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The linearization approach to the evaluation of travel-times of seismic body waves propagating in inhomogeneous, slightly anisotropic media is discussed. General linearization equations are specified both for quasi-compressional and quasi-shear waves. Various situations of seismological interest are investigated in detail. This applies, e.g., to the situation where the unperturbed medium is isotropic and to the case where the unperturbed ray is a plane curve. The numerical examples presented suggest that the linearization approach gives travel-times of seismic body waves with an accuracy sufficient to solve direct and inverse kinematic problems for inhomogeneous anisotropic models of the Earth's crust and the uppermost mantle.
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