The offset‐midpoint travel‐time pyramid for P‐wave in 2D transversely isotropic media with a tilted symmetry axis

For pre‐stack phase‐shift migration in homogeneous isotropic media, the offset‐midpoint travel time is represented by the double‐square‐root equation. The travel time as a function of offset and midpoint resembles the shape of Cheops’ pyramid. This is also valid for transversely isotropic media with a vertical symmetry axis. In this study, we extend the offset‐midpoint travel‐time pyramid to the case of 2D transversely isotropic media with a tilted symmetry axis. The P‐wave analytical travel‐time pyramid is derived under the assumption of weak anelliptical property of the tilted transverse isotropy media. The travel‐time equation for the dip‐constrained transversely isotropic model is obtained from the depth‐domain travel‐time pyramid. The potential applications of the derived offset‐midpoint travel‐time equation include pre‐stack Kirchhoff migration, anisotropic parameter estimation, and travel‐time calculation in transversely isotropic media with a tilted symmetry axis.