitesse d’onde . 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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Accepted:
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Keywords: Travel time tomography, elastic waves, microlocal analysis.
Mot clés : Tomographie à temps de parcours, ondes élastiques, analyse microlocale.
Zou, Yuzhou 1
@unpublished{AIF_0__0_0_A82_0, author = {Zou, Yuzhou}, title = {Partial {Global} {Recovery} in the {Elastic} {Travel} {Time} {Tomography} {Problem} for {Transversely} {Isotropic} {Media}}, journal = {Annales de l'Institut Fourier}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, year = {2024}, doi = {10.5802/aif.3617}, language = {en}, note = {Online first}, }
TY - UNPB AU - Zou, Yuzhou TI - Partial Global Recovery in the Elastic Travel Time Tomography Problem for Transversely Isotropic Media JO - Annales de l'Institut Fourier PY - 2024 PB - Association des Annales de l’institut Fourier N1 - Online first DO - 10.5802/aif.3617 LA - en ID - AIF_0__0_0_A82_0 ER -
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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