Analytical representation of offset-midpoint traveltime equation is very important for pre-stack Kirchhoff migration and velocity inversion in anisotropic media. For VTI media, the offset-midpoint traveltime resembles the shape of Cheop’s pyramid. In this study, we have extended the offset-midpoint traveltime pyramid to the case of TTI media. The stationary phase method is employed to derive the analytical representation of traveltime equation. The Shanks transformation is applied to improve the accuracy of horizontal slowness and vertical slowness in traveltime equation. The traveltime pyramid is derived both depth- and time-domain. Numerical example indicates that the minimum of the traveltime pyramid in TTI media is shifted due to the influence of tilted angle of TI symmetry axis. The potential application of the derived offset-midpoint traveltime equation is the prestack Kirchhoff migration and anisotropic parameter estimation in TTI media.


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