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We consider the inverse problem of determining slight anisotropy of an elastic medium from the results of measurements of compression or (and) shear waves. The background isotropic medium is assumed to be vertically inhomogeneous, and the slight anisotropy is assumed to possess symmetry that characterizes transversally isotropic media. We show that three linear combinations of flve elastic parameters can be recovered from the results of measurements of compression waves. Other three linear combination can be recovered from the results of measurements of shear waves.

Linearized inverse problems of determining the parameters of transversally isotropic elastic media from measurements of refracted waves