The explicit equations for the third and higher partial travel-time derivatives in both isotropic and anisotropic media are derived. The third and higher partial travel-time derivatives may be calculated by simple numerical quadratures along rays.
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Klimes, L.: Calculation of the third and higher travel-time derivatives in isotropic and anisotropic media. In: Seismic Waves in Complex 3-D Structures, Report 6, pp. 157-166, Dep. Geophys., Charles Univ., Prague, 1997.