Traveltime Approximations in VTI Media

As exploration targets have gotten deeper, cable lengths have increased accordingly, making the conventional two term hyperbolic traveltime approximation produce increasingly erroneous traveltimes. To overcome this problem, many traveltime formulas were proposed in the literature that provide approximations of different quality. In this paper, we give an overview over a number of those approximations and compare their quality. Moreover, we propose some new traveltime approximations based on the approximations found in the literature. The main advantage of our approximations is that some of them are have rather simple analytic expressions that makes them easy to use, while achieving the same quality as the better of the established formulas.