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In this paper, I developed an eikonal equation 3D-solver for a tilted TI media. The method is based on an iterative approximation of the vertical slowness. The approximation technique is inserted into a second-order expanding box finite-difference upwind ENO algorithm. Numerical examples of qP-wave traveltime computation for tilted TI media with large anellipticity illustrate the accuracy and efficiency of the proposed eikonal solver.