The relation between travel times and waves in anisotropic media is explained using the geometrical optics method in a phase space setting. This approach also covers caustics and multiple arrivals. We than consider the question of whether one can determine an anisotropic index of refraction by measuring travel times. We show that this is indeed the case if the index of refraction satisfies some additional assumptions.
Recovering Acoustic and Elastic Parameters From Travel Times
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Uhlmann, G, & Hansen, S. "Recovering Acoustic and Elastic Parameters From Travel Times." Proceedings of the ASME 2002 International Mechanical Engineering Congress and Exposition. Noise Control and Acoustics. New Orleans, Louisiana, USA. November 17–22, 2002. pp. 1-6. ASME. https://doi.org/10.1115/IMECE2002-32149
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