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

摘要

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.