Traveltime approximations for q-P waves in vertical transversely isotropy media*

As exploration targets have become 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 concentrate on simple traveltime approximations that depend on a single anisotropy parameter. We give an overview of a collection of such traveltime approximations found in the literature and compare their quality. Moreover, we propose some new single-parameter traveltime approximations based on the approximations found in the literature. The main advantage of our approximations is that some of them are rather simple analytic expressions that make them easy to use, while achieving the same quality as the better of the established formulas.