Recent development of high resolution seismic tomography and an increasing necessity of high precision seismic (acoustic) source locations calls for robust and very precise numerical methods of an estimation of seismic (acoustic) wave travel times and propagation ray paths. In this contribution I present an algorithm based on a parametrisation of ray paths by series of the Chebyshev polynomials. This pseudo-spectral method combined with the accurate Gauss-Lobbato integration procedure allows to reach a very high relative accuracy of travel time calculation of order of 1e-6 or better. Employing of the Genetic Algorithm based optimizer to seek for the shortest travel time path assures an extreme robustness of the algorithm which allows the method to be used in complicated 3D geological structures.


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