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We study the travel time tomography problem for transversely isotropic mediausing the artificial boundary method used in works in X-ray tomography andboundary rigidity problems. The analysis involved requires a modification ofthe scattering pseudodifferential calculus in order to provide parametrices foroperators which are degenerately elliptic; such a calculus is constructed inthis paper and used to solve the tomography problem of interest.

Microlocal Methods for The Elastic Travel Time Tomography Problem for Transversely Isotropic Media