The partial derivatives of travel time with respect to model parameters are referred to as perturbations. Explicit equations for the second-order and higher-order perturbations of travel time in both isotropic and anisotropic media are derived. The perturbations of travel time and its spatial derivatives can be calculated by simple numerical quadratures along rays.
Ray theory, travel time (action function), Hamilton-Jacobi equation, paraxial approximation, perturbation methods, inhomogeneous media, seismic anisotropy.
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