Traveltime parameters, defined through the series coefficients of the traveltime squared as a function of the horizontal offset projections, play an important role in moveout approximations and corrections, and in model parameter inversion. We evaluate an approach to derive the traveltime parameters in a single homogeneous anisotropic layer of tilted orthorhombic symmetry for one- and two-way traveling waves. The approach allows us to obtain the traveltime parameters of pure and converted modes. We use numerical models to illustrate the dependence of the high-order traveltime parameters on the Euler angles and the anisotropy parameters. The traveltime parameter inversion is a strongly ill-posed problem in anisotropic media, and improvements due to inclusion of the high-order traveltime parameters can sufficiently reduce the space of equivalent kinematic models. We perform a numerical model parameter inversion using the concept of artificial neural networks to demonstrate the accuracy improvements due to inclusion of the high-order traveltime parameters over the inversion of the second-order coefficient, conventionally known as normal moveout velocity, only. We demonstrate algebraically and numerically that the presented approach to calculate the traveltime parameters is easily extended to multilayered media. It can be used for Dix-type inversion to obtain the interval medium parameters.